The design is described of a readily useable technology for routine paddock-scale soil porosity estimation. The method is non-contact (proximal) and typically from sensors mounted on a small farm vehicle around 1 m above the soil surface. Challenges arise from the need to have a compact low-power rigid structure and to allow for pasture cover and surface roughness. The high-frequency regime for acoustic reflections from a porous material is a function of the porosity , the tortuosity , and the angle of incidence . There is no dependence on frequency, so measurements must be conducted at two or more angles of incidence in order to obtain two or more equations in the unknown soil properties and . A system requiring a single transmitter/receiver pair to be moved from one angle to another is not viable for rapid sampling. Therefore, the design includes at least two transmitter/reflector pairs placed at identical distances from the ground so that they would respond identically to power reflected from a perfectly reflecting surface. A single 25 kHz frequency is a compromise which allows for the frequency-dependent signal loss from a natural rough agricultural soil surface. Multiple-transmitter and multiple-microphone arrays are described which give a good signal to noise ratio while maintaining a compact system design. The resulting arrays have a diameter of 100 mm. Pulsed ultrasound is used so that the reflected sound can be separated from sound travelling directly through the air horizontally from transmitter to receiver. The average porosity estimated for soil samples in the laboratory and in the field is found to be within around 0.04 of the porosity measured independently. This level of variation is consistent with uncertainties in setting the angle of incidence, although assumptions made in modelling the interaction of ultrasound with the rough surface no doubt also contribute.

During the last decade, Bangladesh has been experienced a significant climatic anomalies which lead to an increase in magnitude and frequency of various climate relate extreme events. Climate scientists substantiate that global temperature and precipitation pattern is expected to change, which may result in consequential impact on agriculture, livelihood, and ecosystem. Bangladesh is therefore likely to face substantial challenges in the coming decades. In order to adequately understand this complex, dynamic phenomena, Analyzing historical Climate change scenarios as well as projecting its future trends is a great concern for researcher. This study aims to analyzes/ historical climatic data from (1901-2020), and predict future temperature and precipitation patterns in Bangladesh using CMIP6 data. Data used in this study (Observed data is from CRU TS 4.05 and future data is from CMIP6) have been acquired from WorldClim v2.1. Various methods including correlation, regression, standard deviation, correlation matrix, percentiles, cell statistics, and IDW interpolation were performed to analyze the trends, variability and spatial patterns of temperature and rainfall. This study revealed that Over the historical study period (1901-2020) Bangladesh has been experienced a significant warming trend with an average increase in temperature 2°C and with annual decline of the total precipitation 607.26 mm along with a shift towards drier conditions despite weak correlation with hotter years. Projected climate models represents that Bangladesh minimum temperature is expected to increase from 1°C to 4.4°C as well as maximum temperatures from 1°C to 4.1°C by 2100. Moreover, projected precipitation is expected to increase by 480.38 mm, with the biggest rises during monsoon months. Regional variations in temperature and precipitation are again expected, with the Southeast (SE) likely experiencing the most significant warming and the Northeast (NE) seeing the most substantial increase in precipitation.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

Global warming may increase the potential evapotranspiration (Etp), thereby affecting the amount of clean water resources available in a region. In this study, the systematic biases in temperature outputs of 24 global climate models (GCMs) under 3 emission scenarios are corrected by using 8 bias correction methods. The trend of Etp in Yangzi River Delta in the 21st century is projected by using 4 Etp calculation formulas. The uncertainty of the projections is estimated and decomposed by using multi-way analysis of variance. The influence of uncertainty on the projected change signal is quantified by using the signal-to-noise ratio. The results show that, relative to the reference period (1971~2000), the annual mean daily Etp in Yangzi River Delta will increase by 0.14~0.17mm/d during the period 2021~2050 and by 0.21~0.41mm/d during the period 2061~2090, respectively. During 2021~2050, the uncertainty of Etp increase projections is dominantly contributed by the main effects of GCM (63%) and Etp calculation formula (24%). During 2061~2090, it is mainly contributed by the main effect of GCM (36%), followed by the main effects of emission scenario (34%) and Etp calculation formula (18%). The increase projections of Etp are generally reliable and robust during the two projection periods.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

In this paper, we provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.

The inverse system identification toolbox named INVSID 1.0 for MATLAB, which is used to identify the inversion of single-input single-output systems, is developed. The complete process of developing the toolbox is demonstrated. Afterwards, a numerical example is illustrated to describe how the toolbox can be used to solve inverse identification problems. Simulation results demonstrate the effectiveness of the toolbox.

The poly lactic acid (PLA) is one of the most used bio-derived thermoplastic polymers in 3D and 4D printing applications. The determination of PLA surface properties is of capital importance in 3D/4D printing technology. (1) Background: The surface thermodynamic properties of PLA polymer were determined by using the inverse gas chromatography (IGC) technique at infinite dilution. The determination of the retention volume of polar and non-polar molecules adsorbed on the PLA particles filling the column allowed us to obtain the dispersive, polar, and Lewis’s acid-base surface properties at different temperatures from 40 °C to 100 °C. (2) Methods: the applied surface method was based on our recent model that used the London dispersion equation and the new chromatographic parameter function of the deformation polarizability and the harmonic mean of the ionization energies of the PLA polymer and organic molecules. (3) Results: The application of this new method led to the determination of the dispersive and polar free surface energy of adsorption of molecules on the polymeric material, as well as the glass transition and the Lewis acid-base constants. (4) Conclusions: four interval temperatures were distinguished showing four zones of the variations of the surface properties of PLA as a function of the temperature before and after the glass transition.

Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we discuss the possibility of constructing a quantum clock, which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

In this note we generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions.

The adoption of ADS-B in Latin America has been gradual but steady. Some countries, such as Brazil, Chile and Mexico, have made significant progress in the implementation of this system, while others are still in the early stages. It should be noted that the implementation of ADS-B is used in both military and civilian environments. For this reason, this research aims to provide information on the different characteristics that make up the surveillance systems. However, there are fundamental factors to promote the adaptation of ADS-B in Latin America, since they reduce the risk of collisions and air accidents by providing accurate and real-time information on the position and altitude of aircraft. On the other hand, it allows optimizing flight routes and reducing waiting time on the ground, which translates into fuel and cost savings for airlines. ADS-B increases the number of aircraft that can safely operate in the same airspace, which is especially important in regions with growing air traffic. ADS-B adoption in Latin America is expected to continue to grow in the coming years. The drivers for ADS-B adoption remain in place, and governments in the region are taking steps to accelerate its implementation.

This article introduces the Theory of Inverse Discrete Dynamical Systems (TIDDS), a novel methodology for modeling and analyzing discrete dynamical systems via inverse algebraic models. Key concepts such as inverse modeling, structural analysis of inverse algebraic trees, and the establishment of topological equivalences for property transfer between a system and its inverse are elucidated. Central theorems on homeomorphic invariance and topological transport validate the transfer of cardinal attributes between dynamic representations, offering a fresh perspective on complex system analysis. A significant application presented is an alternative proof of the Collatz Conjecture, achieved by constructing an associated inverse model and leveraging analytical property transfers within the inverted tree structure. This work not only demonstrates the theory's capability to address and solve open problems in discrete dynamics but also suggests vast implications for expanding our understanding of such systems.

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension.

In this paper, the set-membership affine projection (SM-AP) algorithm is utilized to censor non-informative data in big data applications. To this end, the probability distribution of the additive noise signal and the excess of mean-squared error (EMSE) in steady-state are employed in order to estimate the threshold parameter of the single threshold SM-AP (ST-SM-AP) algorithm aiming at attaining the desired update rate. Furthermore, by defining an acceptable range for the error signal, the double threshold SM-AP (DT-SM-AP) algorithm is proposed to detect very large errors due to the irrelevant data such as outliers. The DT-SM-AP algorithm can censor non-informative and irrelevant data in big data applications, and it can improve misalignment and convergence rate of the learning process with high computational efficiency. The simulation and numerical results corroborate the superiority of the proposed algorithms over traditional algorithms.

The spatiotemporal variations of rainfall erosivity in the Hengduan Mountains, charac-terized by rugged terrain and high potential soil erosion risks, over the past 30 years was exam-ined. The changing trends of rainfall erosivity for 2025-2040 was also be investigated under the comprehensive scenario of moderate socio-economic development (SSP2-4.5) combined with me-dium-low radiative forcing, using four global climate models (GCMs) based on CMIP6. The results indicated that: (1) The annual distribution of rainfall erosivity in the Hengduan Mountains exhib-ited significant seasonal variations, with the order of erosivity being summer > autumn > spring > winter on a seasonal scale. (2) Over the past 30 years, there has been a slight decrease in annual precipitation and a slight increase in rainfall erosivity, with periodic extreme values occurring every 6-8 years. (3) Rainfall erosivity showed a decreasing gradient from southeast to northwest in terms of spatial distribution. There was a significant positive correlation between rainfall ero-sivity and precipitation, while a significant negative correlation existed with elevation in the ver-tical direction. Moreover, there was an increasing trend of rainfall erosivity in the northeastern part of the Hengduan Mountains and a decreasing trend in the southern region. (4) Under the joint driving forces of increased precipitation and erosive rainfall events, rainfall erosivity in the future is expected to significantly increase, posing a more severe risk of soil erosion in the Heng-duan Mountains.

Afghanistan is overwhelmed with food insecurity that is a large percentage of the population lacks reliable access to food supplies. Grains play a vital role in the country's food security due to their importance in terms of consumption and production quantity. This paper estimates cereal self-sufficiency and then makes a food balance forecast of the three major food crops cultivated in Afghanistan over six-decades. Descriptive statistics and coarse metric techniques were employed to determine cereal self-sufficiency and food balance forecast. The econometric analysis demonstrated that (1) Afghanistan is not yet self-sufficient in meeting grain consumption, and the production and consumption ratio declined from 0.9 to 0.55 from 1979 to 2030. (2) The gap of theoretical food imbalance will increase, and by the year 2030, cereal production will likely be sufficient for only 49.8 percentage of inhabitants, leaving a high shortage equivalent to the amount required by 24.4 million people. By evaluating the quantitative food balance and the growing population change, this study presents an analysis of the emerging threat to Afghanistan's food security and suggests a solution for food security, should increase the size of public agricultural expenditure, improve the level of agriculture infrastructure, and continue to introduce a policy to achieve higher yield.

Olfactory ensheathing cells (OECs) are the glial cells that accompany axons from the olfactory epithelium to their targets in the olfactory bulb. They possess unique features that have made them the subject of much study as being potentially useful in cell-based therapeutic approaches to CNS repair. Investigation of OECs has demonstrated antigenic and morphological heterogeneity in their population. No marker specific to and selective for OECs have yet been identified, and many of the markers used are variably expressed by other glial cells. Even among OECs, these markers appear to vary in vivo (depending on their anatomical location, contact with other cells, and developmental timing) and in vitro. The variation across the population of OECs has compromised their isolation and characterization. It has also made the task of identifying meaningful subpopulations - with greater or lesser therapeutic utility - dependent on identifying the source of their variability. Such information would aid in both the harvest and experimental manipulation of OECs to optimize their therapeutic effect. One way to understand the nature of this variability is to seek its potential causes in vivo. This must begin with an examination of the structure of the olfactory nerve. Here, the structure and development of the primary olfactory projection are thoroughly reviewed with an emphasis on OECs and the cells with which they make contact. The relevant experimental results are also discussed. The weight of anatomical evidence indicates that the structural variations described in different locations and across species are mostly the result of spatiotemporal developmental factors. As such, the formation of the olfactory projection is mediated primarily by the source tissue, the olfactory epithelium. Cell-autonomous development is common elsewhere, and suits the evolutionary age and importance of olfaction, as well as its continued regenerative capacity. Our findings provide a more systematic anatomical understanding of this nerve. That understanding indicates that variation in axon ensheathment by OECs is an inherent feature arising from the flexibility of the ensheathing program. This perspective, along with the anatomical data reviewed here, can inform more carefully controlled laboratory investigations designed to uncover the detailed mechanisms governing OEC biology.

Multi-cameras system is widely applied in 3D computer vision especially when multiple cameras are distributed on both sides of the measured object. The calibration methods of multi-cameras system are critical to the accuracy of vision measurement and the key is to find an appropriate calibration target. In this paper, a high-precision camera calibration method for multi-cameras system based on transparent glass checkerboard and ray tracing is described, which is used to calibrate multiple cameras distributed on both sides of the glass checkerboard. Firstly, the intrinsic parameters of each camera is obtained by Zhang’s calibration method. Then, multiple cameras capture several images from the front and back of the glass checkerboard with different orientations, and all images contain distinct grid corners. As the cameras on one side are not affected by the refraction of glass checkerboard, extrinsic parameters can be directly calculated. However, the cameras on another side are influenced by the refraction of glass checkerboard, and the direct use of projection model will produce calibration error. A multi-cameras calibration method using refractive projection model and ray tracing is developed to eliminate this error. Furthermore, both synthetic and real data are employed to validate the proposed approach. The experimental results of refractive calibration show that the error of the 3D reconstruction is smaller than 0.2 mm, the relative errors of both rotation and translation are less than 0.014%, and the mean and standard deviation of reprojection error of 4-cameras system are 0.00007 and 0.4543 pixel. The proposed method is flexible, high accurate, and simple to carry out.

This study evaluates the historical mean surface temperature (hereafter T2m) and examines how T2m changes over East Africa (EA) in the 21^st century using CMIP6 models. An evaluation was conducted based on mean state, trends, and statistical metrics (Bias, Correlation Coefficient, Root Mean Square Difference, and Taylor skill score). For future projections over EA, five best performing CMIP6 models (based on their performance ranking in historical mean temperature simulations) under the shared socioeconomic pathways SSP2-4.5 and SSP5-8.5 scenarios were employed. The historical simulations reveal an overestimation of the mean annual T2m cycle over the study region with fewer models depicting underestimations. Further, CMIP6 models reproduce the spatial and temporal trends within the observed range proximity. Overall, the best performing models are as follows: FGOALS-g3, HadGEM-GC31-LL, MPI-ESM2-LR, CNRM-CM6-1, and IPSL-CM6A-LR. During the three-time slice under consideration, the Multi Model Ensemble (MME) project many changes during the late period (2080 – 2100) with expected mean changes at 2.4 °C for SSP2-4.5 and 4.4 °C for the SSP5-8.5 scenario. The magnitude of change based on Sen’s slope estimator and Mann-Kendall test reveal significant increasing tendencies with projections of 0.24°C decade-1 (0.65°C decade-1) under SSP2-4.5 (SSP5-8.5) scenarios. The findings from this study illustrate higher warming in the latest model outputs of CMIP6 relative to its predecessor, despite identical instantaneous radiative forcing.

We propose a computer-generated hologram method for near-eye virtual reality and augmented reality 3D display. A 3D object located near the holographic plane is projected onto a projection plane to obtain a plurality of projected images with different angles. The hologram is calculated by superposition of projected image convolution with a specific PSF through the interference of reference wave with object wave. Holographic 3D display systems with LED as illumination, 4f optical filtering system and lens as eyepiece for near-eye VR display and HOE as combiner for near-eye AR display are designed. The results show that the proposed method is about 38 times faster than the conventional point cloud method. The proposed method is flexible to produce speckle noise free high-quality VR and AR images with efficient focus and defocus capabilities.

A human eye has about 120 million rod cells and 6 million cone cells. This huge number of light sensing cells inside a human eye will continuously produce a huge quantity of visual signals which flow into a human brain for daily processing. However, the real-time processing of these visual signals does not cause any fatigue to a human brain. This fact tells us the truth which is to say that human-like vision processes do not rely on complicated formulas to compute depth, displacement, and colors, etc. On the other hand, a human eye is like a PTZ camera. Here, PTZ stands for pan, tilt and zoom. We all know that in computer vision, each set of PTZ parameters (i.e., coefficients of pan, tilt and zoom) requires a dedicated calibration to determine a camera’s projection matrix. Since there is an infinite number of PTZ parameters which could be produced by a human eye, it is unlikely that a human brain stores an infinite number of calibration matrices for each human eye. Therefore, it is an interesting question for us to answer, which is to say whether simpler formulas of computing depth and displacement exist or not. Moreover, these formulas must be calibration friendly (i.e., easy process on the fly or on the go). In this paper, we disclose an important discovery of a new solution to 3D projection in a human-like binocular vision system. The purpose of doing 3D projection in binocular vision is to undertake forward and inverse transformations (or mappings) between coordinates in 2D digital images and coordinates in a 3D analogue scene. The formulas underlying the new solution are accurate, easily computable, easily tunable (i.e., to be calibrated on the fly or on the go) and could be easily implemented by a neural system (i.e., a network of neurons). Experimental results have validated the discovered formulas.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Ultrafast pump-probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates' lifetimes and coherent oscillation frequencies, is an example of the inverse problems of chemical kinetics. This article describes a consistent approach for solving this inverse problem that avoids the common obstacles of simple least-squares fitting that can lead to unreliable results. The presented approach is based on the regularized Markov Chain Monte Carlo sampling for the strongly nonlinear parameters, allowing for a straightforward solution of the ill-posed nonlinear inverse problem. The software to implement the described fitting routine is introduced and the numerical examples of its application are given. We will also touch on critical experimental parameters, such as the temporal overlap of pulses and cross-correlation time and their connection to the minimal reachable time resolution.

The thermal surface properties of graphenes and carbon materials are of crucial importance in chemistry of materials, chemical engineering, and many industrial processes. (1) Background: The determination of these surface properties is carried out using inverse gas chromatography at infinite dilution which leads to the retention volume of organic solvents adsorbed on solid surfaces. This experimental and fundamental parameter actually reflects the surface thermodynamic interactions between injected probes and solid substrates. (2) Methods: The London dispersion equation and the Hamieh thermal model were used to quantify the London dispersive and polar surface energy of graphenes and carbon fibers as well their Lewis acid-base constants by introducing the coupling amphoteric constant of materials. (3) Results: The London dispersive and polar acid-base surface energies, the free energy of adsorption, the polar enthalpy and entropy, and the Lewis acid-base constants of graphenes and carbon materials were determined. (4) Conclusions: it was showed that graphene exhibited the highest values of London dispersive surface energy, polar surface energy, and Lewis’s acid-base constants. These highest characteristics of graphene justify its great potentiality and uses in many industrial applications.

In this paper we provide an ``expository overview" of classic epidemic projection models. Starting with the simple case of an epidemic that grows exponentially we then investigate ``compartmental" models. These assume that the growth of an infected population is limited endogenously by the size of the underlying pool of susceptibles. We then describe a new family of so-called "Exo-r" statistical models, which hinge on an exogenously driven growth rate of the infected population. This family, which can be used to model both infections and deaths, captures parsimoniously both the depletion of susceptibles and the effect of interventions such as lockdowns and ``social distancing". The model is used to fit numbers of Covid-19 infections in China. It is also used to model and project deaths in the United States. Results are used to inform a discussion on i) the challenges at hand and ii) the extent to which epidemic projection models may be useful despite being wrong.

The temperature effect plays an important role for an accurate determination of the polar free energy, polar thermodynamic parameters, and enthalpic and entropic Lewis’s acid base properties of oxides, polymers and composites polymers/oxides. The adsorption of polymers on other solid surfaces is crucial in many industrial applications, coatings, paints, catalysis, colloids and adhesion processes. (1) Background: Inverse gas chromatography at infinite was used for the physico-chemical characterization of solid substrates by determining the thermodynamic parameters of adsorption of model organic solvents on solid surfaces such as polymers, metallic oxides, carbon fibers, pharmaceutical or 3D/4D printing substrates. (2) Methods: A new method based on the London dispersion equation was applied with a new parameter associating the deformation po-larizability and the harmonic mean of the ionization energies of solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained as well as the Lewis acid-base parameters and the transition temperatures of the different composites. (3) Results: This new methodology gave very interesting results on the behavior of PMMA adsorbed on silica. An important effect of the temperature and the recovery fraction on the various physicochemical and thermodynamic properties was highlighted. The variations of all interaction parameters showed the presence of three transition temperatures for the different PMMA adsorbed on silica with the various coverage rates with a shift of these temperatures for a recovery fraction of 31% (4) Con-clusions: An important variation of the polar enthalpy and entropy of adsorption, the Lewis ac-id-base parameters and the intermolecular separation distance as a function of the temperature and the recovery fraction of PMMA on silica.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Seismic velocity inversion is one of the most critical issues in the field of seismic exploration and has long been the focus of numerous experts and scholars. In recent years, the advancement of machine learning technologies has infused new vitality into the research of seismic velocity inversion and yielded a wealth of research outcomes. Typically, seismic velocity inversion based on machine learning lacks control over physical processes and interpretability. Starting from wave theory and the physical processes of seismic data acquisition, this paper proposes a method for seismic velocity model inversion based on Physical Embedding Recurrent Neural Networks. Firstly, the wave equation is a mathematical representation of the physical process of acoustic waves propagating through a medium, and the finite difference method is an effective approach to solving the wave equation. With this in mind, we introduce the architecture of recurrent neural networks to describe the finite difference solution of the wave equation, realizing the embedding of physical processes into machine learning. Secondly, in seismic data acquisition, the propagation of acoustic waves from multiple sources through the medium represents a high-dimensional causal time series (wavefield snapshots), where the influential variable is the velocity model, and the received signals are the observations of the wavefield. This forms a forward modeling process as the forward simulation of the wavefield equation, and the use of error back-propagation between observations and calculations as the velocity inversion process. Through time-lapse inversion and incorporating the causal information of wavefield propagation, the non-uniqueness issue in velocity inversion is mitigated. Through mathematical derivations and theoretical model analyses, the effectiveness and rationality of the method are demonstrated. In conjunction with simulation results for complex models, the method proposed in this paper can achieve velocity inversion in complex geological structures.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

Most of the phase change materials (PCMs) have been limited to use as functional additions or sealed in containers, and extra auxiliary equipment or supporting matrix is needed. The emergence of 3D printing technique has dramatically advanced the developments of materials and simplified production processes. This study focuses on a novel strategy to model thermal energy storage crystalline gels with three-dimensional architecture directly from liquid resin without supporting materials through light-induced polymerization 3D printing technique. A mask-projection stereolithography printer was used to measure the 3D printing test, and the printable characters of crystalline thermal energy storage P(SA-DMAA) gels with different molar ratios were evaluated. For the P(SA-DMMA) gels with small fraction of SA, the 3D fabrication was realized with higher printing precision both on mili- and micro-meter scales. As a comparison of 3D printed samples, P(SA-DMAA) gels made by other two methods, post-UV curing treatment after 3D printing and UV curing using conventional mold, were prepared. The 3D printed P(SA-DMAA) gels shown high crystallinity. Post–UV curing treatment was beneficial to full curing of 3D printed gels, but did not lead to the further improvement of crystal structure to get higher crystallinity. The P(SA-DMAA) crystalline gel having the highest energy storage enthalpy that reached 69.6 J·g⁻¹ was developed. Its good thermoregulation property in the temperature range from 25 to 40 °C was proved. The P(SA-DMAA) gels are feasible for practical applications as one kind of 3D printing material with thermal energy storage and thermoregulation functionality.

Inverse gas chromatography at infinite dilution was used to determine the surface thermodynamic properties of silica particles and PMMA adsorbed on silica, and more particularly, to quantify the London dispersive energy γsd, the Lewis acid γs+ and base γs- polar surface energies of PMMA/silica composites as a function of the temperature and the recovery fraction θ of PMMA. The polar acid–base surface energy γsAB and the total surface energy of the different composites were then deduced as a function of the temperature. In this paper, the Hamieh thermal model was used to quantify the surface thermodynamic energy of poly methyl methacrylate (PMMA) adsorbed on silica particles at different recovery fractions. A comparison of the new results was carried out with those obtained by applying other molecular models of the surface areas of organic molecules adsorbed on the different solid substrates. An important deviation of these molecular models from the thermal model was proved. The determination of γsd, γs+, γs-, and γsAB of PMMA in both bulk and adsorbed phases showed an important non-linearity variation of these surface parameters as a function of the temperature. The presence of maxima in the curves of γsd(T) highlighted the second order transition temperatures in PMMA showing beta-relaxation, glass transition and liquid-liquid temperatures. These three transition temperatures depended on the adsorption rate of PMMA on silica. The proposed method gave a new relation between the recovery fraction of PMMA and its London dispersive energy showing an important effect of the temperature on the surface energy parameters of adsorption of PMMA on silica. A universal equation relating γsd(T,θ) of the systems PMMA/silica to the recovery fraction and the temperature was proposed.

This research was devoted to study the effect of the tacticity of PMMA on the surface physicochemical properties such as the London dispersive component of the surface energy of the polymer, the polar and dispersive free energies, the Lewis’s acid-base surface parameters, and the Lewis acid and base surface energies of atactic, isotactic and syndiotactic PMMAs as a function of the temperature. Inverse gas chromatography (IGC) at infinite dilution was used to determine the surface thermodynamic properties of PMMA at different tacticities. The experimental values of the net retention time and volume of model organic molecules adsorbed on the atactic, isotactic and syndiotactic PMMAs, were obtained by IGC technique at infinite dilution. The London dispersion interaction energy was used for the separation of the polar and dispersive energy of the different n-alkanes and polar solvents adsorbed on the different PMMA surfaces. The London dispersive surface energy γ_s^d (T) of PMMAs was determined by applying the Hamieh thermal model that took into account the effect of the temperature on the surface area of adsorbed molecules. The obtained results showed non-linear variations of γ_s^d (T) of atactic, isotactic, and syndiotactic PMMAs with three maxima characterizing the three transition temperatures of PMMAs, T_g, T_g and T_(liq-liq) with a shift of these temperatures with the isotactic and syndiotactic PMMAs. It was showed that the polar interaction free energy ∆G_a^p (T) also showed the presence of the three above transition temperatures of the polymers. The study showed an important non-linearity variation of the different acid-base parameters in the various polymer surfaces proving the highest effect of the temperature and the tacticity on these parameters. The determination of the enthalpic and entropic Lewis’s acid-base parameters showed an amphoteric character for the different PMMAs. The basicity of the atactic PMMA was about four times larger than its acidity outside the neighborhood of the transition temperatures of the polymer. Whereas, the isotactic PMMA was about 2 to 2.5 times more basic than acid, while the syndiotactic PMMA exhibited the highest basicity by showing a surface 5 to 8 times more basic than acid. However, the Lewis acid-base parameters strongly depended on the temperature and sudden variations of these surface parameters were observed around the transition temperatures largely depending on the PMMA tacticity. The determination of the polar acid and base surface energies of the three PMMAs led to the same previous transition temperatures with an important effect of the tacticity of PMMA on the values of these acid-base surface energies.

The correct selection of the value of p is a complex and iterative procedure that requires experience in the interpretation of the obtained interpolated maps. Inverse Distance Weighting is a method applied to the porosities of the K and L hydrocarbon reservoirs, discovered in the Neogene (Lower Pontian) subsurface sandstones in the northern Croatia (Pannonian Basin System). They represent small and large data samples. Also a standard statistical analysis of the data was made, followed by the qualitative-quantitative analysis of the maps, based on the selection of different values of the power distance exponent (p-value) for the K and L reservoirs maps. According to the qualitative analysis, for a small data set, p-value could be set on 1 or 2 giving the most optimal result, while for a large data set, a p value of 3 and 4 could be applied. By quantitative analysis, for the case of small data p=2 is recommended, resulting in a root mean square error value of 0.03458, a mean absolute error of 0.02013 and a median absolute deviation of 0.00546. Oppositely, a p-value of 3 and 4 is selected as appropriate for a large data set, with root mean square errors of 0.02435 and 0.02437, mean square errors of 0.01582 and 0.01509 and median absolute deviations 0.00896 and 0.00444. Eventually for a small data set, it is recommended to use a p-value of 2, and for a large data set, a p-value of 3 or 4.

The spread of high-performance personal computers, frequently equipped with powerful Graphic Processing Units (GPU), raised the interest on a set of techniques able to extract models of electromagnetic phenomena (and devices) directly from available examples of the desired behavior. Such approaches are collectively referred to as Machine Learning (ML). A typical representative ML approach is the so called “Neural Network” (NN). Using such data-driven models allows evaluating the output in a much shorter time when a theoretical model is available, or allows predicting the behavior of the systems and devices when no theoretical model is available. With reference to a simple yet representative benchmark electromagnetic problem, some of the possibilities and the pitfalls of the use of NN for the interpretation of measurements (inverse problem) or to obtain the required measurements (optimal design problem) are discussed. The investigated aspects include the choice of the NN model; the generation of the dataset(s); the selection of hyperparameters (hidden layers, training paradigm). Finally, the capabilities in the handling of ill-posed problems are critically revised.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Vein segmentation and projection correction constitute the core algorithms of auxiliary venipuncture device, responding to the accurate venous positioning to assist puncture and reduce the number of punctures and pain of patients. This paper proposes an improved U-Net for segmenting vein and a coaxial correction for image alignment in the self-build vein projection system. The proposed U-Net is embedded by Gabor convolution kernels in the shallow layers to enhance segmentation accuracy. Additionally, to mitigate the semantic information loss caused by channel reduction, the network model is lightweighted by the mean of replacing conventional convolutions with inverted residual blocks. During the visualization process, a method that combining coaxial correction and homography matrix is proposed to address the non-planarity of the dorsal hand in this paper. First, use a hot mirror to adjust the light paths of both projector and camera to be coaxial, and then align the projected image with dorsal hand using a homography matrix. Using this approach, the device requires only a single calibration before use. With the implementation of the improved segmentation method, an accuracy rate of 95.12% is achieved by the dataset. The intersection over union ratio between the segmented and original images is reached at 90.07%. The entire segmentation process is completed in a 0.09 second, and the largest distance error of vein projection onto dorsal hand is 0.53mm. Experiments show that the device has reached practical accuracy and has the value of research and application.

Demographic change is leading to the aging of German society. As long as the baby boom co-horts are still of working age, the working population will also age - and decline as soon as this baby boom generation gradually reaches retirement age. At the same time, there has been a trend towards increasing absenteeism (times of inability to work) in companies since the zero years, with the number of days of absence increasing with age. We present a novel stochastic forecast approach that combines population forecasting with forecasts of labor force participation trends, considering epidemiological aspects. For this, we combine a stochastic Monte Carlo-based cohort-component forecast of the population with projections of labor force participation rates and morbidity rates. This article examines the purely demographic effect on the economic costs associated with such absenteeism due to the inability to work. Under expected future employment patterns and constant morbidity patterns, absenteeism is expected by close to 5 percent by 2050 relative to 2020, associated with increasing economic costs of almost 3 percent. Our results illustrate how strongly the pronounced baby boom/ baby bust phenomenon determines demographic development in Germany in the midterm.

We consider a coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared Patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. In this paper, an iterative list PRM projection algorithm is proposed to supplant the signal detector associated with the inner PRM sequences. In particular, we first propose an enhanced paths-saving algorithm called list PRM projection detection for the single-user scenario that keeps multiple candidates for the first few layers to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for the multi-user scenario. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verified that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ the iterative list detection to two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.

Holographic projection is a simple projection because it enlarges or reduces reconstructed images without using a zoom lens. However, one major problem associated with this projection is the deterioration of image quality as the reconstructed image enlarges. In this paper, we propose a time-division holographic projection, in which the original image is divided into blocks and the holograms of each block are calculated. Using a digital micromirror device (DMD), the holograms were projected at high speed to obtain the entire reconstructed image. However, the holograms on the DMD need to be binarized, thereby causing uneven brightness between the divided blocks. We correct this by controlling the displaying time of each hologram. Additionally, combining both the proposed and noise reduction methods, the image quality of the reconstructed image was improved. Results from the simulation and optical reconstructions show we obtained a full-color reconstruction image with reduced noise and uneven brightness.

The aim of this paper is to at first evaluate the influence of three key parameters including weld current, weld time and electrode force on nugget diameter and tensile strength in resistance projection welding. Then, a 2-D axis-symmetric finite element model is developed to simulate the projection welding and predict the nugget diameter. Finally, the FEM results are compared to experimental data to verify the simulation model and simulated results. In the finite element model, the temperature-dependent material properties were taken into account.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

The rapid growth of Earth's global geospatial data necessitates an efficient system for organizing the data, facilitating data fusion from diverse sources, and promoting interoperability. Mapping the spheroidal surface of the planet presents significant challenges, as it involves balancing distortion and splitting the surface into multiple partitions. The distortion decreases as the number of partitions increases, but at the same time the complexity of data processing increases, since each partition represents a separate data set and is defined in its own local coordinate system. In this paper, we propose the dual orthogonal equidistant cylindrical projection method to mitigate distortion and reduce the number of partitions. Additionally, we use the rotation of projection cylinders to effectively minimize average angular and areal distortions of the Earth’s landmass and reduce the interruption of continental plates caused by partition edges. By incorporating auxiliary latitudes and proposing an approximate authalic latitude, we further enhance the mapping of the ellipsoid onto the sphere, simplifying calculations. Experimental results demonstrate a substantial reduction in distortion and interruption of continental plates. With only two partitions, an average landmass angular distortion of less than 3.56 degrees and an average normalized surface distortion of less than 1.07 were achieved.

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations

This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.

As many if not most ligands at G protein-coupled receptor antagonists are inverse agonists, we have systematically reviewed inverse agonism at the nine adrenoceptor subtypes. Except for β3-adrenoceptors, inverse agonism has been reported for each of the adrenoceptor subtypes, most often for β2-adrenoceptors, including endogenously expressed receptors in human tissues. As with other receptors, detection and degree of inverse agonism depends on the cells and tissues under investigation, i.e. is greatest when the model has a high intrinsic tone/constitutive activity for the response being studied. Accordingly, it may differ between parts of a tissue, for instance atria vs. ventricles of the heart, and within a cell type between cellular responses. The basal tone of endogenously expressed receptors often is low, leading to less consistent detection and smaller extent of observed inverse agonism. The extent inverse agonism depends on specific molecular properties of a compound but clusters by chemical class. While inverse agonism is a fascinating facet in attempts to mechanistically understand observed drug effects, we are skeptical whether an a priori definition of extent of inverse agonism in the target product profile of a developmental candidate is a meaningful option in drug discovery and development.

We present an improved algorithm for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithm is much more accurate than the famous fast inverse square root algorithm and has a similar computational cost. The presented modification concern Newton-Raphson corrections and can be applied when the distribution of these corrections is not symmetric (for instance, in our case they are always negative).

Low Emission Zone (LEZ) is an important mechanism to limit the negative environmental impact of traffic pollution in an urban area. Car traffic in the zone is strictly regulated to meet certain technical and environmental criteria. Such solutions of urban environment protection are gaining popularity, especially in European conurbations. Nowadays there are above 300 zones in Europe, mostly established in Italy and Germany. So far there are no LEZs in Eastern and Central European countries. However, the Warsaw authorities are just discussing launching of a LEZ in the city in 2024. According to the ongoing project, the zone is to be launched gradually, in five phases between 2024 and 2032, with the traffic criteria being tightened accordingly. The progressive emission reductions of the predominant pollutants in LEZ in consecutive phases were estimated on the basis of the Real Driving Emissions (RDE) test, carried out in 2020 by the ICCT. The gradually reduced emissions of NOx and PM were subsequently utilized as the input dataset for the regional CALPUFF model predictions, to calculate concentrations of these main traffic-induced pollutants within the LEZ area. The direct effect of the zone activation is reduction of air pollution in the urban center, which is mostly exposed to the pollution risk due to heavy traffic. Computer simulations reveal that implementation of the zone in the case of Warsaw will result in a quite significant reduction of NOx concentrations within the LEZ, such that its mean concentration in the zone becomes comparable to the rest of the conurbation. However, it will bring only a slight reduction of PM2.5 concentrations. This situation is due to the long-standing dominance of coal combustion in the Polish economy, which also applies to the urban municipal sector. As a consequence, particulate matter emissions of this sector are clearly predominant over the road traffic contribution. Balance can be achieved once the ongoing de-carbonization of the national economy has been completed.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

Data collected at the Cascais tide gauge, located on the west coast of Portugal Mainland, have been analyzed and sea level rise rates have been updated. Based on a bootstrapping linear regression model and on polynomial adjustments, time series are used to calculate different empirical projections for the 21^st century sea level rise, by estimating the initial velocity and its corresponding acceleration. The results are consistent to an accelerated sea level rise, showing evidence of a faster rise than previous century estimates. Based on different numerical methods of second order polynomial fitting, it is possible to build a set of projection models of relative sea level rise. Appling the same methods to regional sea level anomaly from satellite altimetry, additional projections are also built with good consistency. Both data sets, tide gauge and satellite altimetry data, enabled the development of an ensemble of projection models. The relative sea level rise projections are crucial for national coastal planning and management since extreme sea level scenarios can potentially cause erosion and flooding. Based on absolute vertical velocities obtained by integrating global sea level models, neo-tectonic studies and permanent Global Positioning System (GPS) station time series, it is possible to transform relative into absolute sea level rise scenarios, and vice-versa, allowing the generation of absolute sea level rise projection curves and its comparison with already established global projections. The sea level rise observed at the Cascais tide gauge has always shown a significant correlation with global sea level rise observations, evidencing relatively low rates of composed vertical land velocity from tectonic and post-glacial isostatic adjustment, and residual synoptic regional dynamic effects rather than a trend. An ensemble of sea level projection models for the 21st century is proposed with its corresponding probability density function, both for relative and absolute sea level rise for the west coast of Portugal Mainland.

Introduction: Depending on the kind of cancer and neurological disorders, there might be a direct or inverse link between neurodegeneration and cancer. The inverse interaction between cancer and Alzheimer's pathology has garnered substantial interest in medical research. While this inverse interaction between Alzheimer's pathology and cancer presents a fascinating scientific puzzle, there is still limited information and studies on the potential mechanisms involved in this inverse rela-tionship. Aim: This study aims to identify potential genes from Alzheimer's disease that may protect against cancer. Method: The Gene Expression Omnibus (GEO) database provided the Alzheimer's pathology dataset, and GEO 2R was utilized to examine genes that were differentially expressed. The expression of upregulated Alzheimer's pathology genes in breast, colorectal, and prostate cancer was compared using VENN 2.1, colorectal, and prostate cancer was compared using VENN 2.1, and colorectal and prostate cancers were compared using VENN 2.1. Results: Among the upregulated genes associated with Alzheimer's disease, 25 genes are shared among breast cancer, colorectal cancer, and prostate cancer, while 28 of these genes were exclusive to Alzheimer's dis-ease. Gene expression profiling interactive analysis among the shared genes revealed that AQP1, C4A, CSRP2, CRYAB, MACF1, HSPB2, and NEAT1 were downregulated in breast, colorectal, and prostate cancers. These genes have varying roles in cancer progression and suppression. Functional analysis of Alzheimer's disease-related upregulated genes revealed that C1orf56 and HIST1H2AC control cell proliferation, with HIST1H2AC playing a role in necroptosis. Additionally, C1orf56 worked as an oncogenic modifier to support DNMT3B's tumor suppressor properties. Conclusion: Given the role of HIST1H2AC and C1orf56 in the negative control of cell proliferation and their upregulation in Alzheimer's disease, there is a need to further investigate HIST1H2AC and C1orf56 as potential tumor suppressors responsible for Alzheimer's disease and cancer inverse association.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

The direct measurements of the magnetocaloric effect were performed in Heusler Ni44.4Mn36.2Sn14.9Cu4.5 alloy at cryogenic temperatures in magnetic fields up to 10 T. The maximum value of the inverse magnetocaloric effect in a field of 10 T was observed ∆Tad = –2.7 K in the vicinity of the 1st order magnetostructural phase transition at T0 = 117 K. The ab initio and Monte Carlo calculations were performed to discuss the effect Cu doping into Ni-Mn-Sn compound on the ground state structural and magnetic properties. It is shown that with increasing Cu content the martensitic transition temperature decreases and the Curie temperature of austenite slightly increases. In general, calculated transition temperatures, magnetization values are correlated well with the experimental ones.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Giant plasmonic surface enhancement has been observed in gold coated micron sized inverse pyramids entrapping a gold nanoparticle. The amplification of both surface enhanced Raman and photoluminescence signals was found to be dependent on the diameter of trapped gold nanoparticle and around 50-fold enhancement was detected for 250nm diameter sample relatively to the 50nm one. Finite differential time domain simulations, performed to determine the near-field distribution in the structure, showed that when the nanoparticle protrudes into the hotspot zone of the void, coupling of electromagnetic field occurs and the plasmon-related near-field enhancement is concentrated into the close vicinity of the nanoparticle, mainly into the close gaps around the tangential points of the curved sphere and the flat pyramid surface. This results in a more than 15 times increase of the near-field intensity, compared to the empty void.

This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker-Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element software and automatically runs simulations to establish a convergence between the numerical loading-unloading curve and the target data obtained from continuous indentation tests using common indenter geometries. A further module was developed to optimise convergence using an inverse FEM analysis interfaced with a non-linear MATLAB algorithm. A sensitivity analysis determined that the dual Spherical and Berkovich (S&B) approach delivered better results than other dual indentation methods such as Berkovich and Vickers (B&V) and Vickers and Spherical (V&S). It was found that better convergence values can be achieved despite a large variation in the starting parameter values and / or material constitutive model and such behaviour reflects the uniqueness of the dual S&B indentation in predicting complex material systems. The study has shown that a robust optimization method based on a non-linear least-squares curve fitting function (LSQNONLIN) within MATLAB and ABAQUS can be used to accurately predict a unique set of elastic plastic material properties and Drucker-Prager material properties. This is of benefit to the scientific investigation of properties of new materials or obtaining the material properties at different location of a part which might be not be similar due to manufacturing processes (e.g. different heating and cooling rates at different locations).

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti-6Al-4V grade 5 and ELI. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

The paper deals with the Compound Inverse Rayleigh distribution, shown to constitute a proper model for the characterization of the probability distribution of extreme values of wind-speed, a topic which is gaining growing interest in the field of renewable generation assessment, both in view of wind power production evaluation and the wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model - already proven to be a valid model for extreme wind-speeds - by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity to interpret different field data is illustrated, also by means of numerous numerical examples based upon real wind speed measurements. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. In practice, the method allows to express one’s prior beliefs both in terms of parameters, as customary, and/or in terms of probabilities. The results of a large set of numerical simulations – using typical values of wind-speed parameters - are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Our work uses Iterative Boltzmann Inversion (IBI) to study the coarse-grained interaction between 20 amino acids and the representative carbon nanotube CNT55L3. IBI is a multi-scale simulation method that has attracted the attention of many researchers in recent years. It can effectively modify the coarse-grained model derived from the Potential of Mean Force (PMF). IBI is based on the distribution result obtained by All-Atom molecular dynamics simulation, that is, the target distribution function, the PMF potential energy is extracted, and then the initial potential energy extracted by the PMF is used to perform simulation iterations using IBI. Our research results have gone through more than 100 iterations, and finally, the distribution obtained by coarse-grained molecular simulation (CGMD) can effectively overlap with the results of all-atom molecular dynamics simulation (AAMD). In addition, our work lays the foundation for the study of force fields for the simulation of the coarse-graining of super-large proteins and other important nanoparticles.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

TVs and monitors are among the most widely used displays in various environments. However, they have limitations in their physical display conditions, such as a fixed size/position and a rigid/flat space. In this paper, we suggest a new "Display In the Wild" (DIW) concept to overcome the aforementioned problems. Our proposed DIW system allows us to display a flexibly large screen on dynamic non-planar surfaces at an arbitrary display position. To implement our DIW concept practically, we choose a projector as the hardware configuration in order to a generate screen anywhere with different sizes. However, distortion occurs when the projector displays content on a surface that is dynamic and/or non-planar. Therefore, we propose a distortion correction method for DIW to overcome the aforementioned surface-constraints. Since projectors are not capture devices, we propose using a depth camera to determine the distortions on the surfaces quickly. We also propose DIW-specific calibration and fast/precise correction methods. Our calibration method is constructed to easily and quickly detect the projection surface, and also allows our proposed system to accommodate the intrinsic parameters such as a display resolution and field of view. We accomplish a fast undistortion process of the projector by considering only surface boundary pixels, which enables our method to run in real time. In our comprehensive experiments, the proposed DIW system generates undistorted screens such as TVs and monitors on dynamic non-planar surfaces at an arbitrary display position with Unmanned Aerial Vehicles (UAVs) in a fast and accurate manner, demonstrating its usefullness in practical DIW scenarios.

To deal with the uncertainties in modeling offshore wind turbines, we proposed a parameter inversion method for the pile-soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in-situ parameter. The proposed method is confirmed to converge after some iterations, whatever the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed some light on the influence of uncertainties in offshore wind turbines, such as soil parameters in geological surveys.

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

Today, mechanical tracking systems have been downsized to allow them to be used in the field of airborne laser communications and in the military domain. Risley systems are used for this purpose, which work by directing a beam of light to a given target point, this procedure is commonly known as the inverse problem. In this paper, an analytical method, the geometric method, has been designed and developed to determine the beam steering in a Risley system and solve the inverse problem. The method focuses on different geometric shapes, like circumference or ellipse, that are described when the beam passes through the second prism. The accuracy and efficiency of the geometric method has been analysed and found to be faster than the two-step method. Furthermore, the geometric method has been implemented in an iterative process and an accuracy of up to 1 pm has been achieved. This high accuracy would allow the geometric method to be applied in fields such as lithography, stereolithography or 3D printers.

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

The application of instrumented indentation to assess material properties like Young’s modulus and micro-hardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e. kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain-curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-non-destructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

Livestock farming is a major source of greenhouse gas and ammonia emissions. In this study, we estimate methane, nitrous oxide and ammonia emission from livestock sector in the Red River Delta region from 2000 to 2015 and projection to 2030 using IPCC 2006 methodologies with the integration of local emission factors and provincial statistic livestock database. Methane, nitrous oxide and ammonia emissions in 2030 are estimated at 132 kt, 8.3 kt and 34.2 kt, respectively. Total global warming potential is 9.7 MtCO_2eq in 2030, accounts for 33% greenhouse gas emissions from livestock in Vietnam. Pig farming is responsible for half of both greenhouse gases and ammonia emissions in the studied region. Other major livestock for greenhouse gas emission is cattle and for ammonia emission is poultry. Hanoi contributes for the largest emissions in the region in 2015 but will be caught up and surpassed by other provinces in 2030.

Modeling the reaction time required for the removal of chemical oxygen demand (COD) from wastewater is important because can be an indicator of harmful pollutants that may pose risks to human health.. Here, we evaluate the use of an inverse artificial neural network (ANNi) to optimize the removal of COD from aqueous herbicide solutions using sonophotocatalysis as the treatment process.. This algorithm takes the operating conditions as input and estimates the optimal reaction time to reach the required effluent COD. This model was validated by comparison with both experimental measurements and simulated analysis, resulting in low error (0.5%), high Pearson correlation (R2 = 0.9956), and short computing time (less than one minute). The results for the proposed methodology (ANNi-GAs) were efficient and attractive in a reasonable way providing a satisfactory picture of the relationships between the optimal input parameters. Such parameters control the degradation process of herbicides online and can be used to predict the behavior of COD removal, thus taking actions to reduce the impact of aqueous treatment with alazine and gesaprim herbicides on aquatic, soil biota, and human health. Therefore, this technique constitutes a promising framework for predicting the environmental impact of herbicides within a tolerable degree of error.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

In the mean- field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/(2r^2) is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying the angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l + 1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.

In the context of Inverse Analysis in Civil Engineering, parameter identification and model calibration, of a structural system, relying on dynamic measurements, are subjects of a growing research interest. In the present contribution, the topic is tackled with reference both to simplified structural numerical examples and to a specific case study, namely a historical road three-span reinforced concrete arched bridge, with vibrational data previously acquired by standard wired accelerometers on the deck, under operational traffic conditions. In particular, the present work aims at focussing on the identification issues, concerning the definition of a maximum allowable threshold number of sought material parameters (e.g., Young’s moduli and mass densities of different structural components), with respect to the amount of available measurement data, and the investigation of the inverse analysis discrepancy function to be optimised, in order to set the intrinsic issue of multiple “realizations”, in case of a plain use of modal properties, and in view of forming a well–posed optimisation problem. Structural modelling, sensitivity analysis and numerical optimisation approaches are herein combined toward a robust and efficient identification strategy, to be effectively employed in structural assessment and diagnosis, also with respect to originally available or enriched sets of experimental data. The proposed methodology, and collected results, shall outline an efficient identification procedure, in view of automated inverse analysis, practically oriented to the dynamic assessment and structural diagnosis in the Civil Engineering context, as applied e.g. to strategic bridge infrastructures.

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation, and errors in structural installation. Therefore, coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks, this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing integrated antenna structure verify the efficient of the method on the reconstruction accuracy of the structural body displacement field.

Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for solution generation to the inverse kinematics problem of redundant robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the redundant degrees of freedom of redundant manipulator. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the manipulator. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link redundant manipulator is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

Globally, the intensity and irregularity of weather and climate extremes are increasing due to climate change. In Ethiopia, the occurrence of extreme events has been increasing, reporting severe impacts on environment which led to losses of lives and livelihood of societies. In this study, Heat Wave Magnitude Index daily (HWMId) was used to analysis heat wave magnitude in the Middle Awash Basin of Ethiopia. Gauge data obtained from Ethiopian Meteorological Institution (EMI) for 1981-2022 period and the future projection was taken from Coupled Model Intercomparison Project Phase 6 (CMIP6) under two socioeconomic pathways (SSP 2 and SSP 5) scenarios. The findings clearly showed that the area aggregated annual temperature anomaly increasing each year, 2015 was one of the warmest year on record with an anomaly of +1.8 °C. Severe to extreme heat wave recorded particularly during the last 10 years. For the future projection, under SSP 2-4.5 forcing scenario, the annual average air temperature projected to be warmer, which increasing 1.7 ℃ to 1.8 ℃ during mid-century and 2.3 ℃ to 2.4 ℃ end of century. Meanwhile, for SSP 5-8.5 forcing, the projection indicated an increment of 2.2 ℃ to 2.5 ℃ under mid-century and 4.4 ℃ to 4.8 ℃ end of century. Concerning the severity of heat wave, extreme to very extreme heat wave projected under SSP 2-4.5 forcing scenario and supper extreme heat wave projected under SSP 5-8.5 forcing scenario, respectively. The increase in extreme events may have a negative impact on health, water availability and food security. Therefore, the result of this study are essential for making wise decisions and for developing suitable strategies for climate change adaptation and mitigation that could minimize the risk of unusually extreme weather events.

Monocarboxylate transporter 8 (MCT8) and organic anion-transporting polypeptide 1C1 (OATP1C1) are thyroid hormones (TH) transmembrane transporters relevant for the availability of TH in neural cells, crucial for their proper development and function. Mutations in MCT8 or OATP1C1 result in severe disorders with dramatic movement disability related to alterations in basal ganglia motor circuits. Mapping the expression of MCT8/OATP1C1 in those circuits is necessary to explain their involvement in motor control. We studied the distribution of both transporters in the neuronal subpopulations that configure the direct and indirect basal ganglia motor circuits using immunohistochemistry and double/multiple labeling immunofluorescence for TH transporters and neuronal biomarkers. We found their expression in the medium-sized spiny neurons of the striatum (the receptor neurons of the corticostriatal pathway), and in various types of its local microcircuitry interneurons, including the cholinergic. We also demonstrate the presence of both transporters in projection neurons of intrinsic and output nuclei of the basal ganglia, motor thalamus and nucleus basalis of Meynert, suggesting an important role of MCT8/OATP1C1 for modulating the motor system. Our findings suggest that a lack of function of these transporters in the basal ganglia circuits would significantly impact motor system modulation, leading to clinically severe movement impairment.

Walking of humanoid robots is dependent on precise tracking of the center of gravity and foot trajectories. Trajectory tracking is achieved by mobilizing the robot joints to produce the correct trajectory. Errors are being occurred because of assumptions on tracking the center of gravity and the foot trajectories. In this study, a numerical algorithm has been developed that produces an exact and single kinematic solution in which the center of gravity and foot trajectories can be tracked with the desired precision. The effectiveness of the algorithm was examined with a dynamic simulation and compared with the method given in the literature The main highlight of this study, using the presented algorithm, the robot can walk even if the position of its center of gravity is lower than its hips, resulting tracking error was smaller than reported in the literature.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

Recent advances in nanomaterials have been heavily influenced by low-dimensional nanocarbon allotropes. In particular, carbyne has attracted attention for its potential as a true one-dimensional carbon chain with sp1 hybridization. To maximize the capabilities of this material, we employ a focused data-driven inverse design approach based on the carbon nanomaterials genome concept. This involves using deep learning neural network models to identify key descriptors tied to desired properties, enabling property prediction and reverse engineering of nanocarbons. Our iterative approach entails: (i) gathering growth/property data on nanostructures; (ii) identifying informative numerical/categorical predictors; (iii) developing deep learning models mapping descriptors to properties; (iv) refining models with new insights; (v) determining required descriptors/conditions for target properties via inverse mapping; (vi) validating models by synthesizing predicted nanostructures; and (vii) enhancing models with validation data. This allows uncovering hidden growth-property connections, precisely tuning nanocarbons for desired attributes. We introduce new methodologies including exciting synergistic effects, synchronizing atomic vibrations, active screen plasma, energy-driven transformations, surface acoustic micro/nano-manipulation, doping and directed self-assembly to expose relationships and integrate insights into the inverse design flow. This research promises to accelerate discovery of next-generation low-dimensional nanocarbons with exceptional properties and applications.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Tomography based on cosmic muon absorption is a rising technique because of its versatility and its consolidation as geophysics tool over the past decade. It allows to address major societal issues such as long-term stability of natural and man-made large infrastructures or sustainable underwater management. Traditionally, muon trackers consist of hodoscopes or multilayer detectors. For applications with challenging available volumes or wide field of view required, a thin time projection chamber (TPC) associated with a Micromegas readout plane can provide a good tradeoff between compactness and performance. This paper details the design of such a TPC aiming at maximizing primary signal and minimizing track reconstruction artifacts. The results of the measurements performed during a case study addressing the aforementioned applications are discussed. The current works lines and perspectives of the project are also presented.

Digital twin, an innovative technology propelled by data and models, plays a seminal role in the digital transformation and intelligent upgrade of ships. This study introduces a digital twin methodology for real-time monitoring of ship structure deformation fields, based on finite discrete strain data, and a visualization tool framework is developed using virtual reality technology. First, the inverse Finite Element Method (iFEM) is employed to derive the deformation field of the ship structure in real time via sensor strain data. Secondly, the deformation field data obtained based on the iFEM algorithm is converted into general visualization data conducive to interpretation within VR applications. Lastly, a digital twin software tool is built to enable synchronous response and interaction between the virtual scene and the physical scene, directly superposing particular virtual objects (data acquired by sensors, CAD virtual models, and deformation field cloud images) onto the physical scene in real-time. The digital twin tool embodies a virtual reality visualization system framework integrating physical data measurement, reconstruction, analysis, expression, storage, rendering and interaction of deformation field data. Through practical application, the flexibility, effectiveness and compatibility of the developed prototype tool are verified. According to the results, the system can enhance the efficiency of scientific communication, model validation, and interdisciplinary sharing during the analysis and evaluation of mechanical properties of ship structures.

We propose an algorithm for generating a panoramic image of a pipe’s inner surface based on inverse perspective mapping (IPM). For efficient crack detection, we used only perspective images of the pipe interior that can be obtained with a single lens camera instead of those taken with a 360-degree camera or a 3D depth camera. Frontal images taken while passing through the pipe were converted to images of the inner surface of the pipe using IPM. We derived a generalized IPM formula that considers the slope of the image plane to correct image distortion caused by the tilt of the plane; this IPM formula was derived based on the vanishing point of the perspective image, which was detected using optical flow techniques. Finally, the multiple transformed images with overlapping areas were combined via image stitching to create a panoramic image of the inner pipe surface. To validate our proposed algorithm, we restored images of pipe inner surface using a 3D pipe model and used these images for crack detection.

Mercury (Hg (II)) contamination is indefatigable global hazard which causes severe permanent damages to human health. Extensive research has been carried out to produce mercury adsorbents however they are still facing certain challenges limiting their upscaling. Herein we reported the synthesis of novel amine impregnated inverse vulcanized copolymer for effective mercury removal. Poly(S-MA) was prepared using sulfur and methacrylic acid employing inverse vulcanization method following by functionalization. The polyethylenime (PEI) was impregnated on poly(S-MA) to increase the adsorption active sites. The developed adsorbent was then characterized using Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). FTIR confirmed formation of copolymer and successful impregnation of PEI and SEM revealed composite porous morphology of the copolymer. Amine impregnated copolymer (amine@poly(S-MA)) outperformed poly(S-MA) in mercury as it showed 20 % superior performance with 44.7 mg/g maximum adsorption capacity. The adsorption data best fits the pseudo second order which indicates that the chemisorption is most influential mechanism in this case indicating the involvement of NH2 in mercury removal. The adsorption is mainly monolayer on homogenous surface as indicated by 0.76 value of Redlich-Peterson exponent (g) which describes the adsorption nature advent from R2 value of 0.99.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

Identifying a vestibular source of pathology in patients complaining of post-traumatic brain injury (TBI) dizziness can be difficult. We describe a possible new method utilizing the reduction of post-TBI symptom (including dizziness) with the use of a noise cancellation device (NCD). This retrospective case series included patients with TBI and dizziness presenting to a binocular vision specialty clinic, who were diagnosed with a vertical heterophoria (VH). If they did not respond adequately to microprism lenses and/or if they experienced hyperacusis, they were evaluated with an NCD. If there was marked reduction of TBI symptoms (including dizziness), the patients were referred to a neuro-otologist for vestibular diagnostic evaluation and treatment. Fourteen patients were identified and found to have abnormalities on vestibular testing consistent with Third Mobile Window Disorder (TMWD). All were treated with a 6-week medical protocol (diuretics, no straining, low sodium/no caffeine diet). Five responded positively, requiring no further treatment. Nine required surgical intervention and responded positively. In conclusion, 14 patients with post-concussive dizziness and VH, a positive response to NCD was associated with abnormal vestibular testing, a diagnosis of TMWD, and symptom reduction/resolution with a medical or surgical approach. The removal of sound resulting in reduction or resolution of vestibular symptoms represents an Inverse Tullio Phenomena.

The Geostationary Ocean Color Imager (GOCI) of the Communication, Ocean, and Meteorological Satellite (COMS) increases the chance of acquiring images with greater clarity at eight times a day and is equipped with spectral bands suitable for monitoring crop yield with a moderate spatial resolution. The objectives of this study were to classify nationwide paddy fields and to project rice (Oryza sativa) yield and production using the grid-based GRAMI-rice model and GOCI satellite products over South Korea from 2011 to 2014. Solar insolation and temperatures were obtained from COMS and the Korea local analysis and prediction system for model inputs, respectively. The paddy fields and transplanting dates were estimated using Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance and land cover products. The crop model was calibrated using observed yield data in 11 counties and was applied to 62 counties in South Korea. The overall accuracies of the detected paddy fields ranged from 89.5 to 90.2%. The simulated rice yields statistically agreed with observed yields, with root-mean-square errors of 0.219 to 0.451 ton ha-1 and Nash–Sutcliffe efficiencies of 0.241 to 0.733 in four years, respectively. According to paired t-tests (α = 0.05), the simulated and observed rice yields were not significantly different. These results demonstrate the possible development of a crop information delivery system that can classify land cover, simulate crop yield, and monitor regional crop production on a national scale.

Large water bodies such as the Laurentian Great Lakes have significant influences on local and regional climate through their unique physical features. Due to the coarse spatial resolution of general circulation models (GCMs), the Great Lakes are geometrically ignored in most GCMs. Thus, the dynamical downscaling technique serves as a necessary and feasible solution to bridge the gap. The Weather Research and Forecasting model (WRF) with an updated lake scheme is employed to downscale from a GCM, GFDL-CM3. The WRF-Lake’s performance is evaluated against observations, the GCM, as well as 23 other GCMs. Results show that the coupled air-lake model, with a fine spatial resolution and realistic lake bathymetries, reproduced a more reasonable spatiotemporal climatology than GCMs, as well as the lake-induced characteristics that were missed in GCMs. With lakes present, the seasonal variability of air temperature was reduced in WRF-Lake relative to GFDL-CM3, especially in summer. A reduced air temperature trend, about 4.5 °C/100 year in the 21st century, was projected in WRF-Lake. The seasonal evolutions of lake surface temperature and lake ice coverage were well captured by the lake model. The lake surface temperature was projected to be warming by 3.5-4 °C and the lake ice diminishing by 58.9% - 86%. Those results brought by the WRF-Lake model suggest that a fine resolution of the topography and the incorporation of the lake-atmosphere interactions are crucial to improve the understanding of the climate and climate change in the Great Lakes region.

Subglottal Impedance-Based Inverse Filtering (IBIF) allows for the continuous, non-invasive estimation of glottal airflow from a surface accelerometer placed over the anterior neck skin below the larynx, which has been shown to be advantageous for the ambulatory monitoring of vocal function. However, during long-term ambulatory recordings over several days, conditions may drift from the laboratory environment where the IBIF parameters were initially estimated due to sensor positioning, skin attachment, and temperature, among other factors. Observation uncertainties and model mismatch may result in significant deviations in the glottal airflow estimates, but are very difficult to quantify in ambulatory conditions due to a lack of a reference signal. To address this issue, we propose a Kalman filter implementation of the IBIF filter, which allows for both estimating the model uncertainty and adapting the airflow estimates to correct for signal deviations. One-way ANOVA results from laboratory experiments using the Rainbow Passage indicate a an improvement on amplitude-based measures for PVH subjects compared to IBIF which shows a statistically difference with respect to the reference oral airflow (p=0.02,F=4.1). MFDR from PVH subjects is slightly different to the oral airflow when compared to IBIF (p=0.04, F=3.3). Other measures did not have significant differences with either Kalman or IBIF, with the exception of H1H2, whose performance deteriorates for both methods. Overall, both methods show similar flottal airflow measures, with the advantage of Kalman by improving amplitude estimation. Moreover, Kalman filter deviations from the IBIF output airflow might suggest a better representation of some fine details in the ground-truth glottal airflow signal. Other applications may take more advantage from the adaptation offered by the Kalman filter implementation.

Spiral galaxies and their rotation curves have key characteristics of differentially spinning objects. Oblate spheroid shapes are a consequence of spin and reasonably describe galaxies, indicating that their matter is distributed in gravitationally interacting homeoidal shells. Previously published equations describing differentially spinning oblate spheroids with radially varying density are here applied to 51 galaxies, mostly spirals. A constant volumetric density (rho, kg m-3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RC being reported simply as a function of equatorial radius r. We construct parameter-free inverse models that uniquely specify mass inside any given r, and thus directly constrain rho vs. r solely from velocity v(r) and galactic aspect ratios (assumed as 1:10 when data are unavailable). Except for their innermost zones, rho is proven to be closely proportional to rn, where n for all 36 spirals studied equals -1.80±0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated rho at galactic edges agrees with estimated rho of intergalactic media (IGM). Our finding that central densities increase with galaxy size is consistent with behavior exhibited by diverse self-gravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no non-baryonic component. Empirical luminosity-velocity relationships for galaxies, such as the Tully-Fisher rule, originate in Newtonian physics.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.