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This special issue of the Journal Mathematical Methods in the Applied Sciences on the topic of Modelling, Analysis, and Applications is devoted to the development of mathematical modelling, analysis, and applications, from theoretical and numerical perspectives, involving different applied sciences and engineering. It collects invited contributions, from selected quality full papers submitted to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC2022). The conference took place in Porto, Portugal in 27–29 June 2022 (https://www.isep.ipp.pt/Page/ViewPage/ICMASC). [ABSTRACT FROM AUTHOR]

In 1966, A. J. M. Spencer gave an inaugural lecture on continuum mechanics on the occasion of his appointment to a professorship at the University of Nottingham. The lecture gave an accurate, but nontechnical, picture of the interaction of mathematics and continuum mechanics at that time, together with a prediction of their subsequent hoped-for interactions. This article responds to Spencer's lecture by surveying these fields as of 1966, by tracing their developments, interactions, and lack thereof in the subsequent years, and by commenting on the prospects for the future. [ABSTRACT FROM AUTHOR]

A power-law formula with a critical exponent α was used to analyze the anomalous behavior of the specific heat for guanidine zinc sulfate (GZS) crystal close to the phase transition temperature of TC = 178.4 K. The obtained values of 0.13 and 0.14 for α below (T < TC) and above (T > TC) the phase transition temperature, respectively, were almost the same value of 0.13 (1/8) that predicted from the 3-D Ising model. Also, the internal energy U , the entropy S and the free energy G of this crystal were calculated as a function of temperature close to the phase transition temperature of TC = 178.4 K. [ABSTRACT FROM AUTHOR]

The frequency and full width at half maximum (FWHM) data of the Ag Raman modes (95.4, 231.4 and 263.2 cm−1) in strontium stannate crystal have been analyzed using the Balkanski model and the fitting parameters were determined. Also, the isobaric Grüneisen parameter of Ag Raman modes studied here was computed below the room temperature. This computation was performed from the unit cell volume and the observed frequency data of this crystal. Finally, values of the activation energy were extracted close to the structural phase transition temperatures of 160 and 265 K using the observed FWHM data of strontium stannate. [ABSTRACT FROM AUTHOR]

The frequency and full width at half maximum (FWHM) data of the Ag Raman modes (95.4, 231.4 and 263.2 cm−1) in strontium stannate crystal have been analyzed using the Balkanski model and the fitting parameters were determined. Also, the isobaric Grüneisen parameter of Ag Raman modes studied here was computed below the room temperature. This computation was performed from the unit cell volume and the observed frequency data of this crystal. Finally, values of the activation energy were extracted close to the structural phase transition temperatures of 160 and 265 K using the observed FWHM data of strontium stannate. [ABSTRACT FROM AUTHOR]

Mathematical analysis was conceived in XVII century in the works of Newton and Leibniz. The issue of logical rigor in definitions was however first considered by Arnauld and Nicole in ''Logique ou l'art de penser''. They were the first to distinguish between the bulk of the concept and its structure. They created a tradition which was strong in mathematics till XIX century, especially in France. The definitions were in binomial nomenclature mostly, but another type of definition appears in Cantor theory -- it was the descriptive definition. As it used to be in humanities, first the object had only one characteristic, then as research continued it got enriched with new characteristics leading to a fledged concept. In this way mathematics acquired its own creativity. In 1915 Luzin laid down a new principle of the descriptive theory: a structural characteristic is done, the analytical form had to be found. New schools of descriptive set theory appeared in Moscow in the first half of the 20th centu [ABSTRACT FROM AUTHOR]

Since addition possesses an inverse in the quotient space of fuzzy numbers based on Mareš equivalence relation, in this paper, we introduce a metric on the quotient space of fuzzy numbers, and then deal with fuzzy mappings of a real variable whose values are equivalence classes of fuzzy numbers. We study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation. Finally, some examples are given to illustrate the main theorems. [ABSTRACT FROM AUTHOR]

The aim of this study is to create and verify a numerical model for a Medin Modular orthopedic knee-joint implant by investigating contact pressure, its distribution and contact surfaces. An experiment using Fuji Prescale pressure sensitive films and a finite element analysis (FEA) using Abaqus software were carried out. The experimental data were evaluated using a special designed program and were compared with the results of the analysis. The designed evaluation program had been constructed on the basis of results obtained from a supplementary calibration experiment. The applicability of the numerical model for the real endoprosthesis behavior prediction was proven on the basis of their good correlation. [ABSTRACT FROM AUTHOR]

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

Abstract: The problem about synthesis of an original adaptive gripper with simplified structure is formulated and solved. The synthesized gripper is mainly oriented to automatic manipulation devices, which are designed for carrying, and assembly work-pieces under production of appliances and electrical-industrial articles. A developed example illustrates the application of the compound mathematical models for gripper synthesis and results evaluation. [Copyright &y& Elsevier]

Abstract: This article presents a d-statistic for single-case designs that is in the same metric as the d-statistic used in between-subjects designs such as randomized experiments and offers some reasons why such a statistic would be useful in SCD research. The d has a formal statistical development, is accompanied by appropriate power analyses, and can be estimated using user-friendly SPSS macros. We discuss both advantages and disadvantages of d compared to other approaches such as previous d-statistics, overlap statistics, and multilevel modeling. It requires at least three cases for computation and assumes normally distributed outcomes and stationarity, assumptions that are discussed in some detail. We also show how to test these assumptions. The core of the article then demonstrates in depth how to compute d for one study, including estimation of the autocorrelation and the ratio of between case variance to total variance (between case plus within case variance), how to compute power using a macro, and how to use the d to conduct a meta-analysis of studies using single-case designs in the free program R, including syntax in an appendix. This syntax includes how to read data, compute fixed and random effect average effect sizes, prepare a forest plot and a cumulative meta-analysis, estimate various influence statistics to identify studies contributing to heterogeneity and effect size, and do various kinds of publication bias analyses. This d may prove useful for both the analysis and meta-analysis of data from SCDs. [Copyright &y& Elsevier]

Abstract: The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem – the need to find a signal belonging to this model, given a set of corrupted measurements of it. Several pursuit methods have already been proposed based on relaxation and a greedy approach. In this work we pursue this question further, and propose a new family of pursuit algorithms for the cosparse analysis model, mimicking the greedy-like methods – compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). Assuming the availability of a near optimal projection scheme that finds the nearest cosparse subspace to any vector, we provide performance guarantees for these algorithms. Our theoretical study relies on a restricted isometry property adapted to the context of the cosparse analysis model. We explore empirically the performance of these algorithms by adopting a plain thresholding projection, demonstrating their good performance. [Copyright &y& Elsevier]

Abstract: The epsilon substitution method was proposed by D. Hilbert as a tool for consistency proofs. A version for first order predicate logic had been described and proved to terminate in the monograph “Grundlagen der Mathematik”. As far as the author knows, there have been no attempts to extend this approach to the second order case. We discuss possible directions for and obstacles to such extensions. [Copyright &y& Elsevier]

We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more complex) counterexamples daily in class. We provide perspective on these observations in the context of an informative body of related work in undergraduate mathematics studies. [ABSTRACT FROM PUBLISHER]

Abstract: After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments, and provide a detailed study of the model associated with the 2D finite difference analysis operator, a close cousin of the TV norm. [Copyright &y& Elsevier]

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by another, and continuous functions with discontinuities. This paper uncovers these issues and resolves them in five guided classroom discoveries ideal for students in a first course in real analysis, an honors calculus course, or a course on transitions to higher-level mathematical thinking. The conclusion provides definitions consistent with analysis in a setting for the general student of calculus. [ABSTRACT FROM PUBLISHER]

Abstract: First, the notion of a family of generalized L-fuzzy norms on vector spaces is proposed. Then, the L-topology induced by a family of generalized L-fuzzy norms is investigated. Finally, a necessary and sufficient condition for an L-topological vector space to be generalized L-fuzzy normable is obtained, which can be viewed as the generalized normability theorem for L-topological vector spaces compared with that by Yan and Fang in 2002. [Copyright &y& Elsevier]

This note explores the common core of constructive, intuitionistic, recursive and classical analysis from an axiomatic standpoint. In addition to clarifying the relation between Kleene's and Troelstra's minimal formal theories of numbers and number-theoretic sequences, we propose some modified choice principles and other function existence axioms which may be of use in reverse constructive analysis. Specifically, we consider the function comprehension principles assumed by the two minimal theories EL and M, introduce an axiom schema CF asserting that every decidable property of numbers has a characteristic function, and use it to describe a precise relationship between the minimal theories. We show that the axiom schema AC of countable choice can be decomposed into a monotone choice schema AC (which guarantees that every Cauchy sequence has a modulus) and a bounded choice schema BC. We relate various (classically correct) axiom schemas of continuous choice to versions of the bar and fan theorems, suggest a constructive choice schema AC (which incidentally guarantees that every continuous function has a modulus of continuity), and observe a constructive equivalence between restricted versions of the fan theorem and correspondingly restricted bounding axioms $${AB_{1/2,0}^{2^{\mathbb{N}}}}$$. We also introduce a version WKL!! of Weak König's Lemma with uniqueness which is intermediate in strength between WKL and the decidable fan theorem FT. [ABSTRACT FROM AUTHOR]

Abstract: The generalization of the concept of H-differentiability can be of great help in the dynamic study of fuzzy differential equations. In this paper, the concept of generalized differentiability is described from a new perspective. On the basis of this concept, the class of differentiable fuzzy set-valued mappings is enlarged. The Cauchy problem for fuzzy differential equations is investigated in this enlarged setting. As a result, some new solutions are obtained. The lengths of the support sets of these solutions may be non-monotonic. Several examples are also shown. [Copyright &y& Elsevier]

A combination of two complex normalized least mean square (NLMS) adaptive filters that adapt oil the same input signal at the same time is investigated. One of the filters has a large and the other one has a small step size. The outputs of the filters are combined together through a mixing parameter λ. This combination is an interesting new way of achieving simultaneously a fast initial convergence and a small steady state error of an adaptive algorithm. The mixing parameter is computed from the output signals of the individual filters. The expressions characterizing the time evolution of the mean square deviation and the excess mean square error of the combination scheme are derived. The theoretical results are verified by simulations. [ABSTRACT FROM AUTHOR]

Abstract: We use two different frameworks to calculate the electrostatic potential created by a uniformly charged disk in its plane. We first implement a standard direct integration approach and carry out the calculations to the extent possible while keeping them simple. We then apply a different method that relies on Bessel function transformations. This method allows us to derive compact analytic expressions for the electrostatic potential in terms of complete elliptic integrals of the first and second kind. By comparing the results obtained through the application of the two different approaches, we uncover interesting transformation formulas and novel mathematical identities that might be of interest to a broad range of researchers in mathematical and physical sciences. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of a family of L-fuzzy pseudo-norms on vector spaces is proposed and the characterization of L-vector topologies in terms of a family of L-fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-sets in L-topological vector spaces are investigated. [Copyright &y& Elsevier]

Abstract: This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students’ attempt to reach a general formula for a three-dimensional pattern generalizing task. The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate the number of blocks in a three-dimensional tower of different heights. The students’ activity was video- and audio-taped, fully transcribed and lasted for 50min. The analysis discloses several instances of how the students were linking acts of visualization and analysis to reach a general formula. However, regarding flexibility, we found that it was more natural for the students to change visual format than to change analytical position and direction in their attempts to generalize the three-dimensional pattern of the task in a closed formula. [Copyright &y& Elsevier]

We resolve a long-standing question on L completeness of the time-scale (or wavelet) system generated by the Mexican hat function, when p≥2. Our main result concerns frequency-scale systems generated by modulation and dilation of a single function. The mixed frame operator (analysis followed by synthesis) is shown to be bijective from L(ℝ) to itself, for 1≤ q<∞, so that the frequency-scale synthesis operator is surjective. Tools include the discrete Calderón condition and a generalization of the Daubechies frame criterion in L. Completeness of the Mexican hat and other wavelet systems in L then follows for 2≤ p<∞, by Fourier imbedding of frequency-scale systems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the notion of generalized locally bounded L-topological vector spaces is proposed. The relationship between this kind of space and locally bounded L-topological vector space as defined by Yan and Fang [Locally bounded L-topological vector spaces, Inf. Sci. 159 (2004) 273–281] is investigated. In addition, the concept of a family of generalized L-fuzzy quasi-norms is introduced. Based on this notion, generalized locally bounded L-topological vector spaces are characterized. Finally, the Hausdorff separation property, convergence of molecule nets and boundedness of L-fuzzy sets in generalized locally bounded L-topological vector spaces are studied. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we firstly define some new types of fuzzy starshapedness, discuss the relationships among the different types of fuzzy starshapedness, and then present some basic properties of them. Finally we develop several important results on the shadows of starshaped fuzzy sets. [Copyright &y& Elsevier]

A kinematic-geometric calculus modelling of a handling arm mechanism actuated by hydraulic cylinder is derived and presented in this paper. The calculus model leads to an interactive CAD application of studying and design processing several variants of such mechanism. Special emphasis will be placed upon variants of a mechanism used for driving the mobile arm which positions the cutter-loader's ranging drum. The mechanism can also be used in other areas of applied mechanics. [ABSTRACT FROM AUTHOR]

A simple physical model, based on Torricelli's law, may be used as a motivator for topics in intermediate-level mathematical analysis courses. The particular mathematical topics that arise from the model involve the implicit function theorem and related issues. The model provides a concrete setting for highlighting the necessity of investigating the existence and character of implicitly defined functions, and serves as a platform for the use of graphical and numerical means to guide rigorous analysis. The analysis of the mathematical model relies on implicit differentiation and a simple fixed point theorem. [ABSTRACT FROM AUTHOR]

Most existing three-dimensional (3D) slope stability analysis methods are based on simple extensions of corresponding two-dimensional (2D) methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. In this paper, 3D asymmetric slope stability models based on extensions of Bishop’s simplified, Janbu’s simplified, and Morgenstern–Price’s methods are developed. Under these new formulations, the direction of slide is unique and is determined from 3D force/moment equilibrium. Results from the new formulations are similar to the classical methods in normal cases but are numerically stable under transverse load. Further, the writers demonstrate that the present formulation is actually equivalent to the axes rotation formulation by Jiang and Yamagami but is much more convenient to be used for general problems. The writers have also discovered some inherent limitations of 3D limit equilibrium analysis which are absent in the corresponding 2D analysis. [ABSTRACT FROM AUTHOR]

Structural analysis of rubber components is often complicated by significant geometrical non-linearity of deformation, incompressibility, complex constitutive models, and the contact nature of boundary/loading conditions. The last challenge is especially important due to the uniquely high friction of rubber. The article provides an advanced approach to mitigate contact challenges for very large coefficients of friction (COF) in rubber. It is shown that the nature of this challenge fundamentally differs from other rubber-related structural issues (incompressibility, large deformations, etc.). A mathematical description of the challenge is considered in detail in this article. An efficient method is proposed for problems with high COF. The method provides solutions for problems where the desired convergence cannot be achieved using traditional techniques. The proposed approach also offers a simple and convenient capability to check if obtained convergent results are really true solutions. Also, a simple benchmarking problem is proposed for validation of computational contact algorithms at very high friction in rubber. [ABSTRACT FROM AUTHOR]

This article presents the results of a 7-year-long quest into the development of a “dream tool” for our research in information science and scientometrics and more recently, network science. The results are two cyberinfrastructures (CI): The Cyberinfrastructure for Information Visualization and the Network Workbench that enjoy a growing national and interdisciplinary user community. Both CIs use the cyberinfrastructure shell (CIShell) software specification, which defines interfaces between data sets and algorithms/services and provides a means to bundle them into powerful tools and (Web) services. In fact, CIShell might be our major contribution to progress in convergence. Just as Wikipedia is an “empty shell” that empowers lay persons to share text, a CIShell implementation is an “empty shell” that empowers user communities to plug-and-play, share, compare and combine data sets, algorithms, and compute resources across national and disciplinary boundaries. It is argued here that CIs will not only transform the way science is conducted but also will play a major role in the diffusion of expertise, data sets, algorithms, and technologies across multiple disciplines and business sectors leading to a more integrative science. [ABSTRACT FROM AUTHOR]

In this paper, intuitionistic fuzzy Euclidean normed spaces are considered and compactness in these spaces is studied. [ABSTRACT FROM AUTHOR]

New UBV photometry of Algol type binary star U Sge obtained during 1993 are presented, analyzed, and discussed. Wilson-Devinney code was employed to analyze the light curves. Absolute dimensions of the system were obtained, and positions of both components on H-R diagram were specified. Finally through color curve analysis absolute visual magnitudes were determined. [ABSTRACT FROM AUTHOR]

This note is to define the absolute continuity for fuzzy-valued mappings and to give the necessary and sufficient conditions for the Newton–Leibniz formula to hold. [Copyright &y& Elsevier]