We consider the problem of scheduling $n$ jobs with identical processing times and given release as well as delivery times on $m$ uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (``branch less and cut more''). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is $O(\gamma m^2 n\log n)$, where $\gamma$ can be either $n$ or the maximum job delivery time $q_{\max}$. This complexity can even be reduced further by using a smaller number $\kappa<n$ in the estimation describing the number of jobs of particular types. However, this number $\kappa$ becomes only known when the algorithm has terminated.

The grand antiprism A is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff’s construction. Its symmetry group G(A) has been incorrectly described as [[10,2+,10]] or even as an `ionic diminished Coxeter group’. In fact, G(A) is another group of order 400, namely the group ±[D10×D10]·2, in the notation of Conway and Smith.

We analyze the modular geometry of the variable exponent Lebesgue space L^p(.). We show that L^p(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

The following two consequences of the axiom of constructibility V = L are established for every n ≥ 3: 1. Every linear $\bf\Sigma^1_n$ set is the projection of a uniform planar $\bf\Pi^1_{n-1}$ set. 2. There is a planar $\bf\Pi^1_{n-1}$ set with countable cross-sections, not covered by a union of countably many uniform $\bf\Sigma^1_n$ sets. If n = 2 then claims 1,2 hold in ZFC alone, without the assumption of V = L.

In this study, we deal with a nonlinear system of neutral Volterra integro-differential equations (NVIDEs) with infinite delay. We study stability, uniform stability and instability of zero solution of the system of NVIDEs with infinite delay. We obtain three new results with regard to these concepts via two new Lyapunov– Krasovskii functionals (LKFs), respectively. As the main contributions of this work, we improve and generalize some earlier results in the relevant database from the linear case to more general nonlinear cases.

For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first proposes the partition methods under the lattice point sets and obtains several sub-simplexes without common interior points. Furthermore, we present the method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.

In this paper, we will extend the expected value of the function w.r.t the uniform probability measure on sets measurable in the Caratheodory sense to be finite for a larger class of functions, since the set of all measurable functions with infinite or undefined expected values forms a prevalent subset of the set of all measurable functions, which means "almost all" measurable functions have infinite or undefined expected values. Before we define the specific problem in section 2, we will outline some preliminary definitions. We'll then define the specific problem (along with a partial solution in section 3) to visualize the complete solution. Along the way, we will ask a series of questions to clarify our understanding of the paper.

White oak mortality is a significant concern in forest ecosystems due to its impact on biodiversity and ecosystem functions. Understanding the factors influencing white oak mortality is crucial for effective forest management and conservation efforts. In this study, we aimed to investigate the spatial pattern of white oak mortality rates at different locations of the eastern US and explore the underlying processes involved with the spatial distribution patterns. Multicycle Forest Inventory and Analysis data were compiled to capture white oak plots across the eastern US. White oak mortality data were collected across plot systems that utilized Diameter at Breast Height between two periods. Ripley’s K function was used to study the spatial pattern of white oak mortality rate. Results found clustered patterns at both local and broad scales and random patterns at broad scales only across the southern and northern regions. However, the central region indicated both clustered and random patterns at local scale only. We found uniform patterns at a broad scale across all regions. Our findings demonstrated the importance of the spatial pattern of the white oak mortality rate and the underlying factors associated with it. This research can inform forest management practices for the conservation of white oak populations at varying scales. Future research is needed for a comprehensive assessment of biotic and abiotic factors for forest management strategies at various spatial scales aimed at mitigating white oak mortality.

This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle introduced in [Bortolotti et al. arXiv.math.NA/2309.14163], we develop here a new image restoration model and an iterative algorithm for its effective solution. The model incorporates pixel-wise regularization terms and establishes a rule for parameters selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.

This work introduces a new architecture for a time-domain feedback-based beamformer designed to meet real-time processing demands. The primary goal of this design is to locate reflective sources by estimating their direction of arrival (DOA) and signal range. Incorporating a feedback mechanism in this architecture is a unique aspect that refines localization precision. We conduct an in-depth analysis highlighting their respective benefits and limitations to compare the effectiveness of time-domain feedback beamforming against conventional time-domain methods. Our evaluation of the proposed architecture, based on critical performance indicators such as peak-to-sidelobe ratio, mainlobe width, and directivity factor, demonstrates its ability to improve beamformer effectiveness significantly.

Suppose set

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

The paper considers two models of queuing with a varying structure based on the introduction of additional transient intensities into known models or their combinations, which create stationary distributions convenient for calculation. In the first model, it is a probabilistic mixture of known stationary distributions with given weights. In the second model, this uniform distribution is repeatedly used in physical statistics. Both models are based on the selection of states, between which additional transient intensities are introduced. The algorithms used in the paper for introducing new transient intensities are closely related to the concept of flow in a deterministic transport network. The introduced controls are selected so that the marginal distribution of the combined system is a mixture of the marginal distributions of the combined systems with different weights determined by the introduced transient intensities. As a result, the process of functioning of the combined system is obtained by switching processes corresponding to different combined systems at certain points in time.

This article is devoted to overcoming the contradiction between the problem of maximizing the extraction of wind energy as the goal of optimizing wind turbines, and the use of traditional methods based on criteria for the aerodynamic quality of the blades. A modified technique is considered in which the optimization criterion is the directly extracted flow power. It is based on pulse theory methods that use specific power as an optimization criterion. A comparative analysis of the energy efficiency of different types of turbines is carried out, and the effects of blade inversion are considered. A method for calculating multi-rotor turbines based on the concept of uniform power distribution is presented. The compatibility of proprietary and traditional methods is considered by comparing the results of numerical experiments with calculated and experimental data from sources. Optimization computational algorithms generate data from numerical experiments and determine optimal parameter configurations for the turbines under consideration. It is shown that orthogonal Darrieus turbines in high-speed mode provide energy efficiency comparable to collinear turbines, and multi-rotor turbines with power uniformly distributed over the working section are not inferior in energy efficiency to basic turbines, with linear blade velocities halved.

Grid refinement is used to save computing costs while preserving high precision of fluid simulation. In the Lattice Boltzmann Method, grid refinement often uses interpolated values. We found a method, where interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaling the non-equilibrium part of populations, and developed the recalibration procedure that allows to transfer information between different LBM stencils in the simulation domain. Then, we build non-uniform lattice which uses stencils with different shapes on the transition. The resulting procedure is verified on the 2D Poisselle flow and the advected vortex benchmark. In prospect, grids with adaptive geometry can be built with the use of the proposed method.

In this paper, the methods and their analysis for estimating the location of three dimension (3-D) single source buried in lossy medium are presented with uniform circular array (UCA). The mathematical model of the signal in the lossy medium is proposed. Using location information in the covariance matrix obtained by sensors’ output, the equations of the source location (azimuth angle, elevation angle and range) are obtained. The phase and amplitude of the covariance matrix function are used to process these equations respectively. Then, the phase and amplitude of the covariance matrix function are used to process the source localization in the conductive medium together. By analyzing the characteristics of the proposed methods and MUSIC method, the computational complexity and the valid range of these methods are given. From the results, whether the loss is known, we can choose the appropriate method to process the issues (localization in lossless medium or lossy medium).

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

To reduce the carbon emissions during heating in the manufacturing process, microwaves have attracted significant attention. Microwave has a lot of advantages rather than traditional heating method such as rapid heating, lower thermal damage and eco-friendly process. In order to apply microwaves to manufacturing process, uniform and efficient heating is required. We have analyzed the effect of various design parameters such as cavity heights, the application of the reflector, and the number and positions of waveguides for uniform and efficient heating by numerical simulation and verified that by experiment. The results showed that a slight change in the cavity height altered the electromagnetic field distribution and heating parameters, such as the coefficient of variance and power absorption efficiency. With reflectors installed, uniform heating was achieved and power absorption was improved, with the spherical reflector showing the maximum efficiency. The use of double waveguides heated the target material in a uniform manner. An increase in the power supply also led to uniform heating. This large-scale analysis will be helpful in applying microwaves to actual industrial sites.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g. the atom-atom and atom-surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of "elementary catastrophes" with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points ("cusp" catastrophe) and four saddle points ("swallow-tail" catastrophe).

A novel composite consisting of fluorine-doped carbon and graphene double-coated LiMn0.6Fe0.4PO4 (LMFP) nanorods, synthesized via a facile low temperature solvothermal method that employs a hybrid glucose and polyvinylidene fluoride as carbon and fluorine sources. As revealed by physicochemical characterization, F-doped carbon coating and graphene form a ‘point-to-surface’ conductive network, facilitating rapid electron transport and mitigating electrochemical polarization. Furthermore, the uniform thickness of the F-doped carbon coating alters the growth of nanoparticles and prevents direct contact between the material and the electrolyte, thereby enhancing structural stability. Strong electronegative F− is beneficial to inhibit the structural changes of LMFP caused by Li-insertion/extraction during charge/discharge, which effectively reduces the Jahn-Teller effect, and inhibits Mn dissolution. The distinctive architecture of LMFP/C-F/G cathode material exhibits excellent electrochemical properties, exhibiting an initial discharge capacity of 163.1 mAh g−1 at 0.1 C and a constant Coulombic efficiency of 99.7% over 100 cycles. Notably, LMFP/C-F/G cathode material achieves an impressive energy density of 607.6 Wh kg−1 , surpassing that of commercial counterparts. Moreover, it delivers a reversible capacity of 90.3 mAh g−1 at a high current rate of 5 C. The high-capacity capability and energy density of the prepared materials give them great potential for use in next-generation lithium-ion batteries.

In this paper, a swarm trajectory planning method is proposed for multiple autonomous surface vehicles (ASVs) in an unknown and obstacle-rich environment. Specifically, based on the point cloud information of the surrounding environment obtained from local sensors, a kinodynamic path searching method is used to generate a series of waypoints in the discretized control space at first. Next, after fitting B-spline curves to the obtained waypoints, a nonlinear optimization problem is formulated to optimize the B-spline curves based on gradient-based local planning. Finally, a numerical optimization method is used to solve the optimization problems in real-time to obtain collision-free, smooth and dynamically feasible trajectories relying on a shared network. Simulation results demonstrate the effectiveness and efficiency of the proposed swarm trajectory planning method for a network of ASVs.

Optimization using Genetic Algorithms (GA) is a well-known strategy in several scientific disciplines. The crossover is an essential operator of the Genetic Algorithm. It has been an active area of research to develop sustainable forms for this operand. In this work, a new crossover operand is proposed. This operand depends on giving an elicited description for the chromosome with a new structure for alleles of the parents. It is suggested that each allele has two attitudes, one attitude differs contrastingly with the other, and both of them complement the allele. Thus, in case of one attitude is good, the other should be bad. This is suitable for many systems which contain admired parameters and unadmired parameters. The proposed crossover would improve the desired attitudes and damp the undesired attitudes. The proposed crossover can be achieved in two stages: the first stage is a mating method for both attitudes in one parent to improving one attitude at the expense of the other. The second stage comes after the first improvement stage for mating between different parents. Hence, two concurrent steps for improvement would be applied. Simulation experiments for the system shows improvement in the fitness function. The proposed crossover could be helpful in different fields, especially to optimize routing algorithms and network protocols, an application that has been tested as a case study in this work.

The deepening of electricity reform results in increasingly frequent auctions and the surge of generators, it becomes difficult to analyze generators’ behaviors. Since it’s hard to find analytical market equilibriums, approximate equilibriums were obtained instead in previous studies by market simulations, which are strict to initial estimations and simulation results are chaotic in some cases. In this paper, a multi-unit power bidding model is proposed to reveal the bidding mechanism under clearing pricing rule by employing auction approach, for which initial estimations are non-essential. Normalized bidding price is introduced to construct generator's price-related bidding strategy. Nash equilibriums are derived depend on the marginal cost and the winning probability which are computed from bidding quantity, transmission cost and demand distribution. Furthermore, we propose a comparative analysis to explore the impact of uncertain elastic demand on the performance of the electricity market. The result indicates that, there exists market power among generators leading to social welfare decreases even under competitive conditions but elastic demand is an effective way to restrain generators’ market power. The feasibility of the models is verified by a case study. Our work provides decision support for generators and a direction for improving market efficiency.

The VLSI industry is facing parasitic effects that trouble development in the nanoscale domain. However, instead of replacing the traditional MOSFET design, it would be more advantageous to apply different doping profiles and discerning which deal with specific parasitic effects the best. With a review of Gaussian doping, Uniform doping, and Delta doping profiles and analysis of the FET technology characteristics that use these doping profiles, a comparison can be made among them for integrated circuit design engineers. These doping profiles are compared based on how well they perform against non-ideal and ideal environments. Also, both digital and analog performance are measured to ensure the uniqueness of each doping profile that is present. After getting a list of benefits from each doping profile, it is derived to determine which doping profile works best against a host of parasitic effects and what type of application do these doping profiles have

In this paper, a semi-empirical model of air waves induced by falling rock is described. The model is composed of a uniform motion phase (velocity close to 0 m·s^-1) and an acceleration movement phase. The uniform motion phase was determined based on experimentally and the acceleration movement phase was derived by theoretical analysis. A series of experiments were performed to verify the semi-empirical model and elucidated the law of the uniform motion phase. The acceleration movement phase accounted for a larger portion with a greater height of the falling rock. Experimental results of different falling heights of the goaf showed close agreement with theoretical analysis values. The semi-empirical model could accurately and conveniently estimate the velocity of air wave induced by falling rock. Thus, the semi-empirical model can provide a reference and basis for estimating the speed of air waves and designing protective measures in mines.

The Capital Asset Pricing Model is a widely applied model to describe risky markets and to deduce their systematic risk. Its estimation, therefore, remains an important task in Econo-financial studies. Empirically, it focuses on the impact of return interval on the betas. Existing studies somehow turn around the same idea of measuring the value of the beta according to the uniform intervals of time during a fixed period. However, it is noticed easily, and especially in the last decade that many factors such as socio-political, and Econo-environmental ones have led to a perturbation in the timeline of the worldwide development, and especially in countries and regions having political changes. This led us to introduce a new idea of risk estimation taking into account the non-uniform changes in markets by introducing a non-uniform wavelet analysis. We aim to explain the Econo-political situation of Arab spring countries and the effect of the revolutions on the market beta. The main novelty is firstly the construction of a dynamic backward-forward model for missing data, and next the application of random non-uniform wavelets. The proposed procedure will be acted empirically on a sample corresponding to TUNINDEX stock as a representative index of the Tunisian market actively traded over the period January 14, 2016, to January 13, 2021. The chosen 5-years period is important as it constitutes the first 5-years-after the revolution and depends strongly on the Socio-Econo-political stability in the revolutionary countries.

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modeling results with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, that seriously complicates the problem solution. The relations connecting perturbations for acoustic and entropy modes are analytically established and led to the solvable diagnostic equations. These perturbation structures, found as the equation solutions specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. These time-independent diagnostic relations link gas perturbation variables of the acoustic and the entropy modes. Hence, they provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the all accessible heights range. As a prospective model, we consider the diagnostics at the height interval [120;180] km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data, obtained by numerical experiment, are illustrated by the plots for the pure numerical data against ones obtained by the model. The total energy of a flow is determined for both approaches and its height profiles are compared.

Depending on human body conditions and environmental conditions, it is sometimes difficult to conduct subject experiments. In such cases, it is effective to use a thermal manikin. There are few studies that investigate the effect of the non-uniform and asymmetric outdoor thermal environment on the mean skin temperature. The purpose of this study is to clarify the influence of the non-uniform and asymmetric thermal radiation of short-wavelength solar radiation in an outdoor environment on the calculation of the mean skin temperature. The skin temperature of the front of the coronal surface, which was facing the sun and where the body received direct short-wavelength solar radiation, and the skin temperature of the rear of the coronal surface, which was in the shadow and did not receive direct short-wavelength solar radiation were respectively measured. The feet, upper arm, forearm, hand and lower leg, which are susceptible to short-wavelength solar radiation in a standing posture, had a noticeable difference in skin temperature between sites in the sun and in shade. The mean skin temperature of sites facing the sun was significantly higher than the mean skin temperature of those in the shade.

This paper presents a comprehensive evaluation of metal foam employment within polymer electrolyte fuel cells (PEFCs) and compares it with conventional serpentine channels from both experiment viewpoints and computational fluid dynamics simulation. The experiments are designed to study the effects of material, area density, compression ratio, and final thickness of metal foam. Additionally, the influence of housing plate material and relative humidity (RH) is also tested for the first time. The results reveal that at RH=75-100%, the best distributor design is nickel foam with a compression ratio of 70%, a final thickness of 0.5mm, and SS-304 housing plate, which delivers 3110 mA cm^-2 as limiting current density that is scarce in the literature. The PEFC with this foam distributor shows a 10% improvement in maximum power density and 45% in limiting current density compared to the serpentine channel case. While at RH=30%, the same foam flow field with a final thickness of 1mm is a superior option. The experiments also indicate that maximum power density increases by 23% as the compression ratio rises from 0 to 70%, while reducing final thickness from 1 to 0.5 mm causes a 19% enhancement in cell performance. Simulation results reveal that metal foam is more successful in evenly reactant distribution so that the average oxygen mass fraction at the cathode catalyst layer is increased by 38% in the metal foam case compared to the serpentine channel.

In this work, the problem is considered for eliminating a non-uniform rectilinear smearing of an image by mathematical and computer-based way, for example, a picture of several cars taken with a fixed camera and moving with different speeds. The problem is described by a set of 1-dimensional Fredholm integral equations (IEs) of the first kind of convolution type with a 1-dimensional point spread function (PSF) at uniform smearing and by a set of new 1-dimensional IEs of a general type (not convolution type) with a 2-dimensional PSF at non-uniform smearing. The problem is also described by one 2-dimensional IE of convolution type with a 2-dimensional PSF at uniform smearing and by a new 2-dimensional IE of a general type with a 4-dimensional PSF at non-uniform smearing. The problem for solving Fredholm IE of the first kind is ill-posed (unstable). Therefore, IEs of convolution type are solved by the Fourier transform (FT) method and Tikhonov's regularization (TR), and IEs of general type are solved by the quadrature/cubature and TR methods. Moreover, the magnitude of the image smear Δ is determined by the original “spectral method”, which increases the accuracy of image restoration. It is shown that the use of a set of 1-dimensional IEs is preferable to one 2-dimensional IE in the case of non-uniform smearing. In the inverse problem (image restoration), the Gibbs effect (the effect of false waves) in the image may occur. It can be edge or inner. The edge effect is well suppressed by the proposed technique “diffusing the edges". In the case of an inner effect, it is eliminated with difficulty, but the image smearing itself plays the role of diffusing and suppresses the inner Gibbs effect to a large extent. It is shown (in the presence of impulse noise in an image) that the well-known Tukey median filter can distort the image itself, and the Gonzalez adaptive filter also distorts the image (but to a lesser extent). We propose a modified adaptive filter. A software package was developed in MatLab and illustrative calculations are performed.

Photovoltaic materials convert light into electrical voltages. So far, most research in the field are focused on how to refine/improve the existing or standard photovoltaic cells to yield more efficient electricity, to reduce weight, to make more flexible shape, or to minimize costs under standard and uniform sunlight illuminations. In this project, we explore and demonstrate a hypothesis that non-uniform light illumination photovoltages can also be generated due to photo doping induced mobile charge carrier density gradient between light and dark areas in either p-type or n-type photo doping semiconductors. The term non-uniform light illumination was coined to refer to subjecting our photo sensing thin film devices to areas of high and low intensities of light illumination simultaneously, with an intention of creating a charge density gradient and therefore a voltage. Specifically, a polymeric composite thin film composed of P3HT (p-type photo doping semiconductor) and PCBM (photo doping electron acceptor and trap) at varying p-doping levels were studied. We observed that the fabricated photovoltaic cells with about 80% PCBM doped P3HT thin film devices exhibited 0.5-1.2 volts photovoltages under non-uniform light illuminations.

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

The theory of special relativity has reexamined and reconstructed the concepts of space and time, which are indispensable for describing physical laws, consequently instigating a major revolution in physics in general. Although the correctness of the special theory of relativity has been con-firmed by many observations and experiments, it is unclear why the "principle of relativity" and the "principle of the constant speed of light," which form the basis of the idea, are valid. Moreo-ver, although special relativity has advanced our understanding of time, our understanding of the fundamental question, "What is time?" is still limited. The theory of special relativity regards space as a four-dimensional construct consisting of one-dimensional time and three-dimensional space. This paper proposes an alternative framework, wherein real space is uniform and isotropic four-dimensional space, and elementary particles are waves that propagate through this four-dimensional space at a constant speed. This new perspective provides evidence to support two of Einstein’s key principles—the "principle of relativity" and the "principle of the constant speed of light." Furthermore, this model clarifies what time is and why time flows at a constant rate from the past to the future.

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

Through analysis of the constituent components of the observation data from 12 geoe-lectric field stations located approximately 600 km form the epicenter of the Jishishan Ms6.2 earthquake, this study reveals that during earthquake preparation and occurrence, the geoelec-tric field at each station exhibit non-uniform variations. These variations are characterized by significant decreases or increases in correlation coefficients between different azimuths (δxy) and between long and short polar distances within the same azimuth (δxx). Additionally, there are discrete or extruding changes observed in the dominant azimuth angles of the telluric field at the stations, ranging approximately from 40° to 90°. These anomalies indicate local site effects and exhibit quasi-synchronous temporal characteristics. The study found that stations located in regions with intense tectonic activities, such as Menyuan and Jingtai, experience more significant anomalous changes influenced by the tectonic activities of the Qaidam-Qilian Mountain block. When multiple stations with anomalous changes are used to determine the earthquake epicenter, earthquakes often occur within or near the intersection area of the predicted ranges of these sta-tions. The specific time of earthquake occurrence shows no clear relationship with the locations or tectonic activities of the stations.

Rapid advances in the screening, diagnosis, and treatment of genetic disorders has increased the number of conditions that could be detected through universal newborn screening (NBS). However, addition of conditions to the Recommended Uniform Screening Panel (RUSP) and implementation of nationwide screening has been a slow process taking several years to accomplish for individual conditions. Here we describe web-based tools and resources developed and implemented by the newborn screening translational research network (NBSTRN) to advance newborn screening research and support NBS stakeholders. NBSTRN’s tools include the Longitudinal Pediatric Data Resource (LPDR), the NBS Condition Resource (NBS-CR), the NBS Virtual Repository (NBS-VR), and the Ethical, Legal, and Social Issues (ELSI) Advantage. Research programs including the Inborn Errors of Metabolism Information System (IBEM-IS), BabySeq, EarlyCheck, and Family Narratives Use Cases have utilized NBSTRN’s tools, and in turn contributed research data to further expand and refine these this resource. Additionally, we discuss ongoing tool development to facilitate expansion of genetic disease screening in increasingly diverse populations. In conclusion, NBSTRN’s tools and resources provide a trusted platform to enable NBS stakeholders to advance NBS research and improve clinical care for patients and their families.

In order to solve the problem of large eddy current loss and high temperature rise caused by large amount of permanent magnet, a new type of combined magnetic pole permanent magnet motor is proposed in this paper. The sinusoidal distribution subdomain model of non-uniform air gap rotor is established by using Laplace equation, and the analytical expression of eddy current loss of rotor in uniform air-gap and non-uniform air-gap is derived. The effect of rotor eccentricity on eddy current loss is obtained. According to the characteristics of distributed winding of non-uniform air gap combined pole permanent magnet motor, equivalent treatment is performed to obtain the equivalent thermal conductivity, so as to establish equivalent thermal network model of motor, calculate the temperature value of each component of the motor, and verify the correctness of the thermal network model through the method of magnetothermal bidirectional coupling. Finally, an experimental platform is set up to carry out temperature rise experiments on the two prototypes respectively. Experimental results show that the non-uniform air-gap rotor structure can effectively reduce the rotor eddy current loss and motor temperature rise, and also verify the accuracy of the analytical model calculation results.

This paper presents an exact solution to the Timoshenko beam theory (TBT) for first-order analysis, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory (EBBT) neglects shear deformations. Thus, the Euler–Bernoulli beam is a special case of the Timoshenko beam. The moment-curvature relationship is one of the governing equations of the EBBT, and closed-form expressions of efforts and deformations are available in the literature. However, neither an equivalent to the moment-curvature relationship of EBBT nor closed-form expressions of efforts and deformations can be found in the TBT. In this paper, a moment-shear force-curvature relationship, the equivalent in TBT of the moment-curvature relationship of EBBT, was presented. Based on this relationship, first-order and second-order analyses were conducted, and closed-form expressions of efforts and deformations were derived for various load cases. Furthermore, beam stability was analyzed and buckling loads were calculated. Finally, first-order and second-order element stiffness matrices were determined.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

The paper briefly reviews the Clifford algebras of space Cl(3,0) and anti-space Cl(0,3) with a particular focus on the paravector representation, emphasizing the fact that both algebras have an isomorphic center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3Hc. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl(3,0) corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl(0,3) leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.