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QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively simple but complete explanations about how to use QR decomposition for the least squares problem solution. Only basic knowledge of linear algebra and calculus are required. Both Givens rotations and Householder reflections usage for the linear least squares problem were considered. It was shown that the algorithm based on Givens rotations is even easier to program than explicit formation of the normal equations with subsequent usage of Gaussian elimination.

The most famous equation in physics, E = mc[superscript 2], is rarely introduced in middle school physics curricula. Recent research has shown that teaching Einsteinian concepts at the middle school level is feasible and beneficial. This paper analyses an Einsteinian energy teaching module for Year 8 students (13-14 years old), which encompasses the two fundamental energy formulas in modern physics, E = mc[superscript 2] and E = hf. In the context of activity-based learning, the Einsteinian energy module relates to all the forms of energy in traditional school curricula. This study uses a design-based research approach within the Model of Educational Reconstruction framework. Modern experiments, historical events, and educational research helped us identify relevant Einsteinian energy concepts, activities, and assessments. The study included 22 students who participated in nine in-class Einsteinian energy lessons. Analysing results in the post-test showed a 31% mean increase from the pre-test, a clear and significant positive change in students' conceptual understanding. The results demonstrated students' ability to deal with very large and small constants of proportionality and physical concepts involved in the module.

This study builds on the simulation framework of a recent paper by Stanley and Doucouliagos ("Research Synthesis Methods" 2023;14;515--519). S&D use simulations to make the argument that meta-analyses using partial correlation coefficients (PCCs) should employ a "suboptimal" estimator of the PCC standard error when constructing weights for fixed effect and random effects estimation. We address concerns that their simulations and subsequent recommendation may give meta-analysts a misleading impression. While the estimator they promote dominates the "correct" formula in their Monte Carlo framework, there are other estimators that perform even better. We conclude that more research is needed before best practice recommendations can be made for meta-analyses with PCCs.

For a simple, finite, and connected graph G, the spherical maximal operator is defined as ... where ... is the sphere with center at t and having radius r. In this paper, we consider the spherical maximal operator ... on ... spaces and calculate the ... for ... and estimate the ... for ..., when G is Km. Furthermore, We establish the maximum and minimum bounds for the spherical maximum operator on finite graphs and indicate the graphs that achieve these bounds. [ABSTRACT FROM AUTHOR]

Small-signal transmittances of the power stage of a flyback converter in continuous conduction mode are derived on the averaged model obtained by the separation of variables approach. The precise knowledge of these transmittances is necessary in the design process of the converter control circuit. Apart from mathematical formulas for transmittances, the numerical calculations of the frequency dependencies of the transmittances for the assumed set of the converter parameters are presented with the parasitic resistances of components taken into account. The results of the calculations are compared with the measurements performed on the laboratory model of the converter and a good consistency is observed. It is concluded, that the results of the paper may be useful in the designing process of a control circuit of the flyback converter. [ABSTRACT FROM AUTHOR]

The split feasibility problem (SFP), which provides a unified framework to model a wide range of inverse problems, has received much considerable attention in the literature. However, how to efficiently solve SFPs is still an interesting topic. In this paper, we introduce a block-wise formulation for algorithmic design. Specifically, we first introduce an auxiliary variable to formulate the original SFP as a constrained minimization problem with a block structure, which paves a new way to find solutions of SFPs. Then, we show that the employments of some classical gradient-type optimization algorithms produce very simple, yet quite efficient iterative schemes to find a solution of SFPs when the underlying block structure could be exploited. The parallel iterative schemes of the proposed blockwise algorithms are not only efficient to deal with the case that the projections onto the convex sets have explicit representations, but also are possibly valuable for solving large-scale SFPs without explicit projections onto the underlying sets. Some numerical results on synthetic examples support the idea of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of dependent errors in the fixed design nonparametric regression models. Under some mild conditions, we obtain the complete consistency and asymptotic normality for the weighted estimator in the fixed design nonparametric regression models. In addition, a simulation study is undertaken to investigate finite sample behavior of the estimator. [ABSTRACT FROM AUTHOR]

The ordering betweenWigner-Yanase-Dyson function and logarithmic mean is known. Also bounds for logarithmic mean are known. In this paper, we give two reverse inequalities for Wigner-Yanase-Dyson function and logarithmic mean. We also compare the obtained results with the known bounds of the logarithmic mean. Finally, we give operator inequalities based on the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we propose a zero-inflated version of the extended alternative hyper-Poisson distribution of Kumar and Nair (2013b) and investigate some of its important properties and applications. We derive expressions for its probability generating function, mean, variance, etc. along with recursion formulae for probabilities, raw moments and factorial moments. The estimation of the parameters of the distribution is also attempted and it has been fitted to certain real life data sets for highlighting its practical relevance. Further, generalized likelihood ratio test procedure is applied for examining the significance of the parameters of the model and a simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

The Pearson-type family densities are among the most important classes of distributions, also playing key roles in directional statistics. To model data scattered asymmetrically on non-Euclidean spaces, including spheres, the researchers confined themselves to extending particular distributions fromthe class of the Pearson-type family densities. Those specific distributions are symmetric, but their extended versions are usually heavy-tailed. This paper introduces alternative probability density functions in the class of Pearson-type distributions on the sphere with the spherical Student's t, Fisher, and Chi-square densities as the subfamilies. We show that it is intrinsically asymmetric by investigating various theoretical properties of this new subclass. Intensive simulation studies are conducted to explore various aspects of this subclass. Also, modeling two real-life data using the proposed densities and comparing the results with the fits arising from other common spherical distributions are considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternative generalization of a recent test for univariate normality which is based on the empirical moment generating function to the multivariate case. We show, among other properties, that the proposed weighted L²-class of statistics is affine invariant and consistent. The empirical critical values of the proposed test are evaluated for different sample sizes, variable dimensions and values of the smoothing parameter through large scale simulations. The empirical power comparison of the test with a strong competitor shows that the test has a considerably high power performance, especially at large sample sizes as well as under heavy-tailed alternative distributions. The application of the statistic, together with its competitor, to six real-life datasets also supports the considerable good power performance of the proposed statistic as well as its ease of application. [ABSTRACT FROM AUTHOR]

Copyright of Archives of Civil Engineering (Polish Academy of Sciences) is the property of Polish Academy of Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let G be a graph. For a set H of connected graphs, an H-factor of graph G is a spanning subgraph H of G such that every component of H is isomorphic to a member of H. Denote H = {P2}∪{Ci|i ≥ 3}. We call H-factor a perfect 2-matching of G, that is, a perfect 2-matching is a spanning subgraph of G such that each component of G is either an edge or a cycle. In this paper, we define the new concept of perfect 2-matching uniform graph, namely, a graph G is called a perfect 2-matching uniform graph if for arbitrary two distinct edges e1 and e2 of G, G contains a perfect 2-matching containing e1 and avoiding e2. In addition, we study the relationship between some graphic parameters and the existence of perfect 2-matching uniform graphs. The results obtained in this paper are sharp in some sense. [ABSTRACT FROM AUTHOR]

Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Progam. 1992] has inspired intensive attention in analyzing its theoretical convergence properties. This paper is devoted to the linear convergence rate of the semi-proximal GADMM (sPGADMM) for solving linearly constrained convex composite optimization problems. The semi-proximal terms contained in each subproblem possess the abilities of handling with multi-block problems efficiently. We initially present some important inequalities for the sequence generated by the sPGADMM, and then establish the local linear convergence rate under the assumption of calmness. As a by-product, the global convergence property is also discussed. [ABSTRACT FROM AUTHOR]

Today, reinforcement learning is one of the most effective machine learning approaches in the tasks of automatically adapting computer systems to user needs. However, implementing this technology into a digital product requires addressing a key challenge: determining the reward model in the digital environment. This paper proposes a usability reward model in multi-agent reinforcement learning. Well-known mathematical formulas used for measuring usability metrics were analyzed in detail and incorporated into the usability reward model. In the usability reward model, any neural network-based multi-agent reinforcement learning algorithm can be used as the underlying learning algorithm. This paper presents a study using independent and actor-critic reinforcement learning algorithms to investigate their impact on the usability metrics of a mobile user interface. Computational experiments and usability tests were conducted in a specially designed multi-agent environment for mobile user interfaces, enabling the implementation of various usage scenarios and real-time adaptations. [ABSTRACT FROM AUTHOR]

Evaporation from water surfaces is influencing many environmental science processes. Evaporation from pan data is not available as the most well-known method of determining evaporation in many areas, and therefore, the application of experimental mathematical equations in this field is considered. Most of the data for extracting these equations did not belong to cold regions, and as a result, the accuracy of these equations in cold regions has low reliability. In this study, the equations of Trabert (Meteorol Z 13:261–263, 1896), Kohler (Tech Rep Geol Survey Prof Paper 269:127–148, 1954), Kohler et al. (Evaporation from pans and lakes, US Government Printing Office, Washington, 1955), Papadakis (Soil Sci 93:76, 1961), Ântal (Evapotranspiration from com field. Term paper submitted for Dr. R. F. Dale's Agronomy 537 class. Received from personal communication with Dr. Dale (Dept. of Agronomy, Purdue, 1973), Linacre (Agric Meteorol 18:409–424, 1977), Linacre (Water Int 19:5–14, 1994) in Two default and revised modes (14 equations in total) have been used to determine evaporation in cold regions (Emberger climate classifications). Performance index (PI) as an error metric was used to analyze the efficiency of the equations. Findings show that in the absence of proper datasets for revision, Kohler et al. (Evaporation from pans and lakes, US Government Printing Office, Washington, 1955) and Papadakis (Soil Sci 93:76, 1961) equations are more proper options for determining evaporation in cold regions. The revision process increased the efficiency of all equations, with the slightest improvement for Papadakis (Soil Sci 93:76, 1961) and the most improvement for Trabert (Meteorol Z 13:261–263, 1896). According to the behavior of Papadakis (Soil Sci 93:76, 1961) equation in the revision process and its efficiency in both default and revision modes, it can be considered a firm equation in the cold region. The findings reveal that the revised equations have little efficiency difference. It indicates that in cold regions, the influence of the default parameters of the equations on efficiency is more significant than their mathematical formula of the equation. Also, the revision has led to Trabert (Meteorol Z 13:261–263, 1896) equation with relatively good results due to less relative flexibility than other equations. Therefore, it can be concluded that the essential factor to increase the reliability of the application of experimental mathematical equations in determining evaporation from the pan is the use of revised equations with data from cold regions. In addition, among all the equations studied, the revised Kohler et al. (Evaporation from pans and lakes, US Government Printing Office, Washington, 1955) equation was recognized as the most efficient equation for determining evaporation from the pan in the cold regions studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to determine the eigenvalue intervals of μk; 1 < k < n for which an iterative systems of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example for their feasibility. [ABSTRACT FROM AUTHOR]

This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a Quasi B-algebra, building upon the foundational work on Post algebras by G. Epstein and the investigation of semi B-algebras. We systematically explore the properties of Quasi B-algebras, establishing equivalent conditions for the transition from a semi B-algebra to a Quasi B-algebra. [ABSTRACT FROM AUTHOR]

This paper investigates the intergovernmental transfer systems in South Africa, more specifically, the underlying determinants and formula of the unconditional grants of the education component of the Provincial Equitable Share (PES). The PES formula is a weighted shares formula that depends on the demographic shares of the provinces (population) to determine the equitable share outcomes to be transferred to individual provinces. We find that the variables used have two main weaknesses: Firstly, the enrolment variable, which could be contaminated with school repeats and dropouts, is too broad to be an effective measure for representing the real beneficiaries of the transfers. Secondly, infrequent updates about the school-age cohort population variables render the desired PES grant transfers for education outdated as well as serially inconsistent. The paper also provides an analysis of the PES formula's mathematical construct, followed by a few suggested variables to improve the relevance and accuracy of the formula of the revenue transfer. One such improvement is demonstrated by the inclusion of the Enrolment Survival Measure (ESR). More research and data are required to extrapolate nuanced results and to understand the socio-economic impacts of adopting these new variables in the PES formula going forward. [ABSTRACT FROM AUTHOR]

In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a result, many interesting functions of the joint distribution of graph degrees, such as the distribution of the median degree, become amenable to estimation. Our result is established by proving an asymptotic formula conjectured in 1990 for the number of graphs with given degree sequence. In particular, this gives an asymptotic formula for the number of d-regular graphs for all d, as n→∞. The key to our results is a new approach to estimating ratios between point probabilities in the space of degree sequences of the random graph, including analysis of fixed points of the associated operators. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fourth-order compact discretization method for solving a secondorder boundary value problem governed by the nonlinear Fredholm integro-differential equations. Using an efficient approximate polynomial, a compact numerical integration method is first designed. Then by applying the derived numerical integration formulas, the original problem is converted into a nonlinear system of algebraic equations. It is shown that the proposed method is easy to implement and has the third order of accuracy in the infinity norm. Some numerical examples are presented to demonstrate its approximation accuracy and computational efficiency, as well as to compare the derived results with those obtained in the literature. [ABSTRACT FROM AUTHOR]

This paper delves into the identification of upper and lower solutions for a high-order fractional integro-differential equation featuring non-linear boundary conditions. By introducing an order relation, we define these upper and lower solutions. Through a rigorous approach, we demonstrate the existence of these solutions as the limits of sequences derived from carefully selected problems, supported by the application of Arzel\a-Ascoli's theorem. To illustrate the significance of our findings, we provide an illustrative example. This research contributes to a deeper understanding of solutions in the context of complex fractional integro-differential equations. [ABSTRACT FROM AUTHOR]

Let A be a bounded positive operator on a complex Hilbert space ... . The semi-product ..., induces a semi-norm ... on H. Let ωA (T) amd ... denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space ..., respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-inner product space induced by A are derived. In particular, for ... and α ≥ 0, we prove that ... and ... . It is worth noting that our results improve the existing A-numerical radius inequalities. Further, we also give a refinement inequality of A-operator semi-norm triangle inequality. [ABSTRACT FROM AUTHOR]

Let ... be a polynomial of degree n having all its zeros in ..., then Aziz [Proc. Am. Math. Soc., 89, (1983) 259--266] proved ... . In this paper, we prove a polar derivative extension which sharpens the above inequality. As a consequence, we also derive a result on Bernstein type inequality for the class of polynomials having all its zeros in ... . [ABSTRACT FROM AUTHOR]

This paper establishes the mapping properties of the fractional integral operators on the grand Morrey spaces and the grand Hardy-Morrey spaces defined on the Euclidean spaces. We obtain our results by refining the Rubio de Francia extrapolation method as the existing extrapolation method cannot be directly applied to the grand Morrey spaces. This method also yields the mapping properties of nonlinear operators. In particular, we establish the Sobolev embedding, the Poincaré inequality and the mapping properties of the fractional geometric maximal functions on the grand Morrey spaces. [ABSTRACT FROM AUTHOR]

The paper is focused on two-sided splitting inequalities for differences of complex exponentials ... for large ... is real unbounded sequence clustering with appropriate speed. Moreover, it is shown that if ... is a Riesz basis of a Hilbert space H, then for any k ≥ 1 the system ... is complete, minimal but not uniformly minimal in H. Also some properties of systems of functions of real argument t, ... where ..., are discussed. [ABSTRACT FROM AUTHOR]

Let ... and t, r, p ∈ (0, ∞) . In this paper, we introduce the slice Besov-type space ... and the slice Triebel-Lizorkin-type space ..., and establish their φ-transform characterizations in the sense of Frazier and Jawerth. The embedding properties, characterizations via the Peetre maximal function, the Lusin area function, smooth atomic and molecular decompositions of these spaces are also obtained. As applications, we obtain the boundedness on these spaces of Fourier multipliers with symbols satisfying some generalized Hörmander condition. [ABSTRACT FROM AUTHOR]

We in this paper improve the well-known C. R. Johnson's lower bound for the smallest singular value via permutation matrices. A direct algorithm is also given to compute the new lower bound. [ABSTRACT FROM AUTHOR]

In this paper we provide several upper and lower bounds for the Ostrowski difference ... where f : C → R is a convex function, C is a convex subset of a vector space X and w is integrable and nonnegative a.e. on [0,1] . A perturbed version under some natural assumptions on the weight function w is also considered. These results are then employed to obtain several weighted integral inequalities for norms and semi-inner products. The particular case of inner product spaces is analyzed and refinements of the weighted integral midpoint inequality for norms are provided. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Baskakov-type operator. Firstly, we obtain the rate of convergence by using modulus of continuity and then Voronovskaja type asymptotic formula for these operators. [ABSTRACT FROM AUTHOR]

The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is the state space explosion problem. To address this issue, bisimulation minimization has emerged as a prominent method for reducing the number of states in a system, aiming to overcome the difficulties associated with the state space explosion problem. For systems with stochastic behaviors, probabilistic bisimulation is employed to minimize a given model, obtaining its equivalent form with fewer states. In this paper, we propose a novel technique to partition the state space of a given probabilistic model to its bisimulation classes. This technique uses the PRISM program of a given model and constructs some small versions of the model to train a classifier. It then applies supervised machine learning techniques to approximately classify the related partition. The resulting partition is then used to accelerate the standard bisimulation technique, significantly reducing the running time of the method. The experimental results show that the approach can decrease significantly the running time compared to state-of-the-art tools. [ABSTRACT FROM AUTHOR]

The Hub Location Problem (HLP) is a significant problem in combinatorial optimization consisting of two main components: location and network design. The HLP aims to develop an optimal strategy for various applications, such as product distribution, urban management, sensor network design, computer network, and communication network design. Additionally, the upgrading location problem arises when modifying specific components at a cost is possible. This paper focuses on upgrading the uncapacitated multiple allocation p-hub median problem (u-UMApHMP), where a predetermined budget and bound of changes are given. The aim is to modify certain network parameters to identify the p-hub median that improves the objective function value concerning the modified parameters. We propose a non-linear mathematical formulation for u-UMApHMP to achieve this goal. Then, we employ the McCormick technique to linearize the model. Subsequently, we solve the linearized model using the CPLEX solver and the Benders decomposition method. Finally, we present experimental results to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The usual t-test or F-test can not be used to analyze unreplicated two-level factorial designs, since all the observations are used to estimate the factor effects and no observation is left to estimate the error variance. To overcome this difficulty, various procedures have been proposed in the literature and several simulation studies have been carried out to compare the performance of these methods. The results of these studies have been inconclusive, and no test is widely accepted as a "best" test. In this paper, we present results that show theoretically that no test has high power against all possible alternatives; i.e. no test can detect all patterns of active effects. Therefore, in the absence of any prior information concerning active and inactive effects, no test can be preferred to any other test based on power and the choice of a test should be based on other considerations, such as ease of use, control of individual or experimental error rate, the purpose of the experiment, etc. [ABSTRACT FROM AUTHOR]

Reduced-order dynamic models of wireless power transfer (WPT) systems are desired to simplify the analysis and design of power control, phase synchronization, and maximum efficiency tracking. The reduced-order dynamic phasor model is a good choice because of its straightforward physical meaning and concise mathematical formula. However, the model relies on the assumption of loose coupling and loses accuracy when the coupling becomes stronger. In this paper, a model reduction method with split frequency matching is proposed to improve model accuracy under relatively strong coupling conditions, which is suitable for most short-distance WPT applications, such as wireless electrical vehicle charging. Split frequency matching is achieved through a pair of conjugate equivalent mutual inductances, which are derived from the asymmetry characteristics of the full-order dynamic phasor model in the positive and negative frequency domains. The proposed model retains the advantages of the existing model while significantly improving the accuracy under strong coupling conditions. Its characteristics are verified by comparing the experimental results and model predictions under both large step changes and small-signal perturbations. [ABSTRACT FROM AUTHOR]

In this paper, the research hypothesis of conservation of hardness coefficient is put forward, and a mathematical formula for describing and analyzing the relationship between hardness coefficient and bond energy is established in this model. The binding process of two heteronuclear atoms can be represented by Cassini oval in dynamic form, every molecular state corresponds to one of these graphs; then the critical phenomena of molecular deformation are discovered and the calculated potential energy at the critical point is consistent with the experimental dissociation energy of molecules (R is 0.99999, P < 0.0001). [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the local well-posedness and blow up of solutions for a class of time- and space-fractional diffusion wave equation in a fractional power space associated with the Laplace operator. First, we give the definition of the solution operator which is a noteworthy extension of the solution operator of the corresponding time-fractional diffusion wave equation. We have analyzed the properties of the solution operator in the fractional power space and Lebesgue space. Next, based on some estimates of the solution operator and source term, we prove the well-posedness of mild solutions by using the contraction mapping principle. We have also investigated the blow up of solutions by using the test function method. The last result describes the properties of mild solutions when α → 1 − . The main feature of the proof is the reasonable use of continuous embedding between fractional space and Lebesgue space. [ABSTRACT FROM AUTHOR]

In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function. [ABSTRACT FROM AUTHOR]

This paper mainly studies the least-squares solutions of matrix equation A X B = C under a semi-tensor product. According to the definition of the semi-tensor product, the equation is transformed into an ordinary matrix equation. Then, the least-squares solutions of matrix-vector and matrix equations respectively investigated by applying the derivation of matrix operations. Finally, the specific form of the least-squares solutions is given. [ABSTRACT FROM AUTHOR]

In this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given. It is proven that not all of the generalized quaternion algebras have Hopf algebraic structures. When the generalized quaternion algebras have Hopf algebraic structures, we describe all the Hopf algebra structures. Finally, we shall prove that all the Hopf algebra structures on the generalized quaternion algebras are isomorphic to Sweedler Hopf algebra, which is consistent with the classification of 4-dimensional Hopf algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider the commutators associated with the fractional maximal function and sharp maximal function when symbol function b in Lipschitz spaces. We give some characterizations of the Lipschitz spaces via the boundedness of these commutators on total Morrey spaces. [ABSTRACT FROM AUTHOR]

We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogeneous weights, J. Funct. Anal. 268 (2015) 3278–3289], where Hardy's inequalities were considered for the antisymmetric functions in the case of the 1D particles. As a byproduct we obtain some Sobolev and Gagliardo–Nirenberg type inequalities that are applied to the study of spectral properties of Schrödinger operators. [ABSTRACT FROM AUTHOR]

The paper proposes an iterative method for solving a variational inclusion with the sum of two operators in a Hilbert space. The method can be considered as a combination of the proximal contraction method, the regularization method, and the multi-step inertial technique. Theorem of strong convergence is established under mild conditions imposed on cost operators and control parameters. [ABSTRACT FROM AUTHOR]

In this paper, we propose three self-adaptive relaxed CQ-algorithms with projections onto halfspaces for solving a split equality problem. The stepsize of the algorithms is dynamically calculated without any prior information regarding operator norms. Moreover, we prove the strong convergence to the minimum-norm solution of the split equality problem. Finally, we test the validity of our results by conducting some numerical experiments and consider signal recovery problems as applications. [ABSTRACT FROM AUTHOR]

This study conducts an in-depth exploration into the principal factors that influence the reliability of specialized rail cars and auto-rail vehicles. It places a particular emphasis on key performance metrics including the average operational duration prior to failure, the probability of faultless operation, the rate of failure, and the gamma-percentage resource. Additionally, the paper examines various methodologies for computing these metrics and quantitatively evaluating their respective values. It elucidates how specific units of electromechanical equipment, which operate in conjunction with asynchronous motors and clutches, exhibit distribution patterns during failure that overlap between exponential and normal distributions. The study further presents a mathematical formula to approximate the reliability density of the distribution, a critical factor in recalibrating the metrics associated with specialized rail cars. [ABSTRACT FROM AUTHOR]

Increasing global temperatures due to high atmospheric carbon dioxide (CO2) concentrations may cause an imbalance in the carbon circulation on earth. It has been reported that CO2 emissions from natural soils in all terrestrial areas on Earth account for about 25% of atmospheric CO2 emissions in the global carbon cycle. A tendency is well known that the higher the soil temperature with the higher the metabolic activity of microorganisms in the soil. Furthermore, since the global soil CO2 emissions are huge amount that approximately seven times the total atmospheric CO2 emissions from human origin, it is necessary to investigate the increasing rate of soil CO2 emission rate per unit area and unit time on a global scale (global soil CO2 efflux) that is affected by soil temperature rise due to global warming expected in the coming decades. In this paper, we modeled soil CO2 efflux vs. diurnal and seasonal variation in soil temperature at a measurement point using a formula that is an exponential function of soil temperature and then evaluated the effect of increasing average soil temperature due to surface air temperature rise by global warming. We have proposed a method to analogically evaluate the potential of increasing the rate of soil CO2 efflux against a change of 1°C in soil temperature based on the model equation. The power index b (°C-1) just indicates the potential of increasing the rate of soil CO2 efflux to soil temperature rise in any land area with different soil temperatures on earth. Finally, the values of b were obtained from the published literature with field measurement data at 71 locations in 10 countries including our data measured at the Ito campus, Kyushu University. The average rate of potential increase in soil CO2 efflux is 0.10°C-1 regardless of vegetation, annual rainfall (precipitation), soil type, and soil components (carbon and nitrogen content). In conclusion, assuming the average soil temperature rises by 1°C and ignoring any effects reducing soil CO2 reduction due to global warming, the potential increase in annual global soil CO2 efflux is roughly estimated at 22 billion tons-CO2/year. [ABSTRACT FROM AUTHOR]

The definition of Fermatean fuzzy soft sets and some of its features are introduced in this study. A Fermatean fuzzy soft set is a parameterized family of Fermatean fuzzy sets and a generalization of intuitionistic and Pythagorean fuzzy soft sets. This paper presents a definition of the Fermatean fuzzy soft entropy. Also acquired are the formulae for standard distance measures such as Hamming and Euclidean distance. Other formulas have also been proposed for calculating the entropy and distance measurements of FFSSs. Even if the entropy and distance measures are defined for other set extensions, they cannot be applied directly to Fermatean fuzzy soft sets. It can be used to determine the uncertainty associated with a Fermatean fuzzy soft set, discover similarities between any two Fermatean fuzzy soft sets using the proposed distance measures, and compare it to other existing structures in the literature. Fermatean fuzzy soft set applications in decision-making and pattern recognition difficulties are also examined. Finally, comparison studies with other known equations are performed. [ABSTRACT FROM AUTHOR]

This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, Hölder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. [ABSTRACT FROM AUTHOR]

The object of this paper is to study a generalized Mittag-Leffler function and a modified general class of functions which is reducible to several special functions. convergent conditions of these functions are discussed. Some results pertaining to the generalized Mittag-Leffler function and generating relations involving these functions are derived. Further, fractional integrals involving these functions are achieved. Some illustrative exclusive cases of the results are presented. [ABSTRACT FROM AUTHOR]