GNSS have been widely used in navigation, positioning and timing. Nowadays, the multipath errors previously considered detrimental may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), e.g. GPS- Multipath Reflectometry (GPS-MR). In this paper, a new element describing bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model linking the GPS observables (SNR, phase and pseudorange) with detailed vegetation parameters, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that wheat will decrease the amplitudes of GPS multipath observables, if we increase the vegetation moisture contents or the scatters sizes (stem or leaf), the amplitudes of GPS multipath observables (SNR, phase and code) decrease. Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with published results for environmental parameter detections with GPS-MR.

In this study, we present comprehensive climatologies of effective ultraviolet (UV) quantities and photosynthetically active radiation (PAR) over Cyprus for the period 2004 to 2023, leveraging the synergy of earth observation (EO) data and radiative transfer model simulations. The EO dataset, encompassing satellite and re-analysis data for aerosols, total ozone column, and water vapor, alongside cloud modification factors, to capture the nuanced dynamics of Cyprus's atmospheric conditions. With a temporal resolution of 15 minutes and a spatial of 0.05°x0.05°, these climatologies undergo rigorous validation against established satellite datasets and are further evaluated through comparisons with ground-based global horizontal irradiance measurements provided by the Meteorological Office of Cyprus. This dual-method validation approach not only underscores the models' accuracy but also highlights their proficiency in capturing intra-daily cloud coverage variations. Our analysis extends to investigating the long-term trends of these solar radiation quantities, examining their interplay with changes in cloud attenuation, aerosol optical depth (AOD), and total ozone column (TOC). Significant decreasing trends in the noon ultraviolet index (UVI), of -2 to -4% per decade have been found in Autumn, especially marked on the island’s Northeastern part, mainly originating from the (significant) positive trends in TOC. The significant decreasing trends in TOC, of -2 to -3% per decade that were found in Spring do not result in correspondingly significant positive trends in the noon UVI since variations in cloudiness and aerosols also have a strong impact on the UVI in this season. The seasonal trends in the Daylight Integral (DLI) were generally not significant. These insights provide a valuable foundation for further studies aimed at developing public health strategies and enhancing agricultural productivity, highlighting the critical importance of accurate and high-resolution climatological data.

Optical remote sensing can contribute to biodiversity monitoring and species composition mapping in tropical forests. Inferring ecological information from canopy reflectance is complex and data availability suitable to such a task is limiting, which makes simulation tools particularly important in this context. We explored the capability of the 3D radiative transfer model DART to simulate top of canopy reflectance acquired with airborne imaging spectroscopy in complex tropical forest, and to reproduce spectral dissimilarity within and among species, as well as species discrimination based on spectral information. We focused on two factors contributing to these canopy reflectance properties: the horizontal variability in leaf optical properties (LOP) and the fraction of non-photosynthetic vegetation (NPVf). The variability in LOP was induced by changes in leaf pigment content, and defined for each pixel based on a hybrid approach combining radiative transfer modeling and spectral indices. The influence of LOP variability on simulated reflectance was tested by considering variability at species, individual tree crown and pixel level. We incorporated NPVf into simulations following two approaches, either considering NPVf as a part of wood area density in each voxel or using leaf brown pigments. We validated the different scenarios by comparing simulated scenes with experimental airborne imaging spectroscopy using statistical metrics, spectral dissimilarity (within crowns, within species, and among species dissimilarity) and supervised classification for species discrimination. The simulation of NPVf based on leaf brown pigments resulted in the closest match between measured and simulated canopy reflectance. The definition of LOP at pixel level resulted in conservation of the spectral dissimilarity and expected performances for species discrimination. Our simulation framework could contribute to better understand performances for species discrimination and relationship between spectral variations and taxonomic and functional dimensions of biodiversity.

The increasing spatial and spectral resolution of hyperspectral imagers yields detailed spectroscopy measurements from both space-based and airborne platforms. Machine learning algorithms have achieved state-of-the-art material classification performance on benchmark hyperspectral data sets; however, these techniques often do not consider varying atmospheric conditions experienced in a real-world detection scenario. To reduce the impact of atmospheric effects in the at-sensor signal, atmospheric compensation must be performed. Radiative Transfer (RT) modeling can generate high-fidelity atmospheric estimates at detailed spectral resolutions, but is often too time-consuming for real-time detection scenarios. This research utilizes machine learning methods to perform dimension reduction on the transmittance, upwelling radiance, and downwelling radiance (TUD) data to create high accuracy atmospheric estimates with lower computational cost than RT modeling. The utility of this approach is investigated using the instrument line shape for the Mako long-wave infrared hyperspectral sensor. This study employs physics-based metrics and loss functions to identify promising dimension reduction techniques. As a result, TUD vectors can be produced in real-time allowing for atmospheric compensation across diverse remote sensing scenarios.

This study investigates the long-term stability of the Suomi National Polar-orbiting Partnership (S-NPP) Visible Infrared Imaging Radiometer Suite (VIIRS) moderate-resolution Thermal Emissive Bands (M TEBs; M12 – M16) covering a period from February 2012 to August 2020. It also assesses inter-sensor consistency of the VIIRS M TEBs among three satellites-S-NPP, NOAA-20, and NOAA-21 over eight months spanning from March 18 to November 30, 2023. The field of interesting is limited to the ocean surface between 60°S and 60°N, specifically under clear-sky conditions. Taking radiative transfer modeling (RTM) as the transfer reference, we employed the Community Radiative Transfer Model (CRTM) to simulate VIIRS TEB brightness temperature (BTs), incorporating European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data as inputs. Our results reveal two key findings. Firstly, the reprocessed S-NPP VIIRS TEBs exhibit a robust long-term stability, as demonstrated through analyses of the observation minus background BT differences (O-B ∆BTs) between VIIRS measurements (O) and CRTM simulations (B). The drifts of the O-B BT differences are consistently less than 0.105 K/Decade across all S-NPP VIIRS M TEB bands. Notably, observations from VIIRS M14 and M16 stand out with drifts well within 0.04 K/Decade, reinforcing their exceptional reliability for climate change studies. Secondly, excellent inter-sensor consistency among these three VIIRS instruments is confirmed through the double-difference analysis method (O-O). This method relies on the O-B BT differences obtained from daily data. The mean inter-VIIRS O-O BT differences remain within 0.08 K for all M TEBs, except for M13. Even in the case of M13, the O-O BT differences between NOAA-21 and NOAA-20/S-NPP have values of 0.312 K and 0.234 K, respectively, which are comparable to the 0.2 K difference between some TEBs among VIIRS and MODIS. These disparities are primarily attributed to the significant differences in the Spectral Response Function (SRF) of NOAA-21 compared to NOAA-20 and S-NPP. Our study confirms the RTM-based TEB quality evaluation method’s versatility and effectiveness in assessing long-term sensor stability and inter-sensor consistency. The double-difference approach effectively mitigates uncertainties and biases inherent to CRTM simulations, establishing itself a robust mechanism for assessing inter-sensor consistency. In addition, we’ve observed that, except for M13, M12 always exhibits larger spatial variations of O-O BT differences with greater uncertainties compared to the other M TEBs. The influence of solar contribution through sea surface reflection on the Top of Atmosphere (TOA) radiance measurements during daytime in M12 should not be underestimated.

In recent years, the utilization of machine learning algorithms and advancements in Unmanned Aerial Vehicle (UAV) technology have marked significant shifts in remote sensing practices. In particular, the integration of machine learning with physical models and their application in UAV-satellite data fusion have emerged as two prominent approaches for estimating vegetation biochemistry. This study evaluates the performance of five machine learning regression algorithms (MLRAs) for mapping crop canopy chlorophyll at the Kellogg Biological Station (KBS) in Michigan, USA, across three scenarios: (1) application to Landsat 7, RapidEye, and PlanetScope satellite images; (2) application to UAV-satellite data fusion; and (3) integration with the PROSAIL radiative transfer model (hybrid methods PROSAIL + MLRAs). The results indicate that the majority of the five MLRAs utilized in UAV-satellite data fusion perform better than the five PROSAIL + MLRAs. The general trend suggests that the integration of satellite data with UAV-derived information, including the normalized difference red-edge index (NDRE), canopy height model, and leaf area index (LAI), significantly enhances the performance of MLRAs. The UAV-RapidEye dataset exhibits the highest coefficient of determination (R2) and the lowest root-mean-square errors (RMSE) when employing kernel ridge regression (KRR) and Gaussian processes regression (GPR) (R2 = 0.89 and 0.89 and RMSE = 8.99 µg/cm2 and 9.65 µg/cm2, respectively). Similar performance is closely observed for the UAV-Landsat and UAV-PlanetScope datasets (R2 = 0.86 and 0.87 for KRR, respectively). For the hybrid models, maximum performance is attained with Landsat data using KRR and GPR (R2 = 0.77 and 0.51 and RMSE = 33.10 µg/cm2 and 42.91 µg/cm2, respectively), followed by R2 = 0.75 and RMSE = 39.78 µg/cm2 for PlanetScope data upon integrating partial least squares regression (PLSR) into the hybrid model. Across all hybrid models, RapidEye data yielded the most stable performance, with R2 ranging from 0.45 to 0.71 and RMSE ranging from 19.16 µg/cm2 to 33.07 µg/cm2. The study highlights the importance of synergizing UAV and satellite data which enables effective monitoring of canopy chlorophyll in small agricultural lands.

Several problems of radiative transfer are yet unsolved because of the difficulties of the calculations involved in them, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the formulas that were previously derived, into a graphical interface based on the projected solid-angle principle. Such procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled by means of the analytical software DianaX developed at an earlier stage by the authors. With this new approach the often cumbersome procedure of lighting and thermal exchange calculations can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

The exact determination of radiative exchanges between solids and surfaces has been a long sought-for question in heat transfer science. Being the canonical equation that rules such phenomena, a fourfold integral, it is extremely difficult to obtain an accurate solution like a formula or abacus. Over the last thirty years, the author has tried to integrate the canonical expression by sundry procedures and they have published two books and a dozen of articles on the matter, recently by virtue of computational geometry and graphic algorithms as a new way to solve the finite-difference problems that arise on complex geometries. In architectural engineering curved radiant emitters are customary since antiquity, especially in domes and vaults and their oculus, However, a consistent procedure to handle them was not readily available. The principles that are described hereby based on Cabeza-Lainez’ first principle for spherical fragments offer a complete panorama on the manner in which surface sources related or contained in spheres can be interpreted and accounted for without resorting to integration. The main advance is that a variety of unexplained problems of radiative heat transfer, applicable to aerospace engineering, meteorological, architectural and medical sciences can be sorted out as exactly as quickly.

In this work, we develop a software suite for studies of atmosphere – underlying SNOW- spaceborne optical receiver light TRANsmission calculations (SNOWTRAN) with applications for the solution of forward and inverse radiative transfer problems in polar regions. Assuming that aerosol load is extremely low, the proposed theory does not require the numerical procedures for the solution of the radiative transfer equation and is based on analytical equations for the spectral nadir reflectance and simple approximations for local optical properties of atmosphere and snow. The model developed is validated using EnMAP and PRISMA spaceborne imaging spectroscopy data close to the Concordia research station in Antarctica. A new fast technique for the determination of the snow grain size and assessment of the snowpack vertical inhomogeneity is then proposed and further demonstrated on EnMAP imagery over the Aviator Glacier and in the vicinity of the Concordia research station in Antarctica. The results revealed a large increase in precipitable water vapor at the Concordia research station in February 2023 linked to warming event, and a 4 times larger grain size at Aviator Glacier compared to Dome C.

Whenever vegetated areas are monitored over time, phenological changes in land cover should be decoupled from changes in acquisition conditions, like atmospheric components, sun and satellite heights, and imaging instrument. This especially holds when the multispectral (MS) bands are sharpened for spatial resolution enhancement by means of a panchromatic (Pan) image of higher resolution, a process referred to as pansharpening. In this paper, we provide evidence that pansharpening of visible/near-infrared (VNIR) bands takes advantage from a correction of the path radiance term introduced by the atmosphere, during the fusion process. This holds whenever the fusion mechanism emulates the radiative transfer model ruling the acquisition of the Earth’s surface from space, that is, for methods exploiting a multiplicative, or contrast-based, injection model of spatial details extracted from the panchromatic (Pan) image into the interpolated multispectral (MS) bands. The path radiance should be estimated and subtracted from each band before the product by Pan is accomplished. Both empirical and model-based estimation techniques of MS path radiances are compared within the framework of optimized algorithms. Simulations carried out on two GeoEye-1 observations of the same agricultural landscape at different dates highlight that the de-hazing of MS before fusion is beneficial for an accurate detection of seasonal changes in the scene, as measured by the normalized differential vegetation index (NDVI).

The radiative heat transfer in arc plasma models is considered from the point of view of its description in terms of a net emission coefficient, the method of spherical harmonics in its lowest order, and the discrete ordinate method. Net emission coefficients are computed applying approximate and numerical approaches, the multi-band representation of the spectral absorption coefficient with three kinds of its averaging and two datasets. The self-consistent access to the radiative heat transfer is applied to a two-dimensional axisymmetric model of free-burning arc in argon at atmospheric pressure. The results obtained from the models employing the net emission coefficient, the method of spherical harmonics, and the discrete ordinate method are compared.

To understand forest dynamics under today’s changing environmental conditions, it is important to analyze the state of forests at large scales. Forest inventories are not available for all regions, so it is important to use other additional sources of information, e.g. remote sensing observations. Increasingly, remotely sensed data based on optical instruments and airborne LIDAR are becoming widely available for forests. There is great potential in analyzing these measurements and gaining an understanding of forests state. In this work, we combine the new generation radiative transfer model mScope with the individual-based forest model FORMIND to generate reflectance spectra for forests. Combining the two models allows us to account for species diversity at different height layers in the forest. We compare the generated reflectances for forest stands in Finland, in the region of North Karelia, with Sentinel-2 measurements. We investigate which level of forest representation gives the best results. For the majority of the forest stands, we generated good reflectances with all levels forest representation compared to the measured reflectance. Good correlations were also found for the vegetation indices (especially NDVI with R²=0.62). This work provides a forward modelling tool for relating forest reflectance to forest characteristics. With this tool it is possible to generate a large set of forest stands with corresponding reflectances. This opens the possibility to understand how reflectance is related to succession and different forest conditions.

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

The most important plastic resins used for wire coating are Polyvinyl Chloride (PVC), Nylon, Polysulfone and Low-high density polyethylene (LDPE / HDPE). In this article,the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adomian decomposition method (ADM). The convergence of the series solution is established. The results are also verified by Optimal Homotopy Asymptotic Method (OHAM). The effect of different emerging parameters such as non-Newtonian parameters α and β, magnetic parameter M and the Brinkman number Br on solutions (velocity and temperature profiles) are discussed through several graphs. Additionally, the current result also compares with the published work already available in the literature.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

The oscillating heat pipe (OHP) is a new member in the family of heat pipes, and it has great potential applications in energy conservation. However, the fluid flow and heat transfer in the OHP as well as the fundamental effects of inner diameter on them have not been fully understood, which are essential to the design and optimization of the OHP in real applications. Therefore, by combining the high-speed visualization method and infrared thermal imaging technique, the fluid flow and thermal performance in the OHPs with inner diameters of 1, 2 and 3 mm are presented and analyzed. The results indicate that three fluid flow motions, including small oscillation, bulk oscillation and circulation, coexist or, respectively, exist alone with the increasing heating load under different inner diameters, with three flow patterns occurring in the OHPs, viz. bubbly flow, slug flow and annular flow. These fluid flow motions are closely correlated with the heat and mass transfer performance in the OHPs, which can be reflected by the characteristics of infrared thermal images of condensers. The decrease in the inner diameter increases the frictional flow resistance and capillary instability while restricting the nucleate boiling in OHPs, which leads to a smaller proportion of bubbly flow, a larger proportion of short slug flow, a poorer thermal performance, and easier dry-out of working fluid. In addition, when compared with the 2 mm OHP, the increasing role of gravity induces the thermosyphon effect and weakens the 'bubble pumping' action, which results in a little smaller and bigger thermal resistances of 3 mm OHP under small and bulk oscillation of working fluid, respectively.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

Surface initiated atom transfer radical polymerization (SI-ATRP) is one of the most versatile technique to modify the surface properties of material. Recent developed metal free SI-ATRP makes such technique more widely applicable. Herein photo-induced metal-free SI-ATRP of methacrylates, such as methyl methacrylate, N-isopropanyl acrylamide, and N,N- dimethylaminoethyl methacrylate, on the surface of SBA-15 was reported to fabricate organic-inorganic hybrid materials. SBA-15 based polymeric composite with adjustable graft ratio was obtained. The structure evolution during the SI-ATRP modification of SBA-15 was monitored and verified by FT-IR, XPS, TGA, BET, and TEM. The obtained polymeric composite showed enhanced adsorption ability for the model compound toluene in aqueous. This procedure provides a low cost, ready availability, and facile modification way to synthesize the polymeric composites without the contamination of metal.

Due to environmental concerns, natural refrigerants and their use in refrigeration and air conditioning systems are receiving more attention from manufacturers, end users and the scientific community. The study of heat transfer and pressure drop is essential for accurate design and more energy efficient cycles using natural refrigerants. The aim of this work is to provide an overview of the latest outcomes related to heat transfer and pressure drop correlations for ammonia, propane, isobutane and propylene and to investigate the current state of the art in terms of operating conditions. Available data on the existing correlations of heat transfer coefficient and pressure drop for natural refrigerants have been collected through a systematic search. Whenever possible, validity intervals are given for each correlation and the error is quantified. It is the intention of the authors that this could be a valuable support for researchers and an aid to design, with particular reference to heat pumps. A procedure based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was adopted, and the Scopus database was used to query the relevant literature. A total of 135 publications qualified for inclusion in the survey; 34 articles report experimental investigations for not usual geometric conditions. Of the 101 selected papers related to usual geometric conditions, N = 50 deal only with HTC, N = 16 deal only with pressure drop and the remainder (N = 35) analyse both HTC and pressure drop. Among the 85 HTC papers (N = 53) deal with the evaporating condition, N = 30 with condensation and only N = 2 with the heat transfer correlations under both conditions. Most of the 101 articles concern propane and isobutane. The high temperatures are less widely investigated.

This paper presents an innovative multi-agent, data-driven reinforcement learning (RL) approach to develop and utilize the thermal equivalent network model that represents the motor's thermal dynamics. A multi-agent reinforcement learning is designed and trained to adjust the model parameters using data from several motor driving cycles. To ensure the incoming driving cycle matches the historical data before employing the pre-trained RL agents, offline statistical analysis and clustering techniques are developed and used. Numerical simulations highlighted the RL agent's ability to develop strategies that effectively address the variability of driving cycles. The proposed RL framework showed its capability to accurately reflect the motor's thermal behavior under various driving conditions.

The presented results of simulations take into account the optical parameters of the selected sea region (from literature data on the southern Baltic Sea) and two optically extreme types of crude oil (from historical data) which exist in the form of a highly diluted oil-in-water emulsion (10 ppm). The spectral index was analyzed based on the results of modelling the radiance reflectance distribution for almost an entire hemisphere of the sky (zenith angle from 0 to 80o). The spectral index was selected and is universal for all optically different types of oil (wavelengths 650 and 412 nm). The possibility of detecting pollution in the conditions of the wavy sea surface (as a result of wind of up to 10 m/s) was studied. It has been also shown that if the viewing direction is close to a direction perpendicular to the sea surface, observations aimed at determining the spectral index are less effective than observation under the zenith angle of incidence of sunlight for all azimuths excluding the direction of sunlight specular reflection.

With the increasing demand for energy worldwide, researchers from different fields have been striving to improve the sustainability and proper utilization of energy resources. Passive radiative cooling, as a natural energy transport method, can achieve cooling without additional external energy input. This review provides a comprehensive examination of passive radiative cooling, including its fundamental theories and latest development. A particular emphasis is placed on the diverse range of fields where passive radiative cooling has been applied, notably including but not limited to construction and architecture. The current state of applications, potential challenges that may arise with wider adaption and promising research directions for each field are thoroughly discussed. This review underscores the universal applicability and feasibility of passive radiative cooling and contributes to its future development by identifying promising areas for further exploration.

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.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

The Double U-pipe ground heat exchanger, recognized for its straightforward process, cost-effectiveness, high heat exchange efficiency, and low thermal resistance, stands as the predominant ground heat exchanger type in today's shallow geothermal energy development and utilization. Recent years have seen significant research into the heat transfer influencing factors and heat exchange performance of Double U-pipe ground heat ex-changers via experimental testing methods. Yet, studies integrating numerical simulation with in-situ testing have been less frequent. Drawing on the cylindrical heat source model theory and the outcomes of regional in-situ thermal response tests, this paper develops a Double U-pipe ground heat transfer model by establishing physical, mathematical, and heat transfer geometric models. It assesses the impact of varying inlet temperatures, flow rates, and initial ground temperatures on heat exchange efficiency under heating conditions. The results validate the precision of the double U-pipe ground heat exchanger model based on in-situ testing. They show that enhancing the temperature differential between the inlet and initial temperatures, elevating the initial ground temperature, and moderately increasing the flow rate can boost the system's heat exchange efficiency.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

A decade ago, non-radiative wireless power transmission reemerged a promising alternative to deliver electrical power to devices where a physical wiring proved to be unfeasible. However, conventional coupling-based approaches are neither scalable nor efficient when multiple devices are involved, as they are restricted by factors like coupling and external environments. Zenneck waves are excited at interfaces, like surface plasmons and have the potential to deliver electrical power to devices placed on a conducting surface. Here, we demonstrate, efficient and long range delivery of electrical power by exciting non-radiative waves over metal surfaces to multiple loads.Our modeling and simulation using Maxwells equation with proper boundary conditions shows Zenneck type behavior for the excited waves and are in excellent agreement with experimental results. In conclusion, we physically realize a radically different power transfer system, based on a wave, whose existence has been fiercely debated for over a century.

As part of the Earth Climate Observatory space mission concept for the direct observation from space of the Earth Energy Imbalance, we propose an advanced camera suite for the high resolution observation of the Total Outgoing Radiation of the Earth. For the observation of the Reflected Solar Radiation, we propose the use of two multispectral cameras covering the range from 400 to 950 nm, with a nadir resolution of 1.7 km, combined with a high resolution RGB camera, with a nadir resolution of 0.57 km. For the observation of the Outgoing Longwave Radiation, we propose the use of 6 microbolometer cameras, with each a spectral bandwidth of 1 μm in the range from 8 to 14 μm, and with a nadir resolution of 2.2 km.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

Cancer is a leading cause of morbidity and mortality worldwide, yet much is still unknown about its mechanism of establishment and destruction. Recently, studies had shown that tumor cells cannot survive under the high temperature conditions. This treatment technique is called Hyperthermia. This report presents the case of radiative microwave heating of hyperthermia therapy on breast cancer in a porous medium. In this study, the steady state is solved analytically while unsteady state is solved using semi-implicit finite difference to get a more accurate prediction of blood temperature distributions within the breast tissues. A moderate temperature hyperthermia treatment is apply which results into cell death due to an increase in the level of cell sensitivity to radiation therapy and blood flow in tumor and oxygen. The results show that by applying metabolic heat generation rate of $3.97 X 10^{5}Wm^{-3}$, it takes upto 2 minutes for the tumor cells to get the require therapeutic temperature point.

With metal oxide semiconductors being a promising candidate for accurate indoor air quality assessments, multiple drawbacks of the gas sensors prevent their widespread use. Examples include poor selectivity, instability over time, and sensor poisoning. Complex calibration methods and advanced operation modes can solve some of those drawbacks. However, this leads to long calibration times, which are unsuitable for mass production. In recent years, multiple attempts to solve calibration transfer have been made with the help of direct standardization, orthogonal signal correction, and many more methods. Besides those, a new promising approach is transfer learning from deep learning. This article will compare different calibration transfer methods, including direct standardization, piecewise direct standardization, transfer learning for deep learning models, and global model building. The machine learning methods to calibrate the initial models for calibration transfer are feature extraction, selection, and regression (established methods) and a custom convolutional neural network TCOCNN. It is shown that transfer learning can outperform the other calibration transfer methods regarding the root mean squared error, especially if the initial model is built with multiple sensors. It was possible to reduce the number of calibration samples by up to 99.3 % (from 10 days to approximately 2 hours) and still achieve an RMSE for acetone of around 18 ppb (15 ppb with extended individual calibration) if six different sensors were used for building the initial model. Furthermore, it was shown that the other calibration transfer methods (direct standardization and piecewise direct standardization) also work reasonably well for both machine learning approaches, primarily when multiple sensors are used for the initial model.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

Triangles are an ever present feature in nature, which the building construction industry duly echoes. However, an exact expression intended to offer the radiant field due to any triangle in an upright or inclined position had not been identified by previous research. In this case, the author has been able to solve by direct integration, the canonical expression of radiative transfer. This result alone confers a myriad of possibilities that had been inconceivable before, for studying in detail the three-dimensional heat transfer behavior of volumes and figures in which triangles do manifest, such as fins, windows, roof-gables and louvers of various kinds. Typically, shading devices, when tilted, give rise in their extremes to rhomboidal shapes which were difficult to take into account or had to be subject to discretization and subsequent Monte Carlo methods in order to perform an approximate calculation of their emission. This implied a lengthy and inexact procedure that induced many errors and consumed computing time. We can now avoid all the former downsides due to the advances hereby presented. As the novel expression can be converted into an algorithm it will be advantageously employed for simulation. This significant finding dovetails in the intricate puzzle of radiated heat and we believe that their consequences will greatly affect the conception and design of HVAC devices, aircraft manufacturing and specifically building or lighting industries among others.

Noninvasive brain stimulation technique can be used for modulation of motor behaviors such as reaction time (RT). The main aim of this study was to investigate whether RT during a sequential visual isometric pinch task (SVIPT) can be affected by anodal transcranial direct current stimulation (a-tDCS) over three different stimulation sites such as dorsolateral prefrontal cortex (DLPFC), primary motor cortex (M1) or posterior parietal cortex (PPC). We also aimed to assess if stimulation of these cortical sites affect the transfer of learning during SVIPT. A total of 48 right-handed healthy participants were randomly assigned to one of the four a-tDCS groups: 1) left M1, 2) left DLPFC, 3) left PPC and 4) sham. A-tDCS was applied concurrent with SVIPT in which the participants were precisely controlled their forces to reach seven different target forces from 10 to 40% of maximum voluntary contraction (MVC) presenting on a computer screen with right dominant hand. Four test blocks were randomly performed at baseline and 15 min after the intervention including sequence and random blocks with either hand. Our results showed significant differences between a-tDCS groups on ratio RT in the sequence blocks of both the right trained (P = .041) and left untrained hands (P = .023) for target forces of 15% and 30 % of MVC, respectively. In sequence blocks, M1 showed significant elongation in ratio RT for the target force of 15% and 30 % MVC compared to PPC and Sham groups in the right hand. In sequence blocks with left hand, this negative effect were found between M1-DLPFC and M1-Sham groups. In random blocks, no significant differences were found among four groups at each target forces for the left hand while there were significant differences for 15% (P =. 04) and 40% MVC (P =. 035) in the right hand. Our findings suggest that three different stimulation sites (DLPFC, M1 or PPC) were differentially affected by a single session of a-tDCS at some target forces during SVIPT. The effects of a-tDCS on ratio RT were transferred in the left untrained hand for sequence blocks but not random blocks. Further research is needed to understand fundamental aspects of these main areas of the brain on temporal processing in a precision control task such as SVIPT.

The direct radiative effect of aerosols is taken into account in many limited area numerical weather prediction models using wavelength-dependent aerosol optical depths of a range of aerosol species. We study the impact of aerosol distribution and optical properties on radiative transfer, based on climatological and more realistic near real-time aerosol data. Sensitivity tests were carried out using the single column version of the ALADIN-HIRLAM numerical weather prediction system, set up to use the HLRADIA broadband radiation scheme. The tests were restricted to clear-sky cases to avoid the complication of cloud-radiation-aerosol interactions. The largest differences in radiative fluxes and heating rates were found to be due to different aerosol loads. When the loads are large, the radiative fluxes and heating rates are sensitive to the aerosol inherent optical properties and vertical distribution of the aerosol species. Impacts of aerosols on shortwave radiation dominate longwave impacts. Sensitivity experiments indicated the important effects of highly absorbing black carbon aerosols and strongly scattering desert dust.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

Pakistan flora is enriched with potent bioactive compounds that must be explored while Alzheimer's disease (AD) poses a global challenge driven by neurochemical imbalances. Acetylcholinesterase (AChE) inhibitors traditionally alleviate symptoms, but addressing the root cause remains elusive. This gap has led to the exploration of herbal sources for interventions. In this context, we analyzed fifty 50 medicinal plants for their phytochemical composition and antioxidant and acetylcholinesterase inhibition activities. AChE activity was measured using Ellman’s method. Santalum album exhibited significant AChE inhibition (86.2%), surpassing galantamine hydrobromide (81.8%). Promising inhibition was also seen in Bombax ceiba (77.8%), Acacia karoo (52.9%), and Phaseolus lunatus (50.1%). Detailed analysis revealed Santalum album's abundance in terpenoids, flavonoids, tannins, and phenolics, potentially correlating with its antioxidant and AChE inhibitory effects. Acacia karoo demonstrated elevated levels of total alkaloids, antioxidants, terpenoids, and tannins. Both Acacia karoo and Santalum album show promise for AD intervention due to their AChE inhibitory activities and unique phytochemical attributes, warranting further exploration, particularly for Acacia karoo's novel potential in AChE inhibition, to advance targeted AD therapeutics utilizing natural resources. This study contributes to the search for effective AD strategies from nature's pharmacological resources.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

The distribution and variation of top-of-atmosphere longwave cloud radiative forcing (LCRFTOA) has drawn a significant amout of attention due to its importance in understanding the energy budget. Advancements in sensor and data processing technology, as well as a new generation of geostationary satellites, such as the FengYun-4A (FY-4A), allow for high spatial resolutions that are crucial for real-time radiation monitoring. Nevertheless, there is a distinct lack of official top-of-atmosphere outgoing longwave radiation products under clear-sky conditions (OLRclear). Consequently, this study addresses the challenge of constructing LCRFTOA data with high spatiotemporal resolution over the full disk region of FY-4A. After simulating the influence of atmospheric parameters on OLRclear based on SBDART radiation transfer model (RTM), we developed a model for estimating OLRclear using infrared channels from the advanced geosynchronous radiation imager (AGRI) onboard the FY-4A satellite. The OLRclear results showed an RMSE of 5.05 W/m2 and MBE of 1.59 W/m2 compared to ERA5. Besides, the calculated LCRFTOA results were validated against instantaneous, daily average, and monthly average ERA5 and CERES LCRFTOA products, supporting the validity of the algorithm proposed in this paper. Finally, the changes in LCRFTOA due to variaty cloud heights (high, medium, and low cloud) were analyzed. This study provides the basis for comprehensive studies on the characteristics of top-of atmosphere radiation.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

Snow-covered regions are the main source of reflection of incident shortwave radiation (ISR) on Earth’s surface. The deposition of light-absorbing particles (LAPs) on these regions increases the capacity of snow to absorb ISR and decreases surface snow albedo (SSA), which intensifies the radiative forcing leading to accelerated snowmelt and modifications of the hydrologic cycle. In this work we investigate changes in SSA and radiative forcing (RF) induced by LAPs in the Upper Aconcagua River Basin (Chilean central Andes) using remote sensing satellite data (MODIS), in-situ spectral SSA measurements, and the ISR (Chilean Solar Explorer platform) during the austral-winter months (May to August) for the 2004-2016 period. To estimate the changes in SSA and RF, we define two spectral ranges: i) an enclosed range (Ecr) between 841-876 nm, which isolates effects of Black-Carbon, an important LAP derived from anthropogenic activities, and ii) a broadband range (Bbr) between 300-2500 nm. Our results show that percent variations in SSA in the Ecr are higher than in the Bbr, regardless of the total amount of radiation received, which may be attributed to the presence of LAPs as these particles have a greater impact on SSA at wavelengths in the Ecr band than in the Bbr band.

The model internal year-to-year variability (hereafter, internal variability) is a significant source of uncertainty when estimating anthropogenic aerosol effective radiative forcing (ERF). In this study, we investigate the impact of internal variability using large ensemble simulations (600 years in total) with the same climate model under prescribed anthropogenic aerosol forcings. A comparison of the magnitudes (i.e., standard deviation, Std) of these influences confirms that internal variability has negligible impacts on the instantaneous radiative forcing (RF) diagnosed by double radiation calls but has considerable impacts on estimating ERF through rapid adjustments (ADJ). Approximately half of the model grids exhibit strong internal variability influence on ERF (Std > 5 W m−2). These strong internal variabilities lead to a 50% probability that 30-year linear change can reach 2 W m−2, and 10-year linear change can reach 4 W m−2. A 50-year simulation can provide a relatively stable annual mean map of ERF (ERF = ADJ + RF), but it fails for ADJ. The statistically significant areas in the annual mean maps of both ERF and ADJ from a 10-year simulation exhibit instability with evident chaotic features. These analyses contribute to the setup of comparative experiments and a more comprehensive understanding of the modeled anthropogenic aerosol ERF.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The experiments were designed to predict the temporal and spatial resolution of Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The conjugate gradient method is used mostly as an inverse method. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted from the correlations of Churchill and Ozoe (1973) and Kandlikar (1990), respectively. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

The behavior of convective boundary conditions is studied to delineate their role in heat and mass relegation in the presence of radiation, chemical reaction, and hydromagnetic forces in three-dimensional Powell-Eyring nanofluids. Implications concerning non-Fourier’s heat flux and non-Fick’s mass flux with respect to temperature nanoparticle concentration were examined to discuss the graphical attributes of the principal parameters. An efficient optimal homotopy analysis method is used to solve the transformed partial differential equations. Tables and graphs are physically interpreted for significant parameters

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, impulse spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

Radiative budget is one of the key factors influencing climate change. The aim of this study is to analyze radiative regime in Moscow using the MSU-RAD(BSRN) instrumentation complex and to estimate radiative effects of the main atmospheric factors during the 2021-2023 period. Due to variations in aerosol content, the loss of global shortwave irradiance (Q) varies from 37 to 186 W/m2 (or about 18-22%) at different solar elevations with a significant decrease in direct irradiance and increase in diffuse irradiance due to multiple scattering. In winter, we observed the increase in Q of about 45 W/m2 (or 9%) at h=30° due to high surface albedo, smaller aerosol and water vapor content. At the same time, net shortwave irradiance (Bsh) demonstrates a significant decrease due to prevailing effects of snow albedo. A nonlinear dependence of Q and Bsh cloud transmittance on relative sunshine duration (Sd) is observed. Mean changes in Q against the 1955-2020 period are characterized by negative anomalies (-22%) in winter and positive anomalies in summer (+3%) due to the changes in cloudiness, reflected in Sd variations. This is in line with global tendencies in long-term changes of shortwave irradiance in moderate climate in Europe during the last years.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

A human brain can communicate with another one’s brain using quantum entanglement. Similar particles can entangle without interaction. Sensory communication between two individuals from far distances is still not known. Former studies primarily have been performed regarding brain neurons' quantum behavior. The test was performed on two individuals far from each other. These individuals were put under the same music on the basis of brain neuroplasticity property. By activating the brain reward system, aligned thinking was time scheduled in these individuals’ brains. On the basis of entanglement, compressed information was sent and received between these two individuals.

Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Its aim is to develop primitives beyond the reach of classical cryptography or to improve on existing classical implementations. Although much of the work in this field has been dedicated to quantum key distribution (QKD), some important steps were made towards the study and development of quantum oblivious transfer (QOT). It is possible to draw a comparison between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quantum-safe computation. However, the conditions under which QOT is actually quantum-safe have been subject to a great amount of scrutiny and study. In this review article, we survey the work developed around the concept of oblivious transfer in the area of theoretical quantum cryptography, with an emphasis on some proposed protocols and their security requirements. We review the impossibility results that daunt this primitive and discuss several quantum security models under which it is possible to prove QOT security.

Hydrogenases are iron-sulfur enzymes that catalyze proton reduction and H₂ oxidation with outstanding efficiency. They are considered blueprints for the design of transition metal complexes, e.g. as heterogenous catalysts in the context of H₂ production from water. Moreover, hydrogenases are biological model systems for metal hydride chemistry and proton-coupled electron transfer. Depending on the composition of the active site cofactor, [NiFe]-hydrogenases are distinguished from [FeFe]-hydrogenases. The former binds a hetero bimetallic nickel/iron site, embedded in the protein by four cysteine ligands. The later, by contrast, carries a homo bimetallic iron/iron site attached to the protein by only a single cysteine. Carbon monoxide and cyanide ligands (CO/CN) at the active site facilitated detailed investigations of hydrogenase catalysis by infrared spectroscopy, owing to strong signals and redox-dependent frequency shifts. However, the details of proton transfer have not been addressed experimentally.We found that specific redox state transitions in [NiFe]- and [FeFe]-hydrogenase can be triggered by visible light to record extremely sensitive ‘light-minus-dark’ infrared difference spectra monitoring key amino acid residues as shown in the ToC figure. As these transitions are coupled to protonation changes, our data allowed investigating dynamic hydrogen-bonding changes that go well beyond the resolution of protein crystallography. In [NiFe]-hydrogenase, photolysis of the bridging hydride ligand in the ‘Ni-C’ state was followed by rapid accumulation of the ‘Ni-SI_a’ state and/or ‘Ni-L’ state. Infrared difference spectra in various isotopic media clearly indicated the formation of a protonated cysteine residue as well as hydrogen-bonding changes involving the COOH group of a glutamic acid residue and a ‘dangling water’ molecule. These findings are in excellent agreement with crystallographic analyses of [NiFe]-hydrogenase in the Ni-R state and allowed devising a molecular precise model of catalytic proton transfer. In [FeFe]-hydrogenase, an external redox dye was used to accumulate the ‘Hred’ state over the oxidized resting state ‘Hox’. Infrared difference spectra of wild-type enzyme and numerous amino acid variants indicated hydrogen-bonding changes involving the COOH groups of two glutamic acid residues. Moreover, we noted the deprotonation of an arginine residue. Crystallographic analyses of [FeFe]-hydrogenase in the Hox state failed to explain the rapid proton transfer due to a ‘breach’ in the succession of residues. To this end, our findings facilitated a molecular precise model of ‘discontinued’ proton transfer.The comparison of catalytic proton transfer in bimetallic hydrogenases emphasizes the role of the outer coordination sphere. We suggest that the stable protonation of a nickel-ligating cysteine in [NiFe]-hydrogenase has a crucial influence on the preferred direction of proton flow and catalysis (i.e., H₂ oxidation). On the contrary, proton transfer in [FeFe]-hydrogenase involves an adjacent cysteine as a relay group that promotes both proton release and proton uptake. We presume that this causes the notable bidirectionality of [FeFe]-hydrogenase. These observations must guide the design of biomimetic compounds for the production or consumption of H₂.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

An exposition of entropy applications to highlight some potential entropic applications to artificial intelligence and knowledge transfer. Entropy is a basic idea in artificial intelligence that is applied to many different tasks, such as reinforcement learning, data compression, and decision-making. By quantifying uncertainty and information content, it helps artificial intelligence models provide predictions and decisions that are well-informed. Therefore, this paper shines on spotlighting the significance of entropy to attract the attention of artificial intelligence research community to entropy as a powerful tool to advance artificial intelligence.The significance of knowledge transfer (KT), particularly intergenerational knowledge transfer (IGT), in knowledge management is also covered in this paper. To quantify the complexity of knowledge distribution inside an organisation and assess the efficacy of knowledge transfer (KT) initiatives, the notion of knowledge entropy (KE) is presented. Additionally, the KT model—which is based on the conceptions of tacitness and information content—is introduced. It combines personalisation and codification methodologies. Future research directions are offered alongside a few difficult open problems.

Recently, the use of drones/unmanned aerial vehicles (UAVs) has notably increased due to their broad commercial spread and low cost. The wide diffusion of drones increases the hazards of their misuse in illegitimate actions such as drug smuggling and terrorism. Thus, the surveillance and automated detection of drones are crucial for safeguarding restricted regions or special zones from illegal drone interventions. One of the most challenging issues in drone detection in surveillance videos is the apparent similarity of drones and birds against complex backgrounds. In this work, an automated image-based drone-detection system utilizing an advanced deep-learning-based object-detection method known as you only look once (YOLOv5) is introduced for protecting restricted regions or special zones from unlawful drone interventions. Due to the lack of sufficient data, transfer learning was utilized to pretrain the object-detection method to increase the performance. The experiments showed outstanding results, and an average precision of 94.7% was accomplished.

We study the brain segmentation by dividing the brain into multiple tissues. Given possible brain segmentation by deep, machine learning can be efficiently exploited to expedite the segmentation process in the clinical practice. To accomplish segmentation process, a MRI and tissues transfer using generative adversarial networks is proposed. Given the better result, we propose the transfer model using GAN. For the case of the brain tissues, white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) are segmented. Empirical results show that this proposed model significantly improved segmentation results compared to the stat-of-the-art results. Furthermore, a dice coefficient (DC) metric is used to evaluate the model performance.

Since the turn of the 21^st Century Chian has enacted a range of policies to improve its water ecosystem. Some of these measures include (but are not limited to) the creation of Seven River Conservancy Commissions to engage in river basin management and the development (combination and recombination) of series of ministries and departments to address environmental pollution and degradation. The most recent attempt to address the nations polluted waterways and lakes occurred in December 2016, when the General Office of the Chinese Central Committee and the State Council issued The Options on Full Implementation of the River Chief System (RCS) Across the Country. The intent behind Options was not only to fully implemented he river chief system but to bring the nations drinking water supply quality to no worse than category III. Based on the Options Erik Solheim, UN Under Secretary General and Executive Director of the UN Environment Programme, commented ‘I'm convinced that what I have seen in Pujiang County and Anji County will be the future of China, even the future of the world’ (cited in Xianqiang 2021, 435; emphasis added). It is to this observation that the reminder of this article will be directed.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

During last decades, production and consumption of small ruminant milk has been increased. As a result of it, sheep and goat farming has been developing and scientists are focused on these animal researches both clinical and feeding strategies. By the evolutionary challenges and adaptations, colostrum has a crucial role of immune complementation for litter. As a result of these challenges and adaptations neonatal life is especially more important in ruminants because of it affects their whole life and future of livestock. Passive immune transfer is the main mechanism that explained by biological evolution between dam and lamb and also it is effected by factors up to dam and up to the litter. Today importance of passive immune transfer is well known for the future of livestock economy and animal welfare. In the literature, researchers are focused on correlation between colostrum quality (especially immunoglobulin amounts) and blood serum levels of newborns. Aims of present review are to discuss datas of recent studies, point out different effecting factors in colostrum quality and passive immune transfer, enlighten and give new ideas to researchers.

Transformers are increasing replacing older generation of deep neural networks due to their success in a wide range of application. The dominant approach of using transformers is to pre-train them on a large training dataset and then fine-tune them on a downstream task. However, as transformers becoming larger, the fine-tuning approach is become an infeasible approach for transfer learning. In this short survey, we list a few recent methods that makes using transformers based on transfer learning more efficient.

Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.

Three-dimensional transfer functions (3D TFs) are generally assumed to fully describe the transfer behavior of optical topography measuring instruments such as coherence scanning interferometers in the spatial frequency domain. Therefore, 3D TFs are supposed to be independent of the surface under investigation resulting in a clear separation of surface properties and transfer characteristics. In this paper we show that the 3D TF of an interference microscope differs depending on whether the object is specularly reflecting or consists of point scatterers. In addition to the 3D TF of a point scatterer, we will derive an analytical expression for the 3D TF corresponding to specular surfaces and demonstrate this as being most relevant in practical applications of coherence scanning interferometry (CSI). We additionally study the effects of temporal coherence and disclose, that in conventional CSI temporal coherence effects dominate. However, narrowband light sources are advantageous if high spatial frequency components of weak phase objects are to be resolved, whereas for low-frequency phase objects of higher amplitude the temporal coherence is less affecting. Finally, we present an approach that explains the different transfer characteristics of coherence peak and phase detection in CSI signal analysis.

When a microgrid is grid-tied to a distribution system, it can provide surplus power generation to the distribution system, if any abnormality or interruption occurs in the distribution system, the microgrid can operate in standalone mode to isolate the impact of the abnormality or interruption. However, if the microgrid can not collect enough information from the distribution system, it may cause the failure of generation transferring of distribution feeders, or even further influence the stability of the distribution system. In this paper, a strategy for the resilient control of a microgrid is proposed. It can solve the above-mentioned problem, reduce the duration of the outage of loads. This strategy is experimented in the microgrid in the Institute of Nuclear Energy Research (INER), the reliability is also analyzed to evaluate the unavailability of the microgrid in INER, and it is verified that the proposed strategy can reduce the duration of the outage of loads, and hence the reliability of a microgrid can be upgraded.

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

The mind-body problem is the central issue in both of philosophy and life science for several centuries. To date, there is still no conclusive theory to interpret the relation between the mind and the body, even just the mind alone. Here, we promote a novel model, a derived mathematic equation called the entropic system equation, to describe the innate characters of the mind and the mechanism of the mind-body coupling phenomenon. As the semi-open thermodynamic systems far from equilibrium, the living organisms could be logically considered as an entropic system. In the living organisms or the entropic systems, there also are three essential existing elements including mass, energy and information, in which the mind and the body are hypothetically coupled by free energy and entropic force.

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Accurate transfer learning of clinical outcomes, e.g., of the effects and side effects of drugs or other interventions, from one cellular context to another (in-vitro versus ex-vivo versus in-vivo, or across tissues), between cell-types, developmental stages, omics modalities or species, is considered tremendously useful. Ultimately, it may avoid most drug development failing in translation, despite large investments in the preclinical stages, which includes animal experiments requiring careful justification. Thus, when transferring a prediction task from a source (model) domain to a target domain, what counts is the high quality of the predictions in the target domain, requiring molecular states or processes common to both source and target that can be learned by the predictor, reflected by latent variables. These latent variables may form a compendium of knowledge that is learned in the source, to enable predictions in the target; usually, there are few, if any, labeled target training samples to learn from. Transductive learning then refers to the learning of the predictor in the source domain, transferring its outcome label calculations to the target domain, considering the same task. Inductive learning considers cases where the target predictor is performing a different yet related task as compared to the source predictor, making some labeled target data necessary. Often, there is also a need to first map the variables in the input/feature spaces (e.g. of gene names to orthologs) and/or the variables in the output/outcome spaces (e.g. by matching of labels). Transfer across omics modalities also requires that the molecular information flow connecting these modalities is sufficiently conserved. Only one of the methods for transfer learning we reviewed offers an assessment of input data, suggesting that transfer learning is unreliable in certain cases. Moreover, source domains feature their very own particularities, and transfer learning should consider these, e.g., as differences in pharmacokinetics, drug clearance or the microenvironment. In light of these general considerations, we here discuss and juxtapose various recent transfer learning approaches, specifically designed (or at least adaptable) to predict clinical (human in-vivo) outcomes based on molecular data, towards finding the right tool for a given task, and paving the way for a comprehensive and systematic comparison of the suitability and accuracy of transfer learning of clinical outcomes.

In this paper, we revisit a modified version of the classical Whitehead's theory of gravity in which all possible bilinear forms are considered to define the corresponding metric. Although, this is a linear theory that fails to give accurate results for the most sophisticated predictions of general relativity, such as gravity waves, it can still provide a convenient framework to analyze some new phenomena in the Solar System. In particular, recent development in the accurate tracking of spacecraft and the ephemerides of planetary positions have revealed certain anomalies in relation with our standard paradigm for celestial mechanics. Among them the so-called flyby anomaly and the anomalous increase of the astronomical unit play a prominent role. In the first case the total energy of the spacecraft changes during the flyby and a secular variation of the semi-major axis of the planetary orbits is found in the second anomaly. For this to happen it seems that a net energy and angular momentum transfer is taken place among the orbiting and the central body. We evaluate the total transfer per revolution for a planet orbiting the Sun in order to predict the astronomical unit anomaly in the context of Whitehead's theory. This could lead to a more deeply founded hypothesis for an extended gravity model.

Using machine learning or deep learning to solve the problem of garbage recognition and classification is an important application in computer vision, but due to the incomplete establishment of garbage datasets and the poor performance of complex network models on smart terminal devices, the existing garbage classification models The effect is not good.This paper presents a waste classification and identification method base on transfer learning and lightweight neural network. By migrating the lightweight neural network MobileNetV2 and rebuild it, The reconstructed network is used for feature extraction, and the extracted features are introduced into the SVM to realize the identification of 6 types of garbage. The model was trained and verified by using 2527 pieces of garbage labeled data in the TrashNet dataset, which ultimately resulted in a classification accuracy of 98.4% of the method, which proves that the method can effectively improve the classification accuracy and time and overcome the problem of weak data and less labeling. The over-fitting phenomenon encountered by small data sets in deep learning makes the model robust.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.