Recent advancements in cognitive neuroscience, particularly in Electroencephalogram (EEG) signal processing, image generation, and brain-computer interfaces (BCI), have opened up new avenues for research. This study introduces a novel framework, Bridging Artificial Intelligence and Neurological Signals (BRAINS), which leverages the power of AI to extract meaningful information from EEG signals and generate images. The BRAINS framework addresses the limitations of traditional EEG analysis techniques, which struggle with nonstationary signals, spectral estimation, and noise sensitivity. Instead, BRAINS employs Long Short-Term Memory (LSTM) networks and contrastive learning, which effectively handle time-series EEG data and recognize intrinsic connections and patterns. The study utilizes the MNIST dataset of handwritten digits as stimuli in EEG experiments, allowing for diverse yet controlled stimuli. The data collected is then processed through an LSTM-based network employing contrastive learning and extracting complex features from EEG data. These features are fed into an image generator model, producing images as close to the original stimuli as possible. This study demonstrates the potential of integrating AI and EEG technology, offering promising implications for the future of brain-computer interfaces.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

In the past twenty years, the IT industry has moved away from using physical servers for workload management to workloads consolidated via virtualization and, in the next iteration, further consolidated into containers. In the next step, container workloads based on Docker and Podman as underlying container technologies were orchestrated/automated via Kubernetes or OpenShift. On the other hand, high-performance computing (HPC) environments have been lagging in that process, as there’s still much work to figure out how to apply containerization platforms for HPC in real-life scenarios. Kubernetes and OpenShift have many advantages – generally speaking, container technologies use quite a bit less overhead from the computing perspective while providing many benefits in flexibility, modularity, and maintenance. Therefore, they are ideal for tasks requiring a lot of computing power. There are also some tradeoffs regarding the complexity of these two platforms - they’re just not that user-friendly when used by people without years of experience managing them. In this paper, we propose a different architecture based on seamless hardware integration and user-friendly, dynamic workload placement based on real-time performance analysis and prediction coupled with Machine Learning-based scheduling.

The accurate counting of passengers in public transport systems is crucial for optimizing operations, improving service quality, and planning infrastructure. It can also contribute to reducing the number of public transport lines where a high frequency of vehicles is not needed in certain periods during the year, but also by increasing the number of lines where the need is increased. This paper provides a comprehensive review of current methodologies and technologies used for passenger counting, with a focus on image processing and machine learning techniques and concepts. The paper explores various algorithms, including traditional computer vision methods and advanced deep learning approaches, highlighting their strengths and limitations. Additionally, the paper examines the integration of these technologies with other sensing modalities such as infrared sensors, Wi-Fi, and RFID. By analyzing recent advancements and case studies, this review aims to offer insights into the effectiveness, scalability, and practicality of different passenger counting solutions and offers a solution proposal. The paper also analyzed the current GDPR regulation that applies to the European Union and how it affects the use of systems like this. Future research directions and potential areas for technological innovation are also discussed to guide further developments in this field.

In the context of cognitive radio, smart city and Internet-of-Things, the need of advanced radio spectrum monitoring becomes crucial. However, surveillance of a wide frequency band without using extremely expensive high sampling rates devices is a challenging task. The recent development of compressed sampling approaches offers a promising solution to these problems. In this context, the Modulated Wideband Converter (MWC), a blind sub-Nyquist sampling system, is probably the most realistic approach and was successfully validated in real-world conditions. The MWC can be realized with existing analog components and there exist calibration methods which are able to integrate the imperfections of the mixers, filters and ADCs, hence allowing its use in real-world. The MWC underlying model is based on signal processing concepts such as filtering, modulation, Fourier series decomposition, oversampling and undersampling, spectrum aliasing, and so on, as well as in-flow data processing. In this paper we develop an MWC model which is entirely based on linear algebra, matrix theory and block processing. We show that this approach has many interests: straightforward translation of mathematical equations into simple and efficient software programming, suppression of some constraints of the initial model, and providing a basis for the development of an extremely fast system calibration method. With a typical MWC acquisition device we obtained a speed up of a factor greater than 20 of the calibration computation time, compared with a previous implementation.

Collaboration across the agriculture supply chain is essential to address the high-yield demand and sustainable practices amid global overpopulation. Limited resources, such as soil, are compromised by excessive chemical agents and nutrient use. The Internet of Things (IoT) and smart farming offer solutions by optimizing agent application, data analysis, and farm monitoring. Evidence from numerous studies indicates that collaboration in the supply chain, including farmers, can improve efficiency and productivity, reduce costs, and enhance crop quality. This research focuses on implementing IoT technology to enhance decision-making for crop yield optimization and sustainable practices on a real farm. By collaborating with a farm in the southern region of Zagreb, Croatia, farmers were trained on sensor usage and yield monitoring. Small farms in that region face challenges in improving yields due to limited capacity and lack of entrepreneurial skills. The DMAIC methodology was applied to define the problem and measure relevant parameters. The analysis demonstrated consistent patterns between electrical conductivity (EC) measurements and potassium levels in soil. It suggests the potential for estimating potassium concentrations based on EC readings, or vice versa. Leveraging EC as a proxy for potassium levels could offer a cost-effective means of assessing soil fertility and nutrient dynamics. Additionally, the PCA biplot analysis highlighted that pH value behaved independently. Understanding these dynamics enhances knowledge of soil variability and informs sustainable soil management practices.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of mass, particle states are disentangled into left and right handed chiral states, governed by the maximal solvable subgroups sol2± of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, it is argued how the spin-flip contribution is closely related to the occurrence of nonphysical spin operators.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

This paper represents the first investigation into the consensus problem of linear time-varying multi-agent systems utilizing an event-triggered communication scheme. First, a general event-triggered consensus control scheme is proposed for a general category of linear time-varying multi-agent systems. Under some suitable assumptions, it is demonstrated that all agents’ states will converge exponentially, with Zeno behaviour being ruled out. Second, the consensus problem in a network of linear time-varying multi-agent systems with a spanning tree is investigated using the proposed control strategy. It demonstrates that the consensus issue for the specified system can be reformulated as a stabilization problem for an error system through a time-varying linear transformation. Then, the event-triggered consensus problem is just a special instance of the general event-triggered consensus problem mentioned above. Finally, to illustrate the efficacy of the event-triggered method proposed in this study, simulation results are shown.

MicroRNAs (miRNA) exert regulatory actions via base-pairing with their binding sites on target mRNAs. Cooperative-binding, i.e., synergism, among binding sites on a mRNA is biochemically well-characterized. We studied whether this synergism is reflected in global relationship between miRNA-mediated regulatory activity and miRNA-binding-site count on the target mRNAs, i.e., leading to a non-linear relationship between the two. Recently, using our own and public datasets, we have enquired into miRNA regulatory actions: first, we analyzed the power-law distribution pattern of miRNA binding sites; second, strikingly, mRNAs for core miRNA regulatory apparatus proteins have extra-ordinarily high binding site counts, forming self-feedback-control loops; third, we revealed that tumor suppressor mRNAs generally have more sites than oncogene mRNAs; and fourth, we characterized enrichment of miRNA target mRNAs in translationally less-active polysomes relative to more-active polysomes. In these four studies, obvious correlation was observed qualitatively between the extent to which a mRNA is miRNA-regulated and its binding sites count. This paper summarizes the used datasets. We also re-analyzed the correlation by comparative linear and non-linear regression analyses. The results support a non-linear, instead of linear, relationship between the two parameters, conceivably a transcriptome-level reflection of cooperative-binding/synergism among miRNA binding sites on a target mRNA.

We present an exploration of algebra B, a recently published unital and non-associative algebra. Unique complex entities emerged from this algebra, distinct from both quaternion and complex number systems, which we termed treons. We defined the treonic number system and established an isomorphism between this system and the real vector space. Our findings revealed that the treonic representation maintained structural integrity under the defined operations. Based on this foundation, we proceed to determine Euler identity for algebra B within the treonic system. By presenting the fundamental definitions and properties of algebra B, we derived a generalized version of Euler identity applicable within this algebra. This formula revealed the emergence of hyperbolic trigonometric entities, extending the applicability of Euler identity beyond traditional complex numbers. Our results provide a theoretical foundation for a deeper understanding of the properties and behaviors of complex entities within this expanded algebraic framework, thus enabling new theoretical developments and practical applications in the realms of advanced mathematics and theoretical physics.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

This article is the first part of a scientific project under the general title "Geometrized Vacuum Physics". This study is based on two main postulates: 1) independence of the propagation velocity of electromagnetic waves in vacuum from their frequency; 2) the constancy of the averaged zero vacuum balance, associated with the assertion that only mutually opposite formations are born from vacuum, so that on average they completely compensate for each other's manifestations. In this part of the "Geometrized Vacuum Physics" the foundations of the Algebra of Stignatures are laid, which is the mathematical and logical foundation of the entire project. In the next articles of this project it will be shown that the Algebra of Stignatures can be used for the development of "zero" (vacuum) technologies, algebraic genetics, vacuum cosmology, the vacuum standard model of "elementary particles", vacuum gravity and levitation, vacuum energy, ethics and aesthetics and many other branches of knowledge. At the end of this article, one of the many possible applications of the Algebra of Stignatures is given, in particular, the basics of the stignature-spectral analysis are outlined, with the help of which the possibilities of communication channels can be significantly expanded.

This article is the second part of a scientific project under the general name "Geometrized vacuum physics". On the basis of the Algebra of Stignatures presented in the previous article [1], this article develops the main provisions of the Algebra of Signatures. Both of the above algebras are aimed at studying the properties of an ideal vacuum, but at the same time they are universal and can be applied in various branches of knowledge. It is shown that the signature of a quadratic form is related to the topology of the metric space for which the given quadratic form is a metric. Conditions are given under which an additive imposition of metric spaces with different topologies (or signatures) leads to a total Ricci flat space similar to a Calabi-Yau manifold. A spin-tensor representation of metrics with different signatures is considered and a Dirac bundle of quadratic forms is presented. This article does not contain physical applications of the Algebra of Signatures, but the potential power of this mathematical apparatus will be demonstrated in subsequent articles of this project.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

The aim of the article is to develop geometrized physics of a vacuum on the basis of two basic postulates: 1) the constancy of the speed of light (more precisely, the speed of propagation of electromagnetic waves) in the vacuum; 2) the ‘vacuum balance condition’ associated with the statement that only mutually opposite formations are born from the vacuum, so that, on average, they completely compensate of the manifestations of each other. The Algebra of signatures is proposed as a mathematical basis for geometrized physics of a vacuum.

Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension $1+2$ and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreove, we propose an extension of the scator product on the whole scator space, including scators with vanishing scalar component.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.

Fresnel incoherent correlation holography (FINCH) is a well-established incoherent imaging technique. In FINCH, three self-interference holograms are recorded with calculated phase differences between the two interfering, differently modulated object waves and projected into a complex hologram. The object is reconstructed without the twin image and bias terms by a numerical Fresnel back propagation of the complex hologram. A modified approach to implement FINCH by a single camera shot by pre-calibrating the system involving recording of the point spread function library and reconstruction by a non-linear cross-correlation has been introduced recently. The expression of the imaging characteristics from the modulation functions in original FINCH and the modified approach by pre-calibration in spatial and polarization multiplexing schemes are reviewed. The study reveals that a reconstructing function completely independent of the function of the phase mask is required for the faithful expression of the characteristics of the modulating function in the image reconstruction. In polarization multiplexing method by cross-correlation, a partial expression was observed, while in spatial multiplexing method by cross-correlation, the imaging characteristics converged towards a uniform behavior.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

For a nonzero normed linear space X‎, ‎we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals‎. ‎Also separate continuity of the elements of each class are investigated‎. ‎The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces‎.

Observed ENSO statistics exhibits a non-gaussian behavior, which is indicative of the presence of nonlinear processes. In this paper we use the Recharge Oscillator model (ROM), a largely used Low-Order Model (LOM) of ENSO, as well as methodologies borrowed from the field of statistical mechanics to identify which aspects of the system may give rise to nonlinearities that are consistent with the observed ENSO statistics. In particular, we are interested in understanding whether the nonlinearities reside in the system dynamics or in the fast atmospheric forcing. Our results indicate that one important dynamical nonlinearity often introduced in the ROM cannot justify a non-gaussian system behavior, while the nonlinearity in the atmospheric forcing can instead produce a statistics similar to the observed. The implications of the non-Gaussian character of ENSO statistics for the frequency of extreme El Nino events is then examined.

This paper presents a two-stage ADC based on pseudo-differential operational transconductance amplifier (OTA), which is designed for the readout circuit of X-ray linear array sensor. This hybrid ADC employs an incremental sigma-delta ADC and a cyclic ADC, achieving a good trade-off between accuracy and conversion speed. The two stages share the same hardware to reduce power consumption and die area. A common-mood feedback module is used to suppress the influence of charge injection, and the effectiveness is demonstrated by detailed theoretical analysis. A test chip of 14-bit ADC is fabricated in 0.35μm CMOS technology. The measured root mean square (RMS) value of DNL is 0.254 LSB, and the maximum value of INL is -0.776/+1.56 LSB. The measured effective number of bits (ENOB) is 13.43 bits.

There are many uncertainties and risks in residential electricity consumption during the economic development. Knowledge of the relationship between residential electricity consumption and its key determinant—income—are important to the sustainable development of electric power industry. Using panel data from 30 provinces for the 1995-2012 period, this study investigates how residential electricity consumption changes as incomes increase in China. Previous studies typically used linear or quadratic double-logarithmic models imposing ex ante restrictions on the indistinct relationship between residential electricity consumption and income. Contrary to those models, we employed a reduced piecewise linear model that is self-adaptive and highly flexible and circumvents the problem of “prior restrictions.” Robust tests of different segment specifications and regression methods are performed to ensure the conservatism of the research. The results provide strong evidence that the income elasticity was approximately one, and it remained stable throughout the estimation period. The income threshold at which residential electricity consumption automatically remains stable or slows has not been reached. To ensure the sustainable development of the electric power industry, introducing higher energy efficiency standards for electrical appliances and improving income levels are vital. And government should emphasize electricity conservation in industrial sector rather than in residential sector.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.

Recently, many authors have been interested to introduce fuzzy implications over t-norms and t-conorms. In this paper, we introduce (S,N) and residuum fuzzy implication for Dubois t-norm and Hamacher's t-norm. Also, new concepts so-called (T,N) and residual fuzzy co-implication in dual Heyting Algebra are investigated. Some examples as well as application are discussed as well.

The increase in population and the challenges caused by it are always among the concerns of decision-makers and policymakers in large countries. One of the most serious concerns is in the field of energy consumption. Optimizing energy use is one of the most effective ways to manage limited resources and energy. Energy consumption in residential houses constitutes a significant percentage of the total energy consumption worldwide; therefore, current research focusing on mathematical models aims to provide a predictive multi-objective linear mathematical model for residential house consumption. For this purpose, the consumption of water, electricity, and gas for 80 residential houses, including 10 household appliances and equipment on a weekly basis, has been considered. The results showed that the mixed-integer multi-objective predictor model is able to optimize household consumption plans compared to the actual state of household energy consumption. Since the goals of household satisfaction and energy consumption costs in the model conflict with each other, the influence coefficient was calculated to demonstrate the simultaneous achievement of these goals. The optimal value achievable with the default model for the model's purposes is 69%.

The aim of this paper is to show how the mathematical basis is used for a precise treatment of double-entry bookkeeping, which was firstly developed in the nineteenth century by Sir William Rowan Hamilton. This is done by using basic notions of matrix algebra with the roots to the idea of using ordered pairs. We also reveal how the complex numbers and the rationals (fractions) developed in a mainstream of accounting science and became a leading platform for the ongoing processes within the Industry 4.0. The paper concludes with the examples on how accounting operations can be represented by matrix equations with a result of the essential report generating. The author represents a mathematical model of accounting which is independent of the specific existential forms but is capable to undertake the form of any of them and thus has the prospect of being understood and accepted by specialists globally.

Linear-width is a well-regarded width parameter in graph theory. The constructs of linear loose tangle and linear tangle present obstacles to attaining linear-width. In this succinct paper, our primary focus will be the exploration of maximal linear loose tangles.

Article explores participant specific study of muscle inherehit dynamics hidden inside the diognostic electromyography (D-EMG) signals during load pull exercises, aiming to uncover underlying patterns and nonlinear behaviors. Employing a multi-step analytical framework, the study first evaluates signal stationarity through Quantile-Quantile (Q-Q) plot and surrogate data analyses, revealing insights into signal stability. Subsequent use of phase space reconstruction techniques exposes intrinsic dynamics within the EMG signals, visualized through Poincar´e maps, elucidating attractor geometry and system dynamics. Histogram analysis further dissects the Poincar´e maps, offering insights into signal behavior relative to physiological processes. Additionally, the study quantifies the largest Lyapunov exponent from the Poincar´e maps, providing a measure of dynamical complexity within the muscle EMG signals during load pull exercises. By integrating these methods, this research sheds light on the nuanced interplay between EMG signals and muscle activity during dynamic exercises, offering valuable insights for rehabilitation strategies.

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Linear Hashing is an important algorithm for many key-value stores. Spiral Storage was invented to overcome the poor fringe behavior of Linear Hashing, but after an influential study by Larson, seems to have been discarded. Since almost 50 years have passed, we repeat Larson’s comparison with in-memory implementation of both to see whether his verdict still stands. Our study shows that Spiral Storage has slightly better look-up performance, but slightly poorer insert performance.

Hybrid power plants have recently emerged as reliable and flexible electricity generation stations by combining multiple renewable energy sources, energy storage systems (ESS), and fossil-based output. However, the effective operation of the hybrid power plants to ensure continuous energy dispatch under challenging conditions is a complex task. This paper proposes a dispatch engine (DE) based on mixed-integer linear programming (MILP) for the planning and management of hybrid power plants. To maintain the committed electricity output, the dispatch engine will provide schedules for operation over extended time periods as well as monitor and reschedule the operation in real-time. Through precise prediction of the PV and wind power output, the proposed approach guarantees optimum scheduling. The precise prediction of the PV and wind power are achieved by employing a predictor of Feed-Forward Neural Network (FFNN) type. With such a dispatch engine, the operational cost of the hybrid power plants, and the use of diesel generators (DGs) are both minimized. A case study is carried out to assess the proposed dispatch engine feasibility. A real-time measurement data pertaining to load, wind, and PV power outputs is obtained from different locations in the Sultanate of Oman. The real-time data is utilized to predict the future output power from PV and the Wind farm over 24 hours. The predicted powers are then used in combination with a PV-Wind-DG-ESS-Grid hybrid plant to evaluate the performance of the proposed dispatch engine. The proposed approach is implemented and simulated using MATLAB. The results of the simulation reveal the proposed Feed-Forward Neural Network’s (FFNN) powerful forecasting abilities. In addition, the results demonstrate that adopting the proposed DE can minimize the use of DG units and reduce plant running expenses.

The exceptional Jordan algebra is the algebra of $3 \times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan’s algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new U(1) gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

This research investigates precision enhancement in regional quasi-geoid refinement through ADS80 tri-linear array scanning stereoscopic imagery for aerial triangulation, coupled with GNSS gravity-potential modeling. Acquiring stereoscopic imagery and analyzing triangulation accuracy with the ADS80 camera, we performed this study over the Qinghai-Tibet Plateau's elevated, desolate terrain, collecting 593 GNSS points following high-precision stereoscopic imagery model. Utilizing 12 gravity satellite models, we computed geoid heights and China 1985 Yellow Sea elevations for 28 benchmarks and GNSS points, thereby refining the Qinghai Province Quasi-Geoid Model (QPQM) using geometric techniques. The findings reveal that POS-assisted ADS80 stereoscopic imagery yields high-precision triangulation with maximal horizontal and elevation accuracies of 0.083/0.116 cm and 0.053/0.09 cm, respectively, across five control point arrangements. The RMSE of normal heights for 1985, processed via these GNSS points, achieved decimeter precision. By applying error corrections from benchmarks to the 1985 elevation data from gravity satellites and performing weighted averaging, the precision of EGM2008, SGG-UGM-2, and SGG-UGM-1 models improved to 8.61 cm, 9.09 cm, and 9.38 cm, respectively, surpassing the QPQM by 9.22 cm to 9.99 cm. This research demonstrates that the proposed methods can significantly enhance the precision of regional quasi-geoid surfaces. Additionally, these methods offer a novel approach for rapidly establishing regional quasi-geoid models in the uninhabited areas of the Qinghai-Tibet Plateau.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

This work investigates the stability conditions for linear systems with time-varying delays via augmented Lyapunov-Krasovskii functional(LKF). Two types of augmented LKFs with cross terms in integral are suggested to improve the stability conditions for interval time-varying linear systems. Through this work, the compositions of the LKFs are considered to enhance the feasible region of stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality(WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality(LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. And then simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in two examples. Two numerical examples show that the proposed Theorem 1 and 2 obtained less conservative results than existing outcomes. Also, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1’s in some specific systems.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

The Process Algebra model has been shown to provide an alternative mathematical framework for non-relativistic quantum mechanics (NRQM). It reproduces the wave functions of non-relativistic quantum mechanics to a high degree of accuracy. It posits a fundamental level of finite, discrete events upon which the usual entities of NRQM supervene. It has been suggested that the Process Algebra model provides a true completion of NRQM, free of divergences and paradoxes, with causally local information propagation, contextuality and realism. Arguments in support of these claims have been mathematical. Missing has been an ontology of this fundamental level from which the formalism naturally emerges. In this paper it is argued that information and information flow provides this ontology. Higher level constructs such as energy, momentum, mass, spacetime, are all emergent from this fundamental level.

The article presents a model for optimizing biomass supply chains using the linear programming framework integrated with a Geographic Information System. Based on the distance from a given type of biomass resource, its calorific value, price, and transportation costs, the model identifies the optimal source of biomass, allowing it to cover the demand for the required total energy value with the lowest possible costs. The case study includes the Połaniec power plant in southeastern Poland and potential sources of forest biomass and agricultural straw within 100 km of the plant. Unit costs of biomass varied depending on biomass availability and energy demands. For energy demand on the level of 1 PJ yearly, the lowest unit costs of biomass (4.08 €/MJ) were when all kinds of biomass were available, and the highest (5.47 €/MJ) was when only stacked wood was available. As energy demand increased, unit costs increased, and the ability to meet this demand with just one type of biomass decreased. The energy biomass sector can utilize the model to benefit both biomass producers and their final buyers.

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.

We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ two linear probe sequences to find empty cells for the keys. Matching lower bounds on the maximum cluster size produced by any algorithm that uses two linear probe sequences are obtained as well.

A numerical application of linear-molecule symmetry properties, described by the D_∞h point group, is formulated in terms of lower-order symmetry groups D_nh with finite n. Character tables and irreducible representation transformation matrices are presented for D_nh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator ${\widehat{L}}_z$ . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D_nh. ¹²C₂H₂ is used as an example of a linear molecule of D_∞h point group symmetry to illustrate the symmetrisation procedure.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emssions. It turns out that the model improves by mostly neglecting them after 1959. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation, that the total carbon sink has a short term component which be explained by temperature changes commonly known as El Nin˜o. The apparent paradox is analysed and explained, why contrary to the short term changes no temperature caused trend can be detected in the model, despite the fact that several contributing processes exhibit temperature dependency. The result of this analysis leads to the model extension, where the total effect of sinks and natural emissions are a linear function of concentration and temperature. This model not only explains current measurements but also paleo climate from ice-core time series.

Oscillons, fundamental to various physical domains, are examined in-depth in this paper. From Josephson junctions in superconducting circuits to classical and quantum field theories, oscillators reveal profound insights into diverse phenomena. The study primarily focuses on oscillons, distinctive field configurations with enduring localization, establishing intriguing connections with well-known models like the Sine-Gordon breather. Surprising parallels in the weak coupling limit illuminate the rich dynamics of oscillators. A semi-classical quantization method, discretizing the field into spatially homogeneous regions, exposes stability angles, providing insights into the quantum nature of oscillons. The application of this quantization framework to specific cases, including the Sine-Gordon breather, showcases its versatility. The results offer a comprehensive perspective on the quantization of oscillons, unraveling the intricate interplay between classical and quantum dynamics. In conclusion, this paper provides a profound exploration of quantum oscillators, unveiling novel connections and presenting a rigorous quantization framework. The gained insights contribute significantly to the broader understanding of oscillatory systems and their pivotal role in diverse physical phenomena.

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each L^p norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.

Wheeled mobile robot dynamics and suitable controller design are challenging but rewarding fields of study. By understanding the dynamics of wheeled mobile robots, it could be possible to design suitable hybrid control schemes for wheeled mobile robots. Since hybrid control schemes involve combining individual control methods to create a more effective overall control strategy. This can be done in a variety of ways, such as using fuzzy linear quadratic Gaussian control. We were therefore inspired to create dynamic models and their controller designs for the wheeled mobile robot by examining the dynamics of the wheeled mobile robot. The novelty of the current paper is to hybridize the different control schemes for wheeled mobile robots in order to get better performance. Entire systems models were simulated in a MATLAB/SIMULINK environment. The results obtained for the settling time response by FLQG were 87.1% over LQG; this study compared the effectiveness of current and previous FLQG controllers in external disturbances and found peak amplitude improvements of 71.25%. Therefore, the proposed controller is suitable for use with the wheeled mobile robot.

Kinetic parameters of SO2 adsorption on unburned carbons from lignite fly ash and activated carbons based on hard coal dust were determined. The model studies were performed using the linear and non-linear regression method for the following models: pseudo first and second-order, intraparticle diffusion, and chemisorption on a heterogeneous surface. The quality of the fitting of a given model to empirical data was assessed based on: R2, R, Δq, SSE, ARE, χ2, HYBRID, MPSD, EABS, and SNE. It was clearly shown that it is the linear regression that more accurately reflects the behaviour of the adsorption system, which is consistent with the first-order kinetic reaction – for activated carbons (SO2+Ar) or chemisorption on a heterogeneous surface – for unburned carbons (SO2+Ar and SO2+Ar+H2O(g)+O2) and activated carbons (SO2+Ar+H2O(g)+O2). Importantly, usually, each of the approaches (linear/non-linear) indicated a different mechanism of the studied phenomenon. A certain universality of the χ2 and HYBRID functions has been proved, the minimization of which repeatedly led to the lowest SNE values for the indicated models. Fitting data by any of the non-linear equations based on the R or R2 functions only, cannot be treated as evidence/prerequisite of the existence of a given adsorption mechanism.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups $F_4$ and $E_6$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ and $E_6$ symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.

We write the mutual information between an input speech utterance and its reconstruction by a Code-Excited Linear Prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare to the performance of the AMR codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

In this paper, we establish the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB=C, and present the general solution expression when solvability is achieved. As an application, we delve into the necessary and sufficient condition for the existence of Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX=C and XB=C. Finally, we provide a numerical example to demonstrate the findings of this paper.

Byers Peninsula (62°34’-62°40’S-60°54’61°13’W), 60 km2 in size, is considered one of the largest ice-free areas in Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes, limnology and microbiology, live cycles, but not albedo. Surface albedo is one of the key physical parameters in the surface energy budget of polar regions. Most of Antarctica is covered by ice sheets; only about 0.44% of the area is permanently ice-free. However, in maritime Antarctica, the ice-free areas, corresponding to small islands, peninsulas, and coastal beaches, account for about 3% of the territory. To incorporate the contribution of these areas into global albedo models, it is necessary to relate the soil properties of the ice-free areas to the surface albedo response. Also, mapping soil properties and albedo have and special interest in these ice-free areas. Image classification using machine learning methods trained with georeferenced soil data could be useful for mapping soil properties and albedo in multispectral optical satellite images. A shallow neural network implemented using the Keras Python module was used to define and train models of soil properties using 15 explanatory variables corresponding to bands and spectral indices of a Sentinel image and a population of 49 soil samples taken from the top 5 centimeters of the soil profile. The soil samples were analyzed in the laboratory and a spectral library in the Vis-Nir range (350-2500 nm) was created. The albedo of the samples was integrated from the ADS spectra. At the same time, a linear regression model of albedo using the soil properties as explanatory variables was performed. The R2 fit of this new model was about 0.82 and the error of estimation was 4.1. The model was extended to the entire Byers Peninsula using the ML soil property models as explanatory variables. The RMSE of the extended models increased up to 8.2. We think that the main cause of this increase (2.6 points) is related to the error propagation, phenomenon due to the use of models as explanatory variables. However, another important part of the error increase could be due, among other reasons, to the use of an image that, although corrected, is not completely free of clouds.

Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on the many-excitation transfer protocol in Ref. , we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protocol allows for efficient two-excitation routing on a fermionic network, although for a spin-12 network only a limited region of the network is suitable for high-quality routing.

In this paper, we present a relapse based demonstrating way to deal with investigate various arrangement MTC information. A commonplace use of this displaying approach incorporates three stages: first, define a model that approximates the connection between quality articulation and trial factors, with boundaries consolidated to address the exploration premium; second, utilize least-squares and assessing condition methods to gauge boundaries and their relating standard blunders; third, register test insights, P-qualities and NFD as proportions of factual criticalness. The benefits of this methodology are as per the following. To begin with, it tends to the exploration interest in a particular, precise way, and maximally uses all the information and other important data. Second, it represents both orderly and irregular varieties related with the information, and the consequences of such examination give not just quality explicit data applicable to the exploration objective, yet additionally its dependability, in this way helping agents to settle on better choices for subsequent investigations. Third, this methodology is truly adaptable, and can undoubtedly be stretched out to different sorts of MTC considers or other microarray explores by detailing various models dependent on the test plan of the investigations.

Mucosal irritation caused by cusps of upper and lower teeth represents a source of persistent, low grade mechanical trauma. This type of trauma can initiate and/or perpetuate oral lichen planus in a few susceptible patients. Here, we report a rare case of bilateral white linear striations in the buccal mucosa of a young patient, associated with sharp cusps. Oral lesions demonstrated a unique cuspal signature highlighting the causal role of subtle mucosal trauma in the genesis of reticular-oral lichen planus. Lesions appeared to be exacerbated by significant psychological distress experienced by the patient. Although the Koebner phenomenon is well reported in the cutaneous lichen planus literature, such presentations are relatively rare in the oral cavity. This report emphasizes the potential role of low-grade cuspal trauma/irritation in conjunction with psychological distress in the genesis of oral lichen planus.

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

Gradual disability worsening in Multiple Sclerosis (MS) is indicative of confirmed progression that mostly involves progression independent of relapse activity (PIRA) and is associated with neurodegeneration. Insights from pathology reveal grey matter involvement (neocortex, hippocampus, spinal cord, and deep grey matter structures) and microglia activation in early stages of MS. Cortical lesions result in thinning and atrophy and are considered accurate predictors of disability progression and cognitive decline.Neuroimaging biomarkers, such as high-resolution 7T MR images and TSPO-PET, have been examined for the detection of cortical pathology linked to cognitive deficits and thus progression, but are limited in clinical practice due to availability, time constraints, and cost.Electroencephalography (EEG) emerges as a non-invasive, cost-effective tool that reflects cortical activity in MS. Its potential in monitoring cognitive impairment is explored by focusing on nonlinear EEG analysis. The MuST PREDICT^TM project aims to extract linear and nonlinear EEG features, investigating their role in predicting disease progression and optimizing treatment. The study employs retrospective, cross-sectional, and prospective designs, utilizing EEGs from various MS forms, cognitive assessments, serum/cerebrospinal fluid biomarkers and neuroimaging. The methodology involves time-based and spectral feature extraction, employing artificial intelligence classifiers and brain criticality-based approaches.The conceptual framework of an innovative modality is herein presented, that would EEG for early MS progression detection. Standardization of the methodology could lead to the creation of a digital tool for better prognostication and treatment strategy optimization.

Time series forecasting has been a challenging area in the field of Artificial Intel-ligence. Various approaches such as linear Neural Networks, Recurrent Linear Neural Networks, Convolutional Neural Networks and recently Transformers have been attempted for the time series forecasting domain. Although, Trans-former-based architectures have been outstanding in the Natural Language Pro-cessing domain, especially in autoregressive language modeling, the initial at-tempts to use transformers in the time series arena have met with mixed success. One of the recent papers demonstrated that modeling the multi-variate time se-ries problem as independent channels on a transformer architecture produced lower mean square and mean absolute errors on benchmarks, however, another recent paper claimed that a simple linear neural network out-performs previous approaches including transformer-based designs. We investigate this paradox in detail comparing the linear Neural Network and Transformer based designs, provide insights to why a certain approach may be better for a particular type of problem. We also improve upon the recently proposed simple linear Neural Network based architecture by using dual pipelines with batch normalization and reversible instance normalization. Our enhanced architecture outperforms all existing architectures for time series forecasting on majority of the popular benchmarks.

With the use of linear regression modeling, this study sought to forecast and analyze rainfall patterns in Ethiopia. The dataset included historical rainfall data as well as pertinent independent variables. The R-squared score and mean squared error (MSE) were used to assess the effectiveness of the linear regression model. The results showed that the model's ability to forecast and analyze rainfall patterns was not very good. Only around 5.3% of the variance in rainfall could be explained by the chosen independent variables, according to the R-squared score of 0.053. This low number indicated that there was little correlation between the selected variables and rainfall, and that a sizable percentage of the variation in the dependent variable was not captured by the model. The model's accuracy in forecasting rainfall was shown to be quite low by the MSE error, with significant squared discrepancies between the expected and actual amounts. These results support the notion that the linear regression model as it is now designed is not appropriate for studying or forecasting Ethiopia's rainfall patterns. Alternative modeling approaches, the inclusion of other pertinent factors, and the assurance of the availability of high-quality data that faithfully captures the intricate dynamics of rainfall in the area all require more investigation.

This study investigates the suitability of the timestamp approach algorithm for predicting blood pressure (BP) using wearable and comfortable devices, showcasing its accuracy even with low-frequency sampled signals. Developed within the SINTEC European project, the algorithm utilizes Electrocardiogram (ECG) and Photoplethysmogram (PPG) sensors, demonstrating promising results in both laboratory and hospital settings. The research emphasizes the algorithm’s potential to transform continuous and non-invasive BP monitoring through wearable technology, offering frequent measurements with minimal discomfort. While the study shows promise, further exploration is needed, focusing on optimizing machine learning coefficients for long-term monitoring applications and addressing potential changes over time. Technological improvements, including the implementation of edge computing algorithms, hold the key to enhancing BP accuracy, denoising techniques, and integrating alarm systems for future wearable solutions. This study emphasizes the adaptability of the algorithm for diverse healthcare environments, paving the way for broader applications in convenient and reliable BP monitoring.

Background: As long-lived organisms, urban trees often encounter development and redevelopment activities in close proximity during their lifespans. These activities can damage tree roots, often through methods like root severing during trenching or excavation. Methods: In 2017, we simulated trenching damage on mature Quercus virginiana Mill. trees at three different distances from the base (3x, 6x, and 12x the stem diameter). After five years, we revisited these trees to assess root regrowth based on the cut root's cross-sectional area (CSA) and distance from the base. Results: We observed regrowth in all but 38 (6.7%) of the 557 cut roots revisited. The lack of regrowth in some roots was not associated with our original treatments, the CSA of the roots at the time of trenching, or distance between the cut root end and the trunk (minimum P-value = 0.841). On average, the observed CSA of the regrowth was 22.2% of the original root's CSA. Only our original trenching treatments significantly predicted the level of regrowth observed five years after pruning (P-value = 0.024). Discoloration due to root pruning was minimal. Conclusion: In summary, our findings indicate that root systems require many years to recover from trenching damage. Increasing the distance between trenching activities and trees may have a minor effect on root regrowth but primarily helps reduce initial stress on the tree.

The particulars of stimulus-response experiments done on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures – so that modal analysis can be used constructively in systems biology model building – for nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output data associated with a structural model – one that includes inputs and outputs explicitly – and for NL as well as linear biosystems. The methodology establishes model dimensionality (size, complexity) from particular data sets; helps select among multiple candidate models (model distinguishability); helps in designing new experiments to extract “hidden” structure; and helps to simplify (reduce) models to their essentials. For NL biosystems, results are not as comprehensive, similarly informative about their dominant dynamical properties, and unified with linear models on invariant 2-dimensional manifolds in phase space. Some automation of these highly technical aspects of biomodeling is also introduced.

This work presents a control scheme to control the grid-connected single-phase photovoltaic (PV) system. The considered system has four 250W solar panels, a non-inverting buck-boost DC-DC converter, and DC-AC inverter with LCL filter. The control system aims to track and operate at the maximum power point (MPP) of PV panels, regulate the voltage of DC link, and supply the grid with a unity power factor. To well achieve these goals, the proposed control system consists of three parts, that are MPP tracking controller module with a fuzzy-based modified incremental conductance (INC) algorithm, a DC-link voltage regulator with a hybrid fuzzy proportional-integral (PI) controller, and a Current Controller module using the linear quadratic regulator (LQR) for grid-connected power. Based on fuzzy control and LQR, this work introduces a full control solution for grid-connected single-phase PV systems. The key novelty of this research is to analyze and prove that the newly proposed method is more successful in numerous aspects by comparing and evaluating the previous and present control methods. The designed control system settles quickly, which is critical for output stability. In addition, as compared to backstepping approach used in our past study, the LQR technique is more resistant to sudden changes and disturbances. Furthermore, backstepping method produces the larger overshoot, which has a detrimental impact on efficiency. Simulation findings under various weather conditions were compared to theoretical ones to indicate that the system can deal with variations in weather parameters.

Epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase that instigates several signaling cascades, including the NF-kB signaling pathway, to induce cell differentiation and proliferation. Overexpression and mutations of EGFR are found in up to 30% of solid tumors and correlate with a poor prognosis. Although it is known that EGFR-mediated NF-kB activation is involved in tumor development, the signaling axis is not well elucidated. Here, we found that PKP2 and the LUBAC complex were required for EGFR-mediated NF-kB activation. Upon EGF stimulation, EGFR recruited PKP2 to the plasma membrane, and PKP2 bridged HOIP, the catalytic E3 ubiquitin ligase in the LUBAC, to the EGFR complex. The recruitment activated the LUBAC complex and the linear ubiquitination of NEMO, leading to IkB phosphorylation and subsequent NF-kB activation. Furthermore, EGF-induced linear ubiquitination was critical for tumor cell proliferation and tumor development. Knockout of HOIP impaired EGF-induced NF-kB activity and reduced cell proliferation. HOIP knockout also abrogated the growth of A431 epidermal xenograft tumors in nude mice by more than 70%. More importantly, the HOIP inhibitor, HOIPIN-8, inhibited EGFR-mediated NF-kB activation and cell proliferation of A431, MCF-7, and MDA-MB-231 cancer cells. Overall, our study reveals a novel linear ubiquitination signaling axis of EGFR, and perturbation of HOIP E3 ubiquitin ligase activity is potential targeted cancer therapy.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we use the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determine variation in the different residuals. Also, we use non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduce WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we show 5-fold cross validation to verify our model.

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.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

Quaternion algebra is used both for the description of the motion of material objects in 4D space-time and for the representation of the energy-momentum density tensor in the same quaternion basis, accurate to some arbitrary scalar fields. Quaternionic generating operators applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy. We show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations.

Linear alkylbenzene sulfonate (LAS) anionic surfactants are widely used, present in wastewater, and can be discharged causing environmental damage. Without considering biodegradation, sorption and desorption reactions play an important role and depend on the characteristics of the aquifer medium such as the content of organic matter and clay. These processes are modelled with PHREEQC using laboratory-obtained data on columns with an input LAS pulse. LAS adsorption and desorption step experiments carried out in sand columns were also modelled with this software and distribution constants were similar to those obtained for pulse. The values of the starting distribution constant provided by batch tests with sand and agricultural soil mixtures establish the maximum value that must be obtained for column modelling. Distribution constants from column experiments obtained by Freundlich and linear isotherms provided very similar results, the latter with more consistent achievement. The modelling results showed longer elution times in the case of the heavier homologues and with a higher percentage of agricultural soil, which would translate into the great persistence of these compounds in the environment. In the case of soil contamination with wastewater-containing surfactants, these results would allow the development of mitigation strategies for these environmental impacts.

The relativistic quantum motion of a scalar particle under the effects of violation of the Lorentz symmetry in the presence of a linear confining potential is investigated. We see that the solution of the bound state to the modified Klein-Gordon equation can be obtained and a quantum effect characterized by the dependence of the magnetic field on the quantum numbers of the system is observed

We explores the hydrodynamical limit of a homogeneous electron gas, considering the interplay between the infrared limit and phenomenological hydrodynamics. Our study involves interactions generated by non-linear coordinate transformations. The focus begins with an analysis of non-linear coordinate transformations and their impact on normal modes in a harmonic system. The Lagrangian for a harmonic oscillator is used as an illustrative example, highlighting the role of position-dependent effective mass in preventing certain coordinate values. Moving beyond single degrees of freedom, we extend the discussion to a system with several harmonic degrees of freedom, introducing a collective variable. The effective dynamics of this collective variable are defined through a Lagrange multiplier term, emphasizing linearity in the description. Our study extends to the Current Two-Point function (CTP) formalism, introducing matrices and their inverses, such as $\hD$ and $\hD^{-1}$. Further, we delve into the dynamics of current in a homogeneous electron gas at finite density and zero temperature. Green's functions are generated using a functional integral approach, and the effective action is constructed via functional Legendre transformation. The quadratic part of the generator functional is expanded to derive the effective action, leading to the Maxwell equation and the subsequent elimination of the photon field. The resulting effective action for current dynamics is expressed in terms of the Current Two-Point function, paving the way for further exploration of the hydrodynamical aspects of the electron gas. Our study combines theoretical developments and mathematical formalism to provide insights into the hydrodynamical behavior of homogeneous electron gases.

The Gol'denveizer problem of a torus was studied analytically by Audoly and Pomeau (2002), and the accuracy of the Audoly and Pomeau linear law was confirmed numerically by Sun (2021). However, the law does not include the major radius R of the torus. To find the influence of the major radius, we used finite element numerical simulation to simulate different cases, and we propose a modified Audoly and Pomeau linear law for vertical deformation, which includes R. A linear law of horizontal deformation is presented as well. Our studies show that the Audoly and Pomeau linear law has high accuracy. With modified vertical and horizontal deformation, a displacement-compatible relation between them is formulated.

Public goods are produced at all levels of the biological hierarchy, from the secretion of diffusible molecules by cells to social interactions in humans. However, the cooperation needed to produce public goods is vulnerable to exploitation by free-riders — the Tragedy of the Commons. The dominant solutions to this problem of collective action are that some form of positive assortment (due to kinship or spatial structure) or enforcement (reward and punishment) is necessary for public-goods cooperation to evolve and be maintained. However, these solutions are only needed when individual contributions to the public good accrue linearly, and the assumption of linearity is never true in biology. We explain how cooperation for nonlinear public goods is maintained endogenously and does not require positive-assortment or enforcement mechanisms, and we review the considerable empirical evidence for the existence and maintenance of nonlinear public goods in microbiology, cancer biology, and behavioral ecology. We argue that it is time to move beyond discussions about assortment and enforcement in the study of cooperation in biology.

We investigate the value distribution of dierence polynomials of entire and meromorphic functions, which can be viewed as the Hayman's conjecture. And we also study the uniqueness of dierence polynomials sharing a common value.

Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.

This paper provides a proof of concept for a linear electric generator that can be used to harvest energy from various sources of linear motion, such as vibrations, free-piston engines and wave energy. The generator can be used to power small electronic devices, such as sensors, or charge household batteries. Literature was reviewed to develop an understanding about the applications, control methods, excitation methods and mechanics of rotating and linear electric machines. A bidirectional, two-sided linear machine was designed with two stator cores and a single mover core. The stator windings and mover winding can be independently excited, allowing for three modes: no mover excitation, DC excited mover, and AC excited mover. Simulations results showed that the magnetic flux generated by DC excited stator cores were concentrated in the centre of the mover core. The use of two stator cores eliminates lateral flux in the mover core when it is not excited, minimising attraction and repulsion forces. Parametric analysis showed that flux cutting occurred in all operation modes, verifying that the generator will produce power when operating. Hardware tests produced an output current when the machine is electrically and mechanically excited, verifying the proposed design.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

This paper presents a new method to model the nonlinear behaviour of masonry double curvature structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. It is meant to be used in professional design, especially for assessment and retrofitting purposes, therefore based on the exploitation of the simplest nonlinear Finite Elements available in a commercial software, namely trusses with elasto-fragile and elasto-ductile behaviour (Cutoff Bars). The numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and lumping nonlinearities on joints. These have been assumed in turn elastic-brittle and elastic-plastic by using 1D elements, respectively Point Contacts, under No-Tension Material hypothesis, and Cutoff Bars, assigning small tensile resistance to the material. The reinforcement, realised with FRP hooping strips, has been successfully modelled in a similar fashion, i.e. by applying perfectly bonded elastic-plastic Cutoff Bars at the extrados of the dome, where the debonding is accounted for in a conventional way limiting the tensile strength according to Italian Standards indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison.

This research work focused on the risks we are faced with on our day to day activities, either directly or indirectly, which can gradually accumulates and results to communal crisis, religious crisis, socio-economic agitations and tribal crises. Nasarawa Eggon Local Government Area of Nasarawa State was used as case study and a well structure close–ended questionnaire was used for data collection as it relates to Controlled Self Risk Assessment (CSRA) and linear programming technique was used to analyze. The results proved that many of this processes were neglected in these communities, making them to be prone to incessant communal crisis. The study recommend that Government should strongly, as a matter of urgency address the unemployment rate, distribution of political position, schools, primary health care and equip security personnel with the modern technology facilities, which happen to record the highest risk level.

We propose an $E_8 \otimes E_8$ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space . Each of the $E_8$ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion generations. The first $E_8$ further branches to the standard model $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ and describes the gauge bosons, Higgs and the left chiral fermions of the standard model. The second $E_8$ further branches into a right-handed counterpart (pre-gravitation) $SU(3)_{grav}\otimes SU(2)_R \otimes U(1)_g$ of the standard model, and describes right chiral fermions, a Higgs, and twelve gauge bosons associated with pre-gravitation, from which general relativity is emergent. We account for 208 out of the 496 degrees of freedom of $E_8 \otimes E_8$ and propose an interpretation for the remaining 288, motivated by the trace dynamics Lagrangian of our theory. We explain how the two copies of $SU(3)_{spacetime}$ together give rise to a 6D spacetime with signature $(3,3)$ which upon symmetry breaking gives rise to our 4D spacetime and to a second 4D anti-spacetime with flipped signature.

Incorporating substantial sustainable development issues into teaching and learning is the ultimate task of Education for Sustainable Development (ESD). The purpose of our study is to identify the confused students who have failed to master the skill(s) given by the tutors as a homework using Intelligent Tutoring System (ITS). We have focused ASSISTments, an ITS in this study and scrutinized the skill-builder data using machine learning techniques and methods. We used seven candidate models that include: Naïve Bayes (NB), Generalized Linear Model (GLM), Logistic Regression (LR), Deep Learning (DL), Decision Tree (DT), Random Forest (RF), and Gradient Boosted Trees (XGBoost). We trained, validated and tested learning algorithms, performed stratified cross-validation and measured the performance of the models through various performance metrics i.e., ROC (Receiver Operating Characteristic), Accuracy, Precision, Recall, F-Measure, Sensitivity & Specificity. We found GLM, DT & RF are high accuracies achieving classifiers. However, other perceptions such as detection of unexplored features that might be related to the forecasting of outputs can also boost the accuracy of the prediction model. Through machine learning methods, we identified the group of students which were confused attempting the homework exercise and can help students foster their knowledge, and talent to play a vital role in environmental development.

In the context of reinforcement learning (RL), ensuring both safety and performance is crucial, especially in real-world scenarios where mistakes can lead to severe consequences. This study aims to address this challenge by integrating temporal logic constraints into RL algorithms, thereby providing a formal mechanism for safety verification. We employ a combination of theoretical and empirical methods, including the use of temporal logic for formal verification and extensive simulations to validate our approach. Our results demonstrate that the proposed method not only maintains high levels of safety but also achieves comparable performance to traditional RL algorithms. Importantly, our approach fills a critical gap in existing literature by offering a solution that is both mathematically rigorous and empirically validated. The study concludes that the integration of temporal logic into RL offers a promising avenue for developing algorithms that are both safe and efficient. This work lays the foundation for future research aimed at generalizing this approach to various complex systems and applications.

In this work, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and response, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and prove the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020 and scalar predictors are GDP and number of beds in hospitals.

Regression models are mostly used in all fields of sciences for modelling the relationship between a dependent variable and independent variable(s). The least square method is often used to estimate the parameters in a linear model because it is the best linear unbiased estimator. These estimates can only be reliable if the assumption of normality is satisfied. In some cases the dependent variable might be bimodal and shows a non-linear relationship with the independent variable(s). In this case, a non-linear model should be used. In non-linear model, the standard errors are often obtained by linearizing the nonlinear function around the parameter, assuming central limit theorem. After the linearization, the least square parameter estimates are obtained. It should be noted that the error of the non-linear model is different from that of the transformed linear model. Thus, there is a need to transform back to the original non-linear model. In this note, a novel non-linear function was developed into a non-linear regression model, called Normal-Power model. The least square method was used to estimate the parameter of the transformed model. Its usefulness in regression model was demonstrated using real data of Nigeria Economy-Tourism model.

A focal plane array (FPA) detector was used for hyperspectral imaging in the infrared (IR) spectral region using thermal and synchrotron light sources. FPA Fourier-transform IR (FTIR) imaging microspectroscopy will be able to monitor real time changes at specific absorption bands when combined with high brightness synchrotron source. In this study, several types of samples with unique structural motifs were selected and used for assessing the capability of the FPA-FTIR imaging technique. It was shown that the time required for polariscopy at IR wavelengths can be substantially reduced by the FPA-FTIR imaging approach. By using natural and laser fabricated polymers with sub-wavelength features, alignment of absorbing molecular dipoles was revealed as well as higher order patterns (laser fabricated structures). Micro-spectroscopy of absorber orientation reveals alignment patterns even when they are not spatially resolved.