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Study Design: Cross-sectional study.Objective: To investigate the equivalence of electronic and paper version of self-report questionnaires for the assessment of disability, pain, fear of movement, depression, and physical activity of patients with chronic low back pain (LBP).Summary Of Background Data: Paper and electronic versions of self-report questionnaires are commonly used for assessment of patients with LBP. However, the equivalence of self-report questionnaires commonly used for assessment of patients with chronic LBP remains unclear.Methods: Seventy-nine individuals with chronic LBP seeking physiotherapy care were recruited. Participants attended the clinic twice with an interval of 1 week and completed the self-reported questionnaires in a random order. The following questionnaires were administered: Roland Morris Disability Questionnaire (RMDQ); 11-point numerical rating scale (NRS); Tampa Scale for Kinesiophobia (TSK); Center for Epidemiological Studies-Depression (CES-D), and Baecke Habitual Physical Activity Questionnaire (BPAQ). To investigate the equivalence between the two questionnaire versions, intraclass correlation coefficient with 95% confidence interval and Bland-Altman plotting was used.Results: The paper and electronic versions of the RMDQ, TSK, and CES-D showed good reliability and the showed moderate reliability. In contrast, the NRS showed poor reliability between the electronic and paper versions.Conclusion: Our findings support that the electronic version of the RMDQ, TSK, CES-D, and BPAQ can be administered in clinical and research settings for assessment of patients with chronic LBP. Nevertheless, electronic version of the NRS for assessment of pain intensity should not be used interchangeably in clinical practice in patients with chronic LBP.Level Of Evidence: 3. [ABSTRACT FROM AUTHOR]

Score equivalency of two Computer-Based Testing (henceforth CBT) and Paper-and-Pencil-Based Testing (henceforth PBT) versions has turned into a controversial issue during the last decade in Iran. The comparability of mean scores obtained from two CBT and PBT formats of test should be investigated to see if test takers' testing performance is influenced by the effects of testing administration mode. This research was conducted to examine score equivalency across modes as well as the relationship of gender, and testing mode preference with test takers' performance on computerized testing. The information on testing mode preference and attitudes towards CBT and its features was supported by a focus group interview. Findings indicated that the scores of test takers were not different in both modes and there was no statistically significant relationship between moderator above variables and CBT performance. [ABSTRACT FROM AUTHOR]

In behavior analysis, research on stimulus equivalence has been an area of high activity for more than 45 years. Murray Sidman's contribution was crucial in the development of this field, and, thus, it seems informative to highlight the experiments that were necessary in the development of the descriptive model of equivalence relations and behavior. The purpose of this paper is to provide an overview of the significant work that gave the historical context for Sidman and colleagues' conceptualization of stimulus equivalence as it was presented in 1982. This article emphasizes the 31 papers and chapters written by Sidman and colleagues that focus on research questions within stimulus control. The chapters and papers are organized according to their dimensions in behavior analysis and according to whether they can be categorized as instruction programs or experimental studies. The issues discussed regarding these papers and chapters include types of stimuli, matching, discriminations, and others. Collectively, this early work influenced methods and considerations about stimulus control issues that have been important to the development of stimulus equivalence. [ABSTRACT FROM AUTHOR]

The increasing number of self-report surveys being collected using computers has led to a body of literature examining the response rates for computerized surveys compared with the more traditional paper-and-pencil method. However, results from individual studies have been inconsistent, and the meta-analyses available on this topic have included studies from a restricted range of years and did not use proper statistical procedures for examining comparability. Consequently, we conducted a meta-analysis with 96 independent effect sizes spanning over two decades of studies; we also assessed potential moderators. Comparability was determined using confidence interval equivalence testing procedures. The meta-analysis indicated nonequivalence, with those in the paper-and-pencil condition being almost twice as likely to return surveys as those in the computer condition. There was large heterogeneity of variance, and 11 of the 18 potential moderators were significant. Two meta-regressions yielded only two significant unique moderators: population and type of measure. Results highlighted issues within the response rate literature that can be addressed in future studies, as well as provided an example of using equivalence testing in meta-analyses. [ABSTRACT FROM AUTHOR]

For many years, reading comprehension in the Programme for International Student Assessment (PISA) was measured via paper‐based assessment (PBA). In the 2015 cycle, computer‐based assessment (CBA) was introduced, raising the question of whether central equivalence criteria required for a valid interpretation of the results are fulfilled. As an extension of the PISA 2012 main study in Germany, a random subsample of two intact PISA reading clusters, either computerized or paper‐based, was assessed using a random group design with an additional within‐subject variation. The results are in line with the hypothesis of construct equivalence. That is, the latent cross‐mode correlation of PISA reading comprehension was not significantly different from the expected correlation between the two clusters. Significant mode effects on item difficulties were observed for a small number of items only. Interindividual differences found in mode effects were negatively correlated with reading comprehension, but were not predicted by basic computer skills or gender. Further differences between modes were found with respect to the number of missing values. [ABSTRACT FROM AUTHOR]

This work is concerned with the consistency conditions for the equations in max plus algebra. The three classes of the max plus linear equations presented in the paper Shinzawa [Ultra discrete permanent and the consistency of max plus linear equations, Linear Algebra Appl. 506 (2016) 445–477] can be equivalently converted into the corresponding system of inequalities. The equivalence relation between ultra discrete permanent and maximum cycle mean is suggested. Thus, the necessary and sufficient conditions for solvability of the equations are obtained using the maximum cycle mean in this note. [ABSTRACT FROM AUTHOR]

The Randić index (R) and the geometric-arithmetic index (GA) are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randić and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randić and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6. [ABSTRACT FROM AUTHOR]

In this tutorial note we consider the class of non-convex semi-infinite optimization problems which are defined by (one or) finitely many objective functions as well as infinitely many constraints in a finitedimensional space. We present an overview of recent results on the so-called p-power transformation which changes the original problem equivalently locally around a solution point. This transformation is a convexification procedure for the Lagrangian where the functions in the original problem are substituted by their p-th powers. As a consequence, the convexity of the so-transformed Lagrangian allows the application of local duality theory and corresponding solution methods locally around this solution point of the original problem. [ABSTRACT FROM AUTHOR]

The sixth paper, "On Some New Ostrowski-Mercer-Type Inequalities for Differentiable Functions", by Sial et al. [[6]], establishes a new integral identity involving differentiable functions and uses it for some new Ostrowski-Mercer-type inequalities for differentiable convex functions. The importance of inequalities in Mathematics is beautifully summarized in a citation attributed to Respected Professor Andrey Nikolaevich Kolmogorov: HT

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper. [ABSTRACT FROM AUTHOR]

In this meta syntheses paper, I explore gender as a social factor that interacts with both the cognitive and affective domains of education by explaining what it means for mathematics to be gendered and how we can use mathematics education to promote gender fairness as a form of social justice. I start by discussing gender as a dichotomy and how educational research transitioned from a physiological to a socio-cultural perspective. Guided by Ferguson’s and Bjerrun-Nielsen’s Four-Perspective Gender model, and Cohen and Martin’s Four Dimensional Model of Gender. I argue that mathematics education can be designed to promote gender equity only by considering these dimensions, and when there is a deliberate effort to examine how our exercise of education widens or narrows gender gap in terms of the four dimensions of gender equality: equality to access, learning experience, educational outcomes, and most importantly, external results. I discuss mathematics as an area perceived to embody a symbolic gender and what can be done through mathematics education to break that stereotype and contribute to the furthering equality to external results. I focus this discussion into the context of the Philippines and why it may be essential for educational reforms to zoom out to include other equally important dimensions of gender other than equality to access. [ABSTRACT FROM AUTHOR]

Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalized previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with nonrational but meromorphic components, it admits an also meromorphic, and in fact rational, inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and instead uses bivariate factoring as a fundamental tool. The algorithm has been implemented in the computer algebra system Maple and can be freely downloaded and used. [ABSTRACT FROM AUTHOR]

In this note we show that the presented proof of [1, th. 12] , being based on a false statement appearing in this proof, is not viable for all of the proclaimed values of the involved parameters. We also determine necessary and sufficient conditions for those parameters, which provides that the considered statement, and therefore [1, th. 12] itself, still remains valid. [ABSTRACT FROM AUTHOR]

The paper presents a critical review and new accomplishments on the equivalence of the first-order displacement-based zigzag theories for laminated composite and sandwich structures. Zigzag theories (ZZTs) have widely spread among researchers over the last few decades thanks to their accuracy in predicting the response of multilayered composite and sandwich structures while retaining the simplicity of their underlying equivalent single-layer (ESL) theory. The displacement field consists of two main contributions: the global one, able to describe the overall structural behaviour, and the local layer-wise one that considers the transverse shear continuity at the layer interfaces that describe the "zigzag" displacement pattern typical of multilayered structures. In the framework of displacement-based linear ZZTs, various assumptions have been made on the local contribution, and different theories have been deduced. This paper aims to provide a unified formulation for first-order ZZTs, highlighting some common aspects and underlying equivalencies with existing formulations. The mathematical demonstrations and the numerical examples prove the equivalence of the approaches to characterising local zigzag enrichment. Finally, it is demonstrated that the kinematic assumptions are the discriminants of the ZZTs' accuracy. [ABSTRACT FROM AUTHOR]

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN 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.)

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]

The paper presents a novel approach to generalize the two-point weighted Ostrowski's formula for Riemann-Stieltjes integrals by utilizing a unique class of functions of bounded r - variation. The proposed approach yields several results that exhibit sharp and better bounds compared to existing established results by using parameters and weights. Additionally, the paper also captures many of the known results as special cases. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a relation between the critical points of the skew-circulant matrix and the eigenvalues of its principal matrix. Furthermore, we reprove the inequality about the zeros of a polynomial and its critical points by using the properties of skew-circulant matrix, which is to show that we can not only find the skew-circulant matrix, but also give more structure matrices to prove this inequality. [ABSTRACT FROM AUTHOR]

In this paper, we present some further refinements of the Tan-Xie inequality for sector matrices and its applications due to Nasiri and Furuichi [J. Math. Inequal., 15 (2021), 1425-1434]. [ABSTRACT FROM AUTHOR]

This paper aims at clarifying the questions regarding the effects of the scaling method on the discrepancy function of the metric measurement invariance model. We provide examples and a formal account showing that neither the choice of the scaling method in general nor the choice of a particular referent indicator affects the value of the discrepancy function. Thus, the test statistic is not affected by the scaling method, either. The results rely on an appropriate application of the scaling restrictions, which can be phrased as a simple rule: "Apply the scaling restriction in one group only!" We develop formulas to calculate the degrees of freedom of χ²-difference tests comparing metric models to the corresponding configural model. Our findings show that it is impossible to test the invariance of the estimated loading of exactly one indicator, because metric MI models aimed at doing so are actually equivalent to the configural model. [ABSTRACT FROM AUTHOR]

In the paper Crucial and unsolved problems on Atanassov’s intuitionistic fuzzy sets, D.-F. Li pointed out that some kind of definitions of operations over Atanassov’s intuitionistic fuzzy sets are incorrect. We can see that, near 30 years after the first Atanassov’s papers, there exist some misunderstandings related not only on the name, but also on the basic operations on IFSs. Those misunderstandings concern, this time, on the operations of the sum and product. Li also casts doubt the equivalence of the intuitionistic fuzzy sets and the interval-valued fuzzy sets. In this paper, the Li’s reasoning is presented and commented. [ABSTRACT FROM AUTHOR]

Tivers' landmark paper about the geographical study of women published in Area in 1978 raised significant issues for the discipline when it was published. I review Tivers' paper and draw attention to three issues that remain pertinent for geographers. First, I explore the need to be critical about the concept of the household. Second, I reflect on the attention that geographers have given to the family. Finally, I re‐emphasise the importance of continuing to focus on structural inequalities as Tivers initially suggested in 1978. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of weakly semiprime ideals and weakly n -systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R − P being a weakly n -system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide. [ABSTRACT FROM AUTHOR]

Running time analysis of evolutionary algorithms for continuous optimization is one research challenge in the field of evolutionary algorithms (EAs). However, the theoretical analysis results have rarely been applied to evolutionary algorithms for continuous optimization in practice, let alone their variants for evolution strategy. In this paper, we regarded the first hitting time of evolution strategy as the stopping time of the renewal process on the basis of the renewal process and in combination with Wald's inequality and stopping time theory. Afterwards, to demonstrate the application of the proposed model in the first hitting time analysis of (1 + 1) ES, we analyzed it with different mutation operators on the sphere function. First, we significantly improved the lower bound on the first hitting time of (1 + 1) ES with a uniform mutation operator, i.e., from Ω (n) to Ω (e c n) . Next, O (n 2 n) was the upper bound on the first hitting time of (1 + 1) ES with a Gaussian mutation operator from the initial distance R to half of the initial distance R /2. The numerical experimental results showed that the theoretical calculation was consistent with the actual running time, which provides a novel method for analyzing the first hitting time of EAs. [ABSTRACT FROM AUTHOR]

This paper addresses the recent body of research in algebra and algebraic thinking from 2018 to 2022. We reviewed 74 journal articles and identified four clusters of content areas: (a) literal symbols and symbolizing, (b) equivalence and the equal sign, (c) equations and systems, and (d) functions and graphing. We present the research on each of these content clusters, and we discuss insights on effective teaching practices and the social processes supporting algebraic reasoning. The research base shows that incorporating algebraic thinking into the elementary grades, emphasizing analytic and structural thinking processes, and emphasizing covariational reasoning supports students' meaningful learning of core algebraic ideas. We close with a discussion of the major theoretical contributions emerging from the past five years, offering suggestions for future research. [ABSTRACT FROM AUTHOR]

This paper studies grade 7 (age 13) students' expressed understanding about the equal sign/notion of equivalence in order to investigate what aspects of the concept that could be seen as an established knowledge at lower secondary school/middle school. Using items from different instruments and combining these to a new one that covered a broad spectrum of procedural and conceptual knowledge, we collected data from 159 students. The different statistical tests showed that if focusing only on separate items, it could confirm that students could be seen either having operational or relational understanding of the equal sign. However, when taking all results into account using several analyses, students' understanding appear to be much more complex. Instead of a dichotomized view, students' expressed knowledge of mathematical equivalence should be seen as a continuum. [ABSTRACT FROM AUTHOR]

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an 'alphabet of human thought'. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract objects, we should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz. [ABSTRACT FROM AUTHOR]

Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and two angularly equivalent norms, it is the case that if one of the norms has a property, then so does the other. In this paper, we show further results in this direction, namely angularly equivalent norms share the property of non-squareness; and that the exposed points of the unit balls are in the same direction, under the condition that these points are assumed to be smooth with respect to both norms. A discussion on (the angular equivalence of) the dual norms of angularly equivalent norms is also given, giving a partial answer to an open problem as stated in the paper by Kikianty and Sinnamon (2017). [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]

In this paper we obtain some refinements and reverses of Callebaut's inequality for isotonic functionals via a result of Young's inequality due to Cartwright and Field. [ABSTRACT FROM AUTHOR]

The overwhelming presence of a procedural meaning of equality and equations reported in previous research has led to a call for suitable pedagogical interventions to nurture a relational meaning of these concepts. This paper is a response to that call. Drawing on the theory of objectification, the first part deals with the configuration of a Grade 3 (8–9-year-old students) teaching–learning activity that seeks to create the classroom conditions for the formation of the mathematical operations and operation-based rules that underpin the algebraic simplification of linear equations. Instead of using problems involving abstract open arithmetic sentences or alphanumeric equations (e.g., 5 + _ _ = 16; 2 n + 3 = 11 ), the teaching–learning activity resorts to story-problems. Two visual semiotic systems serving to model and solve the story-problems were devised. The story-problems were framed in narratives that allowed the teacher and the students to infuse equations, their equating parts, and the mathematical operations with contextual meanings. The first part of the paper includes the theoretical assumptions about the teaching–learning activity and its configuration, and a rationale behind the devisal of the semiotic systems. The second part presents a Vygotskian multimodal genetic analysis of the teaching–learning activity; that is, an analysis that shows the formation of concepts in motion, in the process of their genesis. The genetic analysis sheds some light on the way students, in their work with the teacher, encountered and refined the cultural-historical algebraic meanings of the equal sign and equations, and the concepts required in solving equations. [ABSTRACT FROM AUTHOR]

Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. As a result, certain properties of programs appear non-trivial to formalize in purely logical terms. For example, the current characterization of strong equivalence for LPODs, does not coincide with logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence for LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs, a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs. [ABSTRACT FROM AUTHOR]

Fostering students' relational understanding of the equals sign is a challenge for math educators that begins in the primary levels and persists into tertiary education. In this paper, I develop an entry point, especially for students who only have an operational understanding of the equals sign, to the core idea of equivalence in linear algebra. My approach is informed by the history of mathematics: In the 17th and 18th centuries, mathematics research underwent an algebraicization, with mathematicians replacing their classical geometric questions with novel algebraic investigations. In this paper, I will offer geometric interpretations of two operations developed at the precipice of this monumental shift: algebraic substitution and Gaussian elimination. I will then utilize Lakoff & Johnson's theory of conceptual metaphor to compare and contrast this historically-grounded geometric re-interpretation of modern linear algebra to the direct algebraic interpretation taken in most modern textbooks. [ABSTRACT FROM AUTHOR]

Advanced mathematics is seen as an integral component of secondary teacher preparation, and thus most secondary teacher preparation programs require their students to complete an array of advanced mathematics courses. In recent years, though, researchers have questioned the utility of proposed connections between advanced and secondary mathematics. It is simply not clear in many cases—to researchers, teacher educators, and teachers themselves—exactly how advanced mathematics content is related to secondary content. In this paper, we propose using a conceptual analysis—a form of theory in which one explicitly describes ways of reasoning about a particular mathematical idea—to address this issue. Specifically, we use conceptual analyses for the foundational notions of equivalence and inverse to illustrate how the ways of reasoning needed to support productive engagement with tasks in advanced mathematics can mirror and reinforce those that are similarly productive in school mathematics. To do so, we propose conceptual analyses for the key concepts of equivalence and inverse and show how researchers can use these conceptual analyses to identify connections to school mathematics in advanced mathematical tasks that might otherwise be obscured and overlooked. We conclude by suggesting ways in which conceptual analyses might be productively used by both teacher educators and future teachers. [ABSTRACT FROM AUTHOR]

Alexander Grothendieck suggested creating a new branch of topology, called "topologie modérée". In a paper by N. A'Campo, L. Ji, and A. Papadopoulos the authors conclude that no such tame topology has been developed at a purely topological level. We see our theory of sets with distinguished families of subsets, which we call smopologies, as realising Grothendieck's idea and the demands of the mentioned paper. Dropping the requirement of stability under infinite unions makes it possible to obtain several equivalences of categories of spaces with categories of lattices. We show several variations in Stone duality and Esakia duality for categories of small or locally small spaces and some subclasses of strictly continuous (or bouned continuous) mappings. Such equivalences are better than the spectral reflector functor for usual topological spaces. Some spectralifications of Kolmogorov locally small spaces can be obtained by Stone duality. Small spaces or locally small spaces seem to be generalised topological spaces. However, looking at them as topological spaces with an additional structure is better. The language of smopologies and bounded continuous mappings simplifies the language of certain Grothendieck sites and permits us to glue together infinite families of definable sets in structures with topologies, which was important when developing the o-minimal homotopy theory. [ABSTRACT FROM AUTHOR]

The article explores the connections between Euler's limit and Stirling's estimate, showing that they have deep and surprising connections to each other. The author uses basic tools from a typical second semester calculus course to study the function family and prove the existence of Stirling's constant. The article also briefly discusses asymptotics and introduces the necessary basic ideas from this area. The author presents a new, elementary approach to proving Stirling's constant. This document provides an outline of the main ideas discussed in a previous paper. The paper focuses on the concept of equivalence in mathematical functions and the use of asymptotics. It emphasizes that the concepts discussed are accessible to undergraduate students with a background in calculus. The document also includes additional details to help readers understand the process of exploring new mathematical ideas. The paper introduces the function family and its connection to the Stirling sequence. The given text discusses the sign of the derivative of a function and its relationship to the sign of another function. The author defines a function g_c(x) as the natural logarithm of another function f_c(x), and obtains the derivative of g_c(x) using the Maclaurin expansion of the natural logarithm. The author then analyzes the sign of the derivative of g_c(x) by examining the sign of another function, denoted as η_c(x), for various values of c. The text concludes by showing that η_c(x) converges using the Alternating Series Test. The text discusses the convergence of an alternating power series [Extracted from the article]

In the paper, the authors simply review recent results of inequalities, monotonicity, signs of determinants, determinantal formulas, closed-form expressions, and identities of the Bernoulli numbers and polynomials, establish an identity involving the differences between the Bernoulli polynomials and the Bernoulli numbers, present two identities among the differences between the Bernoulli polynomials and the Bernoulli numbers in terms of a determinant and a partial Bell polynomial, and derive a determinantal formula of the differences between the Bernoulli polynomials and the Bernoulli numbers. [ABSTRACT FROM AUTHOR]

Let X be a 2-connected and 6-dimensional CW-complex such that H3(X) ⊗ Z2 = 0. This paper aims to describe the group E(X) of the self-homotopy equivalences of X modulo its normal subgroup E*(X) of the elements that induce the identity on the homology groups. Making use of the Whitehead exact sequence of X, denoted by WES(X), we define the group GS(X) of G-automorphisms of WES(X) and we prove that E(X)/E*(X) ≌ ΓS(X). [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the existence and uniqueness of the strong solution for the linear time-fractional partial differential equation with purely integral conditions. The aimed investigation is demonstrated based on the so-called energy inequality method and the density of the operator generated by the considered problem. To do so, we first set the position of the problem under consideration coupled with its corresponding equivalent problem, say problem (x). Afterward, we introduce some necessary functional spaces needed for exploring the existence and uniqueness of solution of problem (x). Finally, we investigate the existence and uniqueness of solution of the main operational equation. [ABSTRACT FROM AUTHOR]

In the paper, we establish two inequalities for differentiable bounded functions and Lipschitzian function, which are connected with Iyengar integral inequalities, and we present some new results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the general solution of the following functional inequality ||2 f (x)+2 f (y)+2 f (z)- f (x+y)- f (y+z)|| || || ≤ (x+z)||, and then investigate the generalized Hyers-Ulam stability of this inequality in Banach spaces and in non-Archimedean Banach spaces by using two different approaches. [ABSTRACT FROM AUTHOR]

In this paper, by the use of weight functions and the technique of real analysis, a new Hilbert-type integral inequality with a general nonhomogeneous kernel as H(xv(y)) is given. A few equivalent statements related to the best possible constant factor and parameters are considered. As applications, the equivalent forms, the operator expressions and some corollaries are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we establish two exponential double inequalities generalized Jordan's inequality. [ABSTRACT FROM AUTHOR]

In this paper, we mainly give a generalized refinement of Young's inequality due to Yang and Wang [J. Math. Inequal., 17 (2023), 205-217]. More precisely, we show that... As applications, we obtain some inequalities for operator, Hilbert-Schmidt norm and trace class norm. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in generalized numerical radius inequalities for the off-diagonal part of a positive semidefinite block matrix. These inequalities produce a new set of inequalities for products and sums of matrices and some inequalities related to sectorial matrices. [ABSTRACT FROM AUTHOR]

Let p be an odd prime and Zp the residue class ring modulo p. In this paper, we study representations of any element of Zp as the sum of a Lehmer number and a primitive root in Zp, and give an explicit inequality better than asymptotic formula for the number of representations. From this inequality, we obtained that each element of Zp can be represented as the sum of a Lehmer number and a primitive root for p > 2.5×1014. Moreover, using the algorithm we provided, we examined all the cases when p < 106 by computer. We also analyzed the time complexity of the algorithm and illustrated that it is extremely difficult to verify all the cases up to the bound 2.5×1014, and conjectured that any given element n ∈ Zp can be represented as the sum of a Lehmer number and a primitive root in Zp for all primes p except 2, 3, 5, 7, 11, 19, 31. [ABSTRACT FROM AUTHOR]

In this paper, we consider a degenerate hyperbolic inequality in an exterior domain under three types of boundary conditions: Dirichlet-type, Neumann-type, and Robin-type boundary conditions. Using a unified approach, we show that all the considered problems have the same Fujita critical exponent. Moreover, we answer some open questions from the literature regarding the critical case. [ABSTRACT FROM AUTHOR]

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp's notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs' understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed. [ABSTRACT FROM AUTHOR]

This paper introduces weak logical algebraic domains and a special class of quantum B-algebras, namely, cofinal quantum B-algebras. It proves that there is a dual equivalence between the category of cofinal quantum B-algebras and that of weak logical algebraic domains. In particular, the category of residuated posets is shown to be dual equivalent to that of logical algebraic domains. This correspondence generalizes the classical duality of posets and algebraic domains. [ABSTRACT FROM AUTHOR]