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Each year, the editorial board of Computational Optimization and Applications selects a paper from the preceding year's publications for the Best Paper Award. This derivative-free algorithm relies on randomly generated directions and is analyzed from a probabilistic viewpoint, leading to complexity guarantees for both deterministic and probabilistic versions of the method. First, following recent developments in nonconvex optimization, complexity results have become increasingly popular in derivative-free optimization [[8]]. [Extracted from the article]

Since the proximal gradient method reduces to the standard steepest descent method for the particular case where HT ht , the rate-of-convergence is typically slow (sublinear). In principle, the proximal gradient method has the major advantage that the subproblems (1) can be solved very efficiently (even analytically) for some practically important proximal functions HT ht . The classical proximal gradient method corresponds to the choice HT ht for all I k i with some (penalty or line search parameter) HT ht , whereas HT ht leads to the proximal Newton method, and HT ht with a (limited memory) quasi-Newton approximation of the Hessian is naturally called a (limited memory) proximal quasi-Newton method. [Extracted from the article]

A linear rate for the decay of the expected squared distance to the solution, HT ht , where HT ht is a positive definite matrix defining the norm, was established as well, for a range of stepsizes HT ht and momentum parameters HT ht . Loizou and Richtárik [[10]] further study the decay of the larger quantity HT ht to zero. [Extracted from the article]

We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in Devroye and James (Stat Methods Appl 2014) with particular attention to evolution problems. The contribution of the results collected in the paper is useful in a more wide class of applications in many areas of applied mathematics. [ABSTRACT FROM AUTHOR]

A new and simple proof of the main result of the paper 'Laterally closed lattice homomorphisms' by Toumi and Toumi (J Math Anal Appl 324:1178-1194, ) is given following the paper 'Extension of Riesz homomorphisms, I' by Buskes (J Aust Math Soc Ser A 39(1):107-120, ). [ABSTRACT FROM AUTHOR]

A formal approach to rephrasing nonlinear filtering of stochastic differential equations is the Kushner setting in applied mathematics and dynamical systems. Thanks to the ability of the Carleman linearization, the 'nonlinear' stochastic differential equation can be equivalently expressed as a finite system of 'bilinear' stochastic differential equations with the augmented state under the finite closure. Interestingly, the novelty of this paper is to embed the Carleman linearization into a stochastic evolution of the Markov process. The nonlinear swing equation is the cornerstone and lays the foundation of the power systems dynamics. To illustrate the Carleman linearization of the Markov process, this paper embeds the Carleman linearization into a nonlinear swing stochastic differential equation. Furthermore, we achieve the nonlinear swing equation filtering in the Carleman setting. Filtering in the Carleman setting has simplified algorithmic procedures. The concerning augmented state accounts for the nonlinearity as well as stochasticity. We show that filtering the nonlinear stochastic swing equation in the Carleman framework is more refined as well as sharper in contrast to the benchmark nonlinear extended Kalman filter (EKF). The Carleman filtering framework reduces approximately three times more conditional mean absolute errors as compared to the benchmark EKF method for the application of machine swing dynamics. This paper suggests the usefulness of the Carleman embedding into the stochastic differential equation to filter the concerning nonlinear stochastic differential system. This paper will interest nonlinear stochastic dynamists exploring and unfolding linearization embedding techniques to their research. [ABSTRACT FROM AUTHOR]

This special issue of the Journal of Optimization Theory & Applications focuses on the work of Professors Cornelis Roos and Florian A. Potra in the field of optimization. The issue includes a biographical sketch of both professors, highlighting their achievements. The papers in the special issue cover various topics such as conic optimization, interior point methods, proximal methods, convex optimization, and stochastic optimal control. The authors of the papers have close connections to Professors Roos and Potra, either as students, visitors, or co-authors. The document is a compilation of research papers on interior-point methods (IPMs) and their applications in optimization and conic programming. The papers cover theoretical developments of IPMs, algorithms for linear complementarity problems (LCPs), weighted LCPs, and sufficient linear complementarity problems. There are also papers on new computational approaches for IPMs, applications of IPMs in different fields such as mechanics and support vector machines, and the theory and application of conic optimization. The document also includes papers on proximal methods for convex and non-convex problems, as well as papers on convexity and convex optimization. The volume concludes with acknowledgments to the authors, reviewers, and editor-in-chief. [Extracted from the article]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

The lower-order penalty optimization methods, including the ℓ q minimization method and the ℓ q regularization method (0 < q ≤ 1) , have been widely applied to find sparse solutions of linear regression problems and gained successful applications in various mathematics and applied science fields. In this paper, we aim to investigate statistical properties of the ℓ q penalty optimization methods with randomly noisy observations and a deterministic/random design. For this purpose, we introduce a general q-Restricted Eigenvalue Condition (REC) and provide its sufficient conditions in terms of several widely-used regularity conditions such as sparse eigenvalue condition, restricted isometry property, and mutual incoherence property. By virtue of the q-REC, we exhibit the ℓ 2 recovery bounds of order O (ϵ 2) and O (λ 2 2 - q s) for the ℓ q minimization method and the ℓ q regularization method, respectively, with high probability for either deterministic or random designs. The results in this paper are nonasymptotic and only assume the weak q-REC. The preliminary numerical results verify the established statistical properties and demonstrate the advantages of the ℓ q penalty optimization methods over existing sparse optimization methods. [ABSTRACT FROM AUTHOR]

We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated Π 1 1 -comprehension and the existence of admissible sets, over weak base theories. Our work extends a previous result on the non-iterated case, which had been conjectured in Montalbán's "Open questions in reverse mathematics" (Bull Symb Log 17(3):431–454, 2011). This previous result has already been applied to the reverse mathematics of combinatorial and set theoretic principles. The present paper is a significant contribution to a general approach that connects these fields. [ABSTRACT FROM AUTHOR]

Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group of isometries and additive noise of magnitude σ . Despite significant interest, a clear picture for understanding rates of estimation in this model has emerged only recently, particularly in the high-noise regime σ ≫ 1 that is highly relevant in applications. Recent investigations have revealed a remarkable asymptotic sample complexity of order σ 6 for certain signals whose Fourier transforms have full support, in stark contrast to the traditional σ 2 that arise in regular models. Often prohibitively large in practice, these results have prompted the investigation of variations around the MRA model where better sample complexity may be achieved. In this paper, we show that sparse signals exhibit an intermediate σ 4 sample complexity even in the classical MRA model. Further, we characterize the dependence of the estimation rate on the support size s as O p (1) and O p (s 3.5) in the dilute and moderate regimes of sparsity respectively. Our techniques have implications for the problem of crystallographic phase retrieval, indicating a certain local uniqueness for the recovery of sparse signals from their power spectrum. Our results explore and exploit connections of the MRA estimation problem with two classical topics in applied mathematics: the beltway problem from combinatorial optimization, and uniform uncertainty principles from harmonic analysis. Our techniques include a certain enhanced form of the probabilistic method, which might be of general interest in its own right. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model capable of simulating the human cardiac function. We review the basic equations of the model, their coupling, the numerical approach for the computer solution of this mathematical model, and a few examples of application to specific problems of clinical interest. [ABSTRACT FROM AUTHOR]

In this EPJ Special Topics issue selected contributions on some recent developments in the theory and applications of fractional dynamical systems are presented. Results on topics involving fundamental theory, qualitative theory, iterative methods and numerous applications of fractional-order equations are reported. [ABSTRACT FROM AUTHOR]

The theory of averaging is a classical component of applied mathematics and has been applied to solve some engineering problems, such as in the filed of control engineering. In this paper, we develop a theory of averaging on both finite and infinite time intervals for fractional non-autonomous differential equations. The closeness of the solutions of fractional no-autonomous differential equations and the averaged equations has been proved. The main results of the paper are applied to the switched capacitor voltage inverter modeling problem which is described by the fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we trace back the genesis of Aitken's Δ2 process and Shanks' sequence transformation. These methods, which are extrapolation methods, are used for accelerating the convergence of sequences of scalars, vectors, matrices, and tensors. They had, and still have, many important applications in numerical analysis and in applied mathematics. They are related to continued fractions and Padé approximants. We go back to the roots of these methods and analyze the original contributions. New and detailed explanations on the building and properties of Shanks' transformation and its kernel are provided. We then review their historical algebraic and algorithmic developments. We also analyze how they were involved in the solution of systems of linear and nonlinear equations, in particular in the methods of Steffensen, Pulay, and Anderson. Testimonies by various actors of the domain are given. The paper can also serve as an introduction to this domain of numerical analysis. [ABSTRACT FROM AUTHOR]

The paper presents a method for processing positional observations of near-Earth objects using a numerical model of satellite motion developed at the Research Institute of Applied Mathematics and Mechanics of Tomsk State University (NII PMM TSU). The root-mean-square error of orbit improvement without rejection of observations for such objects does not exceed 0.3″ over a seven-day time interval. The results of the presentation of observations for the next occurrence of the object are obtained, which makes it possible to find the object in a time interval of five months. The orbit has been refined in the joint processing of measurements on several occurrences of the object over a six-month time interval. All results were obtained from observations made on the equipment of the Terskol Observatory Shared Use Center. [ABSTRACT FROM AUTHOR]

In this paper, the extended simplest equation technique is considered to construct various exact optical solutions to the time-fractional nonlinear Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients. The acquired novel optical soliton solutions are illustrated by the hyperbolic functions, the rational functions, and the trigonometric functions. The singular, dark, bright, mixed bright, dark–bright, and wave soliton solutions of the proposed model are successfully constructed. Further, to clarify the magnitude of the present nonlinear time-fractional Schrodinger model several solutions of the new exact optical solutions are plotted via two-dimensional and three-dimensional graphs using suitable values of physical parameters. The results acquired illustrate that the utilized technique is simple and quite efficient for exploring exact soliton solutions for different differential equations of fractional and integer orders arising in optics and applied mathematics. The novel optical solutions can assist researchers with an interest in plasma physics to unravel the mystery of numerous nonlinear phenomena that arise in various plasma models. [ABSTRACT FROM AUTHOR]

After several postponements due to Covid-19, the 5th Brazil-China Symposium on Applied and Computational Mathematics was held in Dongguan, China, between August 22 and August 24, 2021. One of his revolutionary results was an HT ht algorithm for linear programming. Preface to the 5th Brazil-China Symposium on Applied and Computational Mathematics. [Extracted from the article]

In a letter recommending Reilly for a mathematical scholarship Scott called her "a very worthy recipient", citing "an I excellent i paper" she had written for Scott's "Lectures on Special Topics in Geometry" (Scott [35]). Shortly after Reilly's talk on invariants, Scott wrote to Thomas advocating that Reilly should teach "more advanced work" such as graduate courses in mathematics rather than "the numerical drill that the Practical Course will demand." Though without any formal position within the mathematics department at this time, Reilly offered her financial support to the mathematics department in 1908 by donating $500 for the purchase of a set of mathematical models, thus enabling Scott to "have a very good beginning for the collection I have long wished for" (Scott [39]). That spring President Thomas traveled to Egypt for four months, leaving Scott and her two former students, Maddison and Reilly, in charge of college administration. The following year, Reilly requested an unpaid leave of absence from her position as dean in order to continue research in mathematics at the University of Rome after studying Italian for two months at the University of Siena.[10] Reilly had received letters of introduction from Scott and arrived in Rome in mid-November, when the universities opened. [Extracted from the article]

This paper investigates a recently introduced (2 + 1) -dimensional extended Calogero–Bogoyavlenskii–Schiff equation. The considered model is widely used in fluid dynamics, nonlinear optics and plasma physics. The study of the governing equation has provided insights into the dynamical behaviors of wave systems, which is an important area of research in applied mathematics and theoretical physics. Firstly, the description of the generalized Kudryashov and the two variable ( G ′ G , 1 G) -expansion methods is presented. The governing model is converted into a nonlinear ordinary differential equation by utilizing the traveling wave hypothesis. A family of exact traveling wave solutions such as solitons and solitary waves are extracted using the two proposed methods for the governing model. The graphical demonstrations are presented to examine the physical behavior of the constructed solutions. Kink solitary wave, singular kink, W-shape soliton, dark-bright soliton and periodic wave solutions are successfully retrieved. The proposed techniques are utilized to examine the governing model for the first time in this work to the best of our knowledge. The acquired results will help in guiding future investigations of the wave phenomena represented by the considered equation. [ABSTRACT FROM AUTHOR]

This volume collects all eleven survey papers that appeared in volumes 7-10 (2009-2011) of the journal 4OR: A Quarterly Journal of Operations Research. We briefly introduce the collected surveys and those that were included in the first two volumes of this series. [ABSTRACT FROM AUTHOR]

Q -neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real-life problems. Graph theory has now become a major branch of applied mathematics, and it is generally regarded as a branch of combinatorics. In this research paper, we introduce the concept of Q -neutrosophic soft graphs (Q- N S G s ) that are made by combining Q -neutrosophic soft sets with graphs and describe different methods of their construction. A Q -neutrosophic soft graphs model is very much efficient for such real word problems which can construct more precise, flexible, and comparable system as compared to the classical, fuzzy and neutrosophic graph models. In this paper, we first define the concept of Q -neutrosophic soft graph (Q- N S G ). In this paper we introduce the concept of Q - N S G , strong Q- N S G , union and intersection of Q- N S G . The new concept is called Q- N S G multicriteria decision-making method (Q- N S G M C D M for short). Finally, we describe the utility of the Q -neutrosophic soft graph and its applications in communication network and decision-making problem. [ABSTRACT FROM AUTHOR]

John Conway's impact has been felt far across mathematics. One of the first examples is Wagner's theorem, which showed that a graph has no planar embedding if and only if it has HT ht or HT ht as a minor. For instance, take the two rational tangles in Figure 2 given by HT ht and HT ht They both have HT ht and hence they are equivalent. [Extracted from the article]

Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite wavelets to numerically solve partial differential equations. In contrast to well-studied scalar subdivision schemes, Hermite and vector subdivision schemes employ matrix-valued masks and vector input data, which make their analysis much more complicated and difficult than their scalar counterparts. Under the spectral condition or the spectral chain, analysis of Hermite subdivision schemes through factorization of matrix-valued masks has been extensively studied in the literature and sufficient conditions have been given for the convergence of Hermite subdivision schemes through the contractivity of their derived subdivision schemes. We contribute to the study of Hermite subdivision schemes from a different perspective by investigating vector subdivision operators acting on vector polynomials and by establishing connections among Hermite subdivision schemes, vector cascade algorithms, and refinable vector functions. This approach allows us to characterize and construct all masks for Hermite subdivision schemes, to explain the spectral condition and spectral chain in the literature, to characterize convergence and smoothness of Hermite subdivision schemes using vector cascade algorithms, and to provide simple factorizations of Hermite masks through the normal form of matrix-valued masks such that the Hermite subdivision scheme is convergent if and only if its derived subdivision scheme is contractive. We also constructively prove that there always exist arbitrarily smooth convergent Hermite subdivision schemes, whose basis vector functions are splines and have linearly independent shifts. Several examples of Hermite subdivision schemes with short support and high smoothness are presented to illustrate the results in this paper. [ABSTRACT FROM AUTHOR]

Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland's integral for the stellar absorption. In this paper we obtain new Milne-type inequalities, and we apply them to the generalized Riemann–Liouville-type integral operators, which include most of the known Riemann–Liouville integral operators. [ABSTRACT FROM AUTHOR]

In 2021, after a one-year postponement due to the pandemic emergency, the biennial congress of the Italian Society of Industrial and Applied Mathematics (SIMAI) was held at Parma (Italy). The authors compare the two models with state-of-the-art Deep Image Prior models on a variety of test problems. In the second model the need of a regularization parameter is avoided by exploiting the Morozov's discrepancy principle and imposing the data fidelity as a convex constraint for which the noise level is estimated a priori. [Extracted from the article]

This paper presents a study of the heat transfer in objects, considering uncertain parameters such as the thermal diffusion coefficient and the initial condition. The uncertainty is modeled by intervals and fuzzy values. The fuzzy solutions to the problem are obtained from the Zadeh's extension principle. This work presents the characterization of the interval and fuzzy solutions by means of α -cuts, as well as associations between the propagation of uncertainty and the physical properties of materials. A comparison between the classical solution and the solutions obtained by defuzzification methods is also presented. To illustrate the results, some examples are provided, considering different materials. [ABSTRACT FROM AUTHOR]

Problems related to the extremization of functions have been studied for quite a long time not only by Russian experts but also by the world's leading experts in the field of applied mathematics. It should be noted that, nowadays, not all problems on this topic have a solution, despite the ongoing active research in mathematical modeling and mathematical programming. A serious work is underway on a deeper study of the properties of extremizable functions. This is especially topical in the context of our country's transition to a knowledge economy and, as a first step towards this, to the digital economy, when powerful supercomputers with performance of hundreds and thousands of petaflops have arisen and quantum computers begin to occur. The paper is a survey of results associated with a new class of functions that are useful in extremization problems and is based on joint work of the authors. [ABSTRACT FROM AUTHOR]

External beam radiation therapy is a key part of modern cancer treatments which uses high doses of radiation to destroy tumour cells. Despite its widespread usage and extensive study in theoretical, experimental, and clinical works, many questions still remain about how best to administer it. Many mathematical studies have examined optimal scheduling of radiotherapy, and most come to similar conclusions. Importantly though, these studies generally assume intratumoral homogeneity. But in recent years, it has become clear that tumours are not homogeneous masses of cancerous cells, but wildly heterogeneous masses with various subpopulations which grow and respond to treatment differently. One subpopulation of particular importance is cancer stem cells (CSCs) which are known to exhibit higher radioresistence compared with non-CSCs. Knowledge of these differences between cell types could theoretically lead to changes in optimal treatment scheduling. Only a few studies have examined this question, and interestingly, they arrive at apparent conflicting results. However, an understanding of their assumptions reveals a key difference which leads to their differing conclusions. In this paper, we generalize the problem of temporal optimization of dose distribution of radiation therapy to a two cell type model. We do so by creating a mathematical model and a numerical optimization algorithm to find the distribution of dose which leads to optimal cell kill. We then create a data set of optimization solutions and use data analysis tools to learn the relationships between model parameters and the qualitative behaviour of optimization results. Analysis of the model and discussion of biological importance are provided throughout. We find that the key factor in predicting the behaviour of the optimal distribution of radiation is the ratio between the radiosensitivities of the present cell types. These results can provide guidance for treatment in cases where clinicians have knowledge of tumour heterogeneity and of the abundance of CSCs. [ABSTRACT FROM AUTHOR]

Compressed sensing has recently received considerable attention in signal and image processing, applied mathematics, and statistics. In this paper, the problem of sparse signal restoration in non-negative environment is studied. We propose a greedy algorithm for solving non-negative structure of sparse vector and analyze its theoretical performance based on mutual coherence. The feasibility of the proposed algorithm is verified by numerical experiments. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton's perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton's mechanics, but also the problematic aspects of his perfect geometrical methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton's geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton's mathematical concepts. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to use multivariate statistical methods with asymmetric distributions approach, chemical analysis, and inductively coupled plasma–mass spectrometry (ICP-MS) device. We investigate data of heavy metal content from Akcay Riverwater to the Mediterranean involving Finike sea coast at Turkey. We determine the chemical content, origin of heavy metals of the surface water in Akcay River, which flows into the Mediterranean realted to the above-mentioned region by multivariate statistical analysis, pollution indices, and density maps involving numerical comments by numbers. With the help of special numbers represented by special chemical components and simmetric statistical methods given above, in this paper, we obtain many new relations and results. Furhermore, we give some comments, observations, and remarks about the results of this paper. These results have a high potential to be used not only in engineering fields and health sciences, but also in applied mathematics, statistics, and other fields. [ABSTRACT FROM AUTHOR]

One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object, while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional. [ABSTRACT FROM AUTHOR]

The problem of efficient global error estimation and control is studied in embedded nested implicit Runge–Kutta pairs of Gauss and Lobatto types as applied to stiff ordinary differential equations (ODEs). Stiff problems may arise in many areas of engineering, and their accurate numerical solution is an important issue of computational and applied mathematics. A cheap global error estimation technique designed recently for the mentioned Runge–Kutta pairs can severely overestimate the global error when applied to stiff ODEs and, hence, this reduces the efficiency of those solvers. In the present paper, we explain the cause of that error overestimation and show how to improve the mentioned computation techniques for stiff problems. Such modifications not only boost the efficiency of numerical integration of stiff ODEs, but also make the embedded nested implicit Runge–Kutta pairs with scaled modified local and global error controls superior to stiff built-in MATLAB ODE solvers with only local error control when applied to important test examples. [ABSTRACT FROM AUTHOR]

In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan (Nous 45(2): 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic phenomena. The final aim of the paper is directed at proposing a novel account of the syntax–semantics interface while shedding light on empty categories, semantically null forms, underspecified content and compositionality as a whole. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of periodic solutions for a class of nonautonomous second-order discrete Hamiltonian systems in case the sum on the time variable of potential is periodic. The tools used in our paper are the direct variational minimizing method and Rabinowitz's saddle point theorem. [ABSTRACT FROM AUTHOR]

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCA σ (Zermelo–Fraenkel set theory (with Choice) with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents. [ABSTRACT FROM AUTHOR]

We examine two very different approaches to formalising real computation, commonly referred to as "Computable Analysis" and "the BSS approach". The main models of computation underlying these approaches—bit computation (or Type-2 Effectivity) and BSS, respectively—have also been put forward as appropriate foundations for scientific computing. The two frameworks offer useful computability and complexity results about problems whose underlying domain is an uncountable space (such as R or C ). Since typically the problems dealt with in physical sciences, applied mathematics, economics, and engineering are also defined in uncountable domains, it is fitting that we choose between these two approaches a foundational framework for scientific computing. However, the models are incompatible as to their results. What is more, the BSS model is highly idealised and unrealistic; yet, it is the de facto implicit model in various areas of computational mathematics, with virtually no problems for the everyday practice. This paper serves three purposes. First, we attempt to delineate what the goal of developing foundations for scientific computing exactly is. We distinguish between two very different interpretations of that goal, and on the separate basis of each one, we put forward answers about the appropriateness of each framework. Second, we provide an account of the fruitfulness and wide use of BSS, despite its unrealistic assumptions. Third, according to one of our proposed interpretations of the scope of foundations, the target domain of both models is a certain mathematical structure (namely, floating-point arithmetic). In a clear sense, then, we are using idealised models to study a purely mathematical structure (actually a class of such structures). The third purpose is to point out and explain this intriguing (perhaps unique) phenomenon and attempt to make connections with the typical case of idealised models of empirical domains. [ABSTRACT FROM AUTHOR]

For a long time, Soviet students learned 'pure' mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid national curriculum. Even when in the 1990s the world was moving towards including applications in school mathematics, Russian students continued to engage in pure mathematics learning in their mathematics classrooms. It was physics teachers' responsibility to teach applications of mathematics; therefore, physics courses were highly mathematics-intensive, making extensive use of mathematics from algebra to calculus in the formulation of scientific laws and the investigation of their consequences. The collapse of the Soviet Union and some liberalization in educational policy led to changes in graduation requirements in mathematics and physics as well as diversity in mathematics and physics curricula in schools. Based on a review of textbooks, standards, curriculum documents, and other resources, in this paper we analyze changes that affected the teaching and learning of mathematics in physics classrooms in Russia from the Soviet period to the present. [ABSTRACT FROM AUTHOR]

In this series of papers we show that there are exactly ten subfactors, other than A subfactors, of index between 4 and 5. Previously this classification was known up to index $${3+\sqrt{3}}$$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $${3+\sqrt{3}}$$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series. [ABSTRACT FROM AUTHOR]