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The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students' learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students extemalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning. [ABSTRACT FROM AUTHOR]

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [ABSTRACT FROM AUTHOR]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]

In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ and $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ in the cyclotomic field ℚ(ζ n), 2 ∤ n, for a ∈ ℤ, ( a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]

Recent work by Volz (J Math Biol 56:293-310, 2008) has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to account for effects due to heterogeneity and finiteness of degree that are neglected in the standard mass-action SIR equations. In this note we offer an alternate derivation which arrives at a simpler-though equivalent-system of governing equations to that of Volz. This new derivation is more closely connected to the underlying physical processes, and the resulting equations are of comparable complexity to the mass-action SIR equations. We further show that earlier derivations of the final size of epidemics on networks can be reproduced using the same approach, thereby providing a common framework for calculating both the dynamics and the final size of an epidemic spreading on a random network. Under appropriate assumptions these equations reduce to the standard SIR equations, and we are able to estimate the magnitude of the error introduced by assuming the SIR equations. [ABSTRACT FROM AUTHOR]

Abstract  We generalize a result of F. Luca and A. Sankaranarayanan by proving that the set of n for which ϕ(1) ⃛ ϕ(n) is squareful is of zero density. A similar statement holds for σ (n) instead of ϕ(n) and for some other multiplicative functions. [ABSTRACT FROM AUTHOR]

In 1935, Erdös proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai's paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai's paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai's theorem using the Bombieri-Vinogradov theorem. [ABSTRACT FROM AUTHOR]

This paper presents a stabilized meshfree method formulated based on the strong formulation and local approximation using radial basis functions (RBFs). The purpose of this paper is two folds. First, a regularization procedure is developed for stabilizing the solution of the radial point collocation method (RPCM). Second, an adaptive scheme using the stabilized RPCM and residual based error indicator is established. It has been shown in this paper that the features of the meshfree strong-form method can facilitated an easier implementation of adaptive analysis. A new error indicator based on the residual is devised and used in this work. As shown in the numerical examples, the new error indicator can reflect the quality of the local approximation and the global accuracy of the solution. A number of examples have been presented to demonstrate the effectiveness of the present method for adaptive analysis. [ABSTRACT FROM AUTHOR]

We considered in Example 3.1 of the paper [1] an S-structure on R2 n+ s. We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3 s and then it is η-Einstein. [ABSTRACT FROM AUTHOR]

This article provides instructions in preparing a paper for publication in the "Journal of Optimization Theory and Applications." Some of these guidelines are the following: 1)submission of manuscripts in triplicate; 2) reference to English as the official language of the journal; 3) inclusion of an abstract of at least 50 to 100 words in each contribution; and, 4) the abstract should be followed by a list of four to five key words identifying the subject.

Traditionally, "the operator calculus of Born and Wiener" has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener's joint contribution to the topic is generally bypassed in historical accounts of quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener's work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions. [ABSTRACT FROM AUTHOR]

Presents manuscript guidelines for papers to be published in the "Journal of Optimization Theory and Applications."

In [1] Kohli and Vashistha gave an analogue of probabilistic version of Pant's Theorem ([2], Theorem 1). We note that mappings defined in Examples 3.6 to 3.8 of [1] are not self maps as claimed in the Definitions 3.1 and 3.2. In this context, we provide some relevant examples to complete the interesting results. [ABSTRACT FROM AUTHOR]

This is an attachment to a letter of the author to Alexander Zvonkin (dated November 1, 1995). It is reproduced here with the kind permission of the author. [ABSTRACT FROM AUTHOR]

O. Einstein (2008) proved Bollobás-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker variants. [ABSTRACT FROM AUTHOR]

A greater use of recycled wastepaper would preserve virgin forests as well as reducing the amount of wastepaper going to landfills. Theseenvironmental goals depend critically on the elasticity of substitution between pulp and wastepaper in producing paper and paperboard. Since most of the pulp consumed by U.S. paper mills and paperboard mills is transferred internally from vertically integrated pulp mills, the price data on pulp is not available. This paper constructs an econometric model which enables us to estimate the substitution possibility between unpriced pulp and wastepaper in the U.S. paper and paperboard industry. Empirical results show that the elasticity of substitution between unpriced pulp and wastepaper is positive, but not statistically significant. [ABSTRACT FROM AUTHOR]

Abstract??We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction (fission, ?cotensor?,par) against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we callipsilateral: applying such a rule does not make any (sub)formula change sides?from the left to the right of the sequent separator or vice versa. Some possibilities for a semantic characterization of the resulting logic are also explored. The paper concludes with three open questions. [ABSTRACT FROM AUTHOR]

The global stress distribution and state parameter analysis of the building's main structure is an urgent problem to be solved in the online state assessment technology of building structure health. In this paper, a stress curve clustering algorithm of fiber Bragg grating stress sensor based on density clustering algorithm is proposed. To solve the problem of large dimension and sparse sample space of sensor stress curve, the distance between samples is measured based on improved cosine similarity. Aiming at the problem of low efficiency and poor effect of traditional clustering algorithm, density clustering algorithm based on mutual nearest neighbor is used to cluster. Finally, the classification of the daily stress load characteristics of the sensor is realized, which provides a basis for constructing the mathematical analysis model of building health. The experimental results show that the stress curve clustering method proposed in this paper is better than the latest clustering algorithms such as HDBSCAN, CBKM, K-mean++,FINCH and NPIR, and is suitable for the feature classification of stress curves of fiber Bragg grating sensors. [ABSTRACT FROM AUTHOR]

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies. [ABSTRACT FROM AUTHOR]

Doubly salient permanent magnet machine (DSPMM), which is a branch of stator-Permanent Magnet (PM) machine, is becoming more and more attractive due to higher power density and fault-tolerant capability, better mechanical robustness, simpler rotor configuration, lower PM consumption and higher PM material utilization efficiency. Thus, it has great application potential in the fields of transportation electrification and renewable energy generation. However, due to the special doubly salient structure, PM flux-linkage and inductance have the same variation period, which would complicate the relationship between the current and torque, and bring difficulties in the modeling and control (even after Park's transformation). In order to solve these problems, this paper will develop, analyze and compare the different current waveforms which could theoretically reduce the torque ripple and the transformations which could decouple the model in the rotating stationary frame for a simplified DSPMM model neglecting the higher harmonics. Based on the mathematical analysis, this paper would provide a clear relationship between the current waveforms and the torque with the DSPMM parameters, and the possible transformation which could simplify the model and be used in the control system. [ABSTRACT FROM AUTHOR]

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems. [ABSTRACT FROM AUTHOR]

Deterministic (ordinary differential equation) models for the transmission dynamics of vector-borne diseases that incorporate disease-induced death in the host(s) population(s) are generally known to exhibit the phenomenon of backward bifurcation (where a stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Further, it is well known that, in these models, the phenomenon of backward bifurcation does not occur when the disease-induced death rate is negligible (e.g., if the disease-induced death rate is set to zero). In a recent paper on the transmission dynamics of visceral leishmaniasis (a disease vectored by sandflies), titled “A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan,” published in Bulletin of Mathematical Biology, Vol. 79, Pages 1110-1134, 2017, Ghosh et al. (2017) stated that their deterministic model undergoes a backward bifurcation even when the disease-induced mortality in the host population is set to zero. This result is contrary to the well-established theory on the dynamics of vector-borne diseases. In this short note, we illustrate some of the key errors in the Ghosh et al. (2017) study. [ABSTRACT FROM AUTHOR]

The underground pipeline network in the city is so intertwined that the concealed excavation of a metro station inevitably leads to a series of underground pipelines, causing settlement deformation and further risk of leakage. The existing theoretical methods for analysing settlement deformation are mostly for circular chambers, whereas metro stations have a nearly square cross-sectional form and different construction methods are very different, which have a greater impact on the deformation of the overlying pipelines. In this paper, based on the random medium theory and Peck's formula, the improved random medium model for predicting ground deformation is modified, the correction coefficients λ and η for the influence of different construction methods are proposed, the prediction model of underground pipeline deformation under different construction methods is obtained, and the numerical models of four work methods commonly used in urban tunnel construction: pillar hole method, side hole method, middle hole method and Pile-Beam-Arch (PBA) method are constructed through simulation, and the mathematical analysis software was used to fit the results to the model and obtain the range of correction coefficients λ and η for each of the four methods, and the accuracy and applicability of the theoretical model was verified by combining with actual engineering cases. The influence on the overlying pipes is in descending order: side hole method, pillar hole method, middle hole method and PBA method. The theoretical model provided in this paper for predicting the deformation of pipes in any overlying strata of the tunnel is well suited to the actual project and has a high degree of correlation with the measured results. [ABSTRACT FROM AUTHOR]

The article discusses the 2005 best paper awardee of the Computational Optimization and Applications entitled "Hyper-Sparsity in the Revised Simplex Method and How to Exploit It," by Julian Hall and Ken McKinnon of the University of Edinburgh, Scotland. The continuity in the sparsity of the right -hand-side was initially denoted as super-sparsity. The authors observed that the same behaviour was detected when applying the basis matrix factors to the two linear systems that are solved in each process of the revised simple system. For linear programming problems that exhibit hyper-sparsity, the value of it will count on the performance of those elements.

In this note we will show that finitely generated condition is necessary in Theorem 1.2 of the above mentioned paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global exponential synchronization issues for variable-order fractional complex dynamic networks (FCDNs). Firstly, a new derivative operator, which is called as the generalized Caputo variable-order fractional derivative, is developed, and some properties and lemmas are rigorous proved. Secondly, a new dynamic event-triggered control mechanism is designed to realize the synchronization objective, where the generalized Caputo variable-order fractional derivative is applied to characterize the evolution state of internal dynamic variable. And the exclusion for Zeno behavior is verified by contradiction analysis method. Thirdly, a class of functions, which is an extension of the Lipschitz function, is introduced to model the nonlinear dynamics for the considered system. With the aid of fractional Lyapunov functional method, some auxiliary functions and advanced mathematical analysis techniques, the global exponential synchronization conditions are established in terms of linear matrix inequalities (LMIs). Finally, the correctness of the theoretical results and the feasibility of the designed controller in this paper are confirmed by applying a numerical simulation example. [ABSTRACT FROM AUTHOR]

Dictionary learning is an effective feature learning method, leading to many remarkable results in data representation and classification tasks. However, dictionary learning is performed on the original data representation. In some cases, the capability of representation and discriminability of the learned dictionaries may need to be performed better, i.e., with only sparse but not low rank. In this paper, we propose a novel efficient data representation learning method by combining dictionary learning and self-representation, which utilizes both properties of sparsity in dictionary learning and low-rank in low-rank representation (LRR) simultaneously. Thus both the sparse and low-rank properties of the data representation can be naturally captured by our method. To obtain the solution of our proposed method effectively, we also innovatively introduce a more generalized data representation model in this paper. To our best knowledge, its closed-form solution is first derived analytically through our rigorous mathematical analysis. Experimental results show that our method not only can be used for data pre-processing but also can realize better dictionary learning. The samples in the same class can have similar representations by our method, and the discriminability of the learned dictionary can also be enhanced. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, a new application of the Taylor series method (TSM) and its properties is used to solve partial differential equation problems with a singular limit value problem. We are particularly interested in applying this method to a certain class of physical problems such as Lane Emden–Fowler partial differential equations. The results obtained show that this analytical technique is very simple and effective compared to other methods. [ABSTRACT FROM AUTHOR]

In this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections. [ABSTRACT FROM AUTHOR]

The GRG journal's Golden Oldies series has republished more than 80 important old papers in general relativity and gravitation. This announcement updates and replaces the one made in Gen. Relativ. Gravit. 39 (7), 1043 (2007) as modified by the editorial announcement in Gen. Relativ. Gravit. 44 (10), 2419 (2012). [ABSTRACT FROM AUTHOR]

This paper aims at mathematical analyzing of a parabolic chemotaxis model with nonlinear cross-diffusion transposed from the euclidean case into weighted networks. Taking into account certain applications in neurobiology, data transmission and wound healing process, a modified Keller–Segel model with volume-filling effect is studied. The novelty with respect to other related papers lies in the numerical investigation of chemotaxis process in weighted networks and of asymptotic self-similar behavior of solutions by time dependent scaling. The global existence and the large-time dynamics of solutions are detailed. Finally, the theoretical characteristics of the discrete solutions are explored numerically. [ABSTRACT FROM AUTHOR]

This paper is concerned with time-asymptotic nonlinear stability of rarefaction waves to the Cauchy problem for one-dimensional compressible non-isentropic magnetohydrodynamics (MHD) equations (including its isentropic case), which describe the motion of a conducting fluid in a magnetic field. Through some elaborate and rigorous mathematical analysis, we can construct the rarefaction waves v r , u r , θ r , b r (x / t) where magnetic component b r x / t is a nontrivial profile, namely a non-constant function. Then the solution of the compressible MHD equations is proved to tend towards the rarefaction waves time-asymptotically under small initial perturbations and weak wave strength, and also under a technical assumption that the parameter β = v + b + is bounded by a specific constant. The proof of the main result is based on elementary L 2 energy methods. [ABSTRACT FROM AUTHOR]

The presented paper is a compendium or a kind of précis of relationships between the four classical theorems of mathematical analysis. More precisely, the first aim of this paper is to present the equivalence of the four classical theorems: the Hahn–Banach theorem, the Mazur–Orlicz theorem, the Markov–Kakutani fixed-point theorem and the von Neumann theorem on amenability of Abelian groups. The second purpose is to prove these equivalences in Zermelo–Fraenkel set theory with the axiom of choice replaced by the Boolean prime ideal theorem, from which we can also prove the Hahn–Banach theorem. [ABSTRACT FROM AUTHOR]

Object detection is one of the core tasks of computer vision, and bounding box (bbox) regression is one of the basic tasks of object detection. In recent years of related research, bbox regression is often used in the Intersection over Union (IoU) loss and its improved version. In this paper, for the first time, we introduce the Dice coefficient into the regression loss calculation and propose a new measure which is superior to and can replace the IoU. We define three properties of the new measure and prove the theory by mathematical reasoning and analysis of the existing work. This paper also proposes the N-IoU regression loss family. And the superiority of the N-IoU regression loss family is proved by designing simulation experiments and comparative experiments. The main results of this paper are: (1) The proposed new measure is better than IoU which can be used to evaluate bounding box regression, and the three properties of the new measure can be used as a broad criterion for the design of regression loss functions; and (2) we propose N-IoU loss. The parameter n of N-IOU can be debugged, which can be widely adapted to different application scenarios with higher flexibility, and the regression performance is better. [ABSTRACT FROM AUTHOR]

A unique photonic technique has been suggested and explained for different types of waveform generation, the proposed technique employs double LiNbO3 Mach–Zehnder single drive cascading modulators for pulse shaping and responsive modulators for polarization. By ordering the incident light polarized states it can produce accordingly dual distinct Spectra on two components of orthogonal polarization. The desired waveform would be obtained by detecting the photocurrents from the photodetector. This paper describes the complete mathematical analysis of polarization dependent cascade Mach–Zehnder modulators to generate a variety of microwave forms. Comprehensive mathematical analyses including simulations have been presented, and therefore we have successfully developed as well as generated delta waveform, half-wave rectifier waveform, full-wave rectifier waveform, and square wave types waveform. At the end of the paper experimental analysis has been done for the proof of concept purpose while the experimental results of a variety of microwave waveforms are compared with theoretical ones. There are good agreements between theoretical results with experimental ones. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

The emergence of cross-border e-commerce has brought new opportunities to traditional enterprises. This paper discusses the partner selection of cross-border e-commerce companies in the B2B mode. It constructs a theoretical model of partner selection of cross-border e-commerce enterprises based on literature review. Through the mathematical analysis of an asymmetric evolutionary game model, it is considered that the model has an evolutionarily stable strategy. Based on it, a multi-agent model is constructed. The results of the simulation reveal the mediation role of trust between corporate reputation and enterprise cooperation. Simultaneously, it verified the moderation effect of information sharing between the trust and cooperation of cross-border e-commerce companies. It also provides explanations for the inconsistency in the relationship between trust and cooperative behavior. From both mathematical and data perspectives, this paper attempts to test the theoretical model proposed, which enriches the methodology to test the theory. [ABSTRACT FROM AUTHOR]

The popularity of football among fans to analyze the game has been immense with the advent of internet. The concept of making a dream team in football has become a new fashion for the football lovers. The paper focuses in helping achieving this prediction of a football dream team. The aim of this research is to assess the dynamics of a complex topological structure when prompted with random entities whose attributes are known to us. Using graph theory and vectorial distances, the dream team is evaluated on the basis of individual abilities and interplayer synergy. Instead of focusing on discrete events in a match, this framework proposes an idea in which a dream team is quantified on the basis of their positional attributes. Each player is rated in accordance to the position he is playing, which eventually helps in finding the overall team rating. The second part of this research uses graph theory to evaluate structural and topological properties of interpersonal interactions of teammates. Teammates are treated as nodes of a graph, where each edge exemplifies the strength of their interpersonal interaction. The strength of the bond depends on on-field interactions via ball passing, ball receiving and communication which depend on experience of playing together, Nationality and Club. The methodology adopted in this paper can be a formidable basis for similarly situated larger setups involving much larger intricacies. Using this framework, we can see the behavior of a hypothetical topological structure whose node attributes are known to us, thus projecting its performance as a team and individual entities. [ABSTRACT FROM AUTHOR]

A preface to a 2014 issue of the "Journal of Optimization Theory & Applications" is presented.

Introduces a series of articles which appeared in the January 2005 issue. Reference to the papers presented at the 5th International Conference on Optimization: Techniques and Applications in Hong Kong, China; Claim that the papers were divided into three categories which are nonlinear optimization, scheduling and discrete optimization and engineering optimization.

The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB annual meeting in Dundee the Society asked the editor of the BMB to produce an analysis of impact factor, subject matter of papers, submission rates etc. Other members of the society were interested in the handling times of articles and wanted comparisons with other (appropriate) journals. In this article we present a brief history of the journal and report on how the journal impact factor has grown substantially in the last few years. We also present an analysis of subject areas of published papers over the past two years. We finally present data on times from receipt of paper to acceptance, acceptance to print (and to online publication) and compare these data with some other journals. [Copyright &y& Elsevier]

Deblurring is a challenging problem in image restoration. It's important to use both local details and global information of the image for deblurring. Therefore, this paper proposes a deblurring model that integrates Convolution and Transformer in a parallel manner. Unlike existing methods that use single operators or serial combinations, the convolution operation and self-attention mechanism in this model are learned in parallel and extract features separately, and then the features are fused in the frequency domain. The convolution operation is beneficial in extracting local information while the self-attention mechanism focuses more on global information. The parallel structure enables the model to capture both local and global information simultaneously. Additionally, the frequency domain fusion module is proposed based on the analysis of the mathematical model of image blur, and the results indicate that the proposed model is reasonable. Experiments on multiple deblurring datasets verify that the proposed parallel structure of Convolution-Transformer and frequency domain fusion method are effective. [ABSTRACT FROM AUTHOR]