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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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

Nowadays, large part of the technical knowledge associated with collapses of slabs is based on past failures of bridges, floors, flat roofs and balconies. Collapse mechanisms tend to often differ from each other due to unique features which make it difficult to derive a generalised technique that can predict the right mechanism. This paper proposes a novel algorithm for tackling the problem of detection of collapse mechanisms, which is part of a pseudo-lower bound method for assessing concrete slabs in bridges and buildings. The problem is generalised to a combinatorial one, and the solution is based on a set of well-known combinatorial optimization algorithms. The proposed approach enables an identification of the domain of existence of yield-lines potentially leading to collapse. The output provides an estimation of a hampered domain of feasible yield-lines through which engineers can quickly identify zones of the slab and directions in which yield-lines leading to collapse are more likely to occur. Numerical applications of the algorithm are presented herein. [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]

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from 'If A were true, then C would be true' to 'If A and B were true, then C would be true'), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. [ABSTRACT FROM AUTHOR]

Quadratic functions play an important role in applied mathematics. In this paper, we consider the problem of minimizing the integral of a (not necessarily convex) quadratic function in a bounded subset of nonnegative integrable functions defined on a finite-dimensional space that is not compact with respect to any (locally convex) topology in the space of integrable functions. We establish a complete description about the existence or nonexistence of solution in terms of the (strict) copositivity of the matrix involved in the integrand. In addition, we characterize optimality via the Hamiltonian function. [ABSTRACT FROM AUTHOR]

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from 'If A were true, then C would be true' to 'If A and B were true, then C would be true'), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. [ABSTRACT FROM AUTHOR]

Localization operators have a relatively recent development in pure and applied mathematics. Motivated by Wong's approach, we will study in this paper the time–frequency analysis associated with the hypergeometric Wigner transform related to the Cherednik operators in the case of the root system B C d . [ABSTRACT FROM AUTHOR]

Improving student participation and achievement in post-secondary STEM courses continues to be an important concern of many governments and educational institutions since this is one avenue by which the number of STEM professionals can be increased. This paper examines and compares the gendered participation, performance and attrition rate of candidates in two post-secondary mathematics courses over a 5-year period from 2013 to 2017. This study used the Caribbean Advanced Proficiency Examination (CAPE) results from the Caribbean Examinations Council (CXC), which is the main public examination board in the Caribbean, for 15,220 candidates (N = 19,585) from 71 post-secondary educational institutions in Jamaica. 'CAPE' applies to both the course of study and the associated examination. The study found that, on average, approximately one-fifth of the candidates who pursue CAPE courses in Jamaica opt to study a mathematics course and that across the 5 years this remained relatively stable. There was, however, a marked decrease in the number of candidates choosing to enrol in Unit 2 courses on completion of the related Unit 1 course. Another key finding was that, while a higher percentage of males chose to undertake Applied Mathematics Unit 2 and equal proportions of male and female candidates the other three courses, there was a significant difference in the overall performance by gender with females outperforming their male peers. These findings suggest that initiatives are needed which improve student performance and experience in CAPE mathematics Unit 1 subjects which could then reduce student attrition across units. [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, we prove a blow-up criterion in terms of the magnetic field H and the mass density ρ for the strong solutions to the initial boundary value problem of the 3D isentropic compressible MHD equations with zero magnetic diffusion and initial vacuum. More precisely, we show that the upper bounds of (H , ρ) control the possible blow-up (see Rozanova in Proceedings of symposia in applied mathematics, 2009; Xin in Commun Pure Appl Math 51:0229–0240, 1998; Yuan and Zhao in Kinet Relat Models 7:195–203, 2014) for strong solutions. [ABSTRACT FROM AUTHOR]

We can distinguish between two different ways in which mathematics is applied in science: when mathematics is introduced and developed in the context of a particular scientific application; when mathematics is used in the context of a particular scientific application but it has been developed independently from that application. Nevertheless, there might also exist intermediate cases in which mathematics is developed independently from an application but it is nonetheless introduced in the context of that particular application. In this paper I present a case study, that of the Lagrange multipliers, which concerns such type of intermediate application. I offer a reconstruction of how Lagrange developed the method of multipliers and I argue that the philosophical significance of this case-study analysis is twofold. In the context of the applicability debate, my historically-driven considerations pull towards the reasonable effectiveness of mathematics in science. Secondly, I maintain that the practice of applying the same mathematical result in different scientific settings can be regarded as a form of crosschecking that contributes to the objectivity of a mathematical result. [ABSTRACT FROM AUTHOR]

The epilogue, Chapter 7, describes Guccia's death and the decay of the Circolo from the interwar period through the Second World War, when the bombing of Palermo in 1943 destroyed the Palazzo Guccia. Two mathematicians particularly assisted Guccia in improving his mathematical society and the I Rendiconti i : the French Poincaré and the well-known Italian mathematician Vito Volterra (1860-1940). The other important mathematician in Guccia's scientific life was Poincaré, who supported Guccia throughout his career by contributing important papers to the I Rendiconti i . However, the book remains captivating, sheds light on a still little-known story, and contains unpublished documents on the origins of the Guccia family, the role of Guccia's uncle Giulio Fabrizio Tomasi, and the first years of Guccia's life. [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]

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]

Finite difference schemes are widely used in applied mathematics to numerically solve partial differential equations. However, for a given solution scheme, it is usually difficult to evaluate the quality of the underlying finite difference approximation with respect to the inheritance of algebraic properties of the differential problem under consideration. In this paper, we present an appropriate quality criterion of strong consistency for finite difference approximations to systems of nonlinear partial differential equations. This property strengthens the standard requirement of consistency of difference equations with differential ones. We use a verification algorithm for strong consistency, which is based on the computation of difference Gröbner bases. This allows for the evaluation and construction of solution schemes that preserve some fundamental algebraic properties of the system at the discrete level. We demonstrate the suggested approach by simulating a Kármán vortex street for the two-dimensional incompressible viscous flow described by the Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

One of the most interesting and important techniques in applied mathematics is interpolation and approximation. It can be also shown that basic theory of fuzzy sets and operations with fuzzy numbers can be used, and result very convenient, for solving many analytical chemistry problems: as depth profile comparison or calibration with errors in signals and/or concentrations, for spectra interpretation, or even for automatic qualitative analysis or expert systems with X-ray spectroscopy. In this special context, we introduce in this paper a new fuzzy interpolation method of fuzzy data or functions, specially indicated in all these chemical applications. We will use bicubic splines (cubic splines of two variables) of class C 2 as linear combinations of a basis constructed by a tensor product of univariate B-splines in each of these variables. First we establish a bicubic interpolation spline method of a given fuzzy data set or a given fuzzy bivariate function. We proof the existence of a unique solution of this problem and we show a convergence result. Finally, we test the effectiveness of this method by some numerical and graphical examples. [ABSTRACT FROM AUTHOR]

Invasion phenomena for heterogeneous reaction–diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction–diffusion equation when the subdomain where the reaction term is positive is shifting/contracting at a given speed c. This problem arises in particular in the modelling of the impact of climate change on population dynamics. By placing ourselves in the appropriate moving frame, this leads us to consider a reaction–diffusion–advection equation with a heterogeneous in space reaction term, in dimension N ≥ 1 . We investigate the behaviour of the solution u depending on the value of the advection constant c, which typically stands for the velocity of climate change. We find that, when the initial datum is compactly supported, there exists precisely three ranges for c leading to drastically different situations. In the lower speed range the solution always spreads, while in the upper range it always vanishes. More surprisingly, we find that both spreading and vanishing may occur in an intermediate speed range. The threshold between those two outcomes is always sharp, both with respect to c and to the initial condition. We also briefly consider the case of an exponentially decreasing initial condition, where we relate the decreasing rate of the initial condition with the range of values of c such that spreading occurs. [ABSTRACT FROM AUTHOR]

We show in this paper how the convergence of an algorithm for matrix completion can be significantly improved by applying Wynn's e-algorithm. Straightforward generalization of the scalar e-algorithm to matrices fails. However, accelerating the convergence of only the missing matrix elements turns out to be very successful. [ABSTRACT FROM AUTHOR]

The Extrapolation Algorithm is a technique devised in 1962 for accelerating the rate of convergence of slowly converging Picard iterations for fixed point problems. Versions to this technique are now called Anderson Acceleration in the applied mathematics community and Anderson Mixing in the physics and chemistry communities, and these are related to several other methods extant in the literature. We seek here to broaden and deepen the conceptual foundations for these methods, and to clarify their relationship to certain iterative methods for root-finding problems. For this purpose, the Extrapolation Algorithm will be reviewed in some detail, and selected papers from the existing literature will be discussed, both from conceptual and implementation perspectives. [ABSTRACT FROM AUTHOR]

In generalized measure theory, σ-⊕-measure is a generalization of the classical measure defined on a pseudo-addition. In this paper, the class of pseudo-exponential distributions based on a class of σ-⊕-measure is introduced. Some examples of this class are investigated. Then by two real data sets obtained from the last three decades of oil, and the last two decades of the daily natural gas spot prices, we show that the pseudo-exponential distribution is better fitted than exponential distribution using the AIC and BIC information criteria. [ABSTRACT FROM AUTHOR]

In this paper we investigate the extension of the multiple Erdélyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by the way of regularization. The regularization involves derivatives of the function in question and the integration with respect to a kernel expressed in terms of special case of Meijer's G-function. An action of the regularized multiple Erdélyi-Kober operator on some simple kernels leads to decomposition formulas for the generalized hypergeometric functions. In the ultimate section, we define an alternative regularization better suited for representing the Bessel type generalized hypergeometric function p−1Fp. A particular case of this regularization is then used to identify some new facts about the positivity and reality of zeros of this function. [ABSTRACT FROM AUTHOR]

Heisenberg's uncertainty relation is a basic principle in the applied mathematics and signal processing community. The logarithmic uncertainty relation, which is a more general form of Heisenberg's uncertainty relation, describes the relationship between a function and its Fourier transform. In this paper, we consider several logarithmic uncertainty relations for a odd or even signal f( t) related to the Wigner-Ville distribution and the linear canonical transform. First, the logarithmic uncertainty relations associated with the Wigner-Ville distribution of a signal f( t) based on the Fourier transform are obtained. We then generalize the logarithmic uncertainty relation to the linear canonical transform domain and derive a number of theorems relating to the Wigner-Ville distribution and the ambiguity function; finally, the logarithmic uncertainty relations are obtained for the Wigner-Ville distribution associated with the linear canonical transform. We present an example in which the theorems derived in this paper can be used to provide an estimation for a practical signal. [ABSTRACT FROM AUTHOR]

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., , this issue; McAteer et al. in Space Sci. Rev., , this issue; Sharma et al. in Space Sci. Rev. , in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak's own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner ). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers. [ABSTRACT FROM AUTHOR]

In this paper, using the projection operator, we introduce two new dynamical systems for extended general quasi variational inequalities. These dynamical systems are called extended general implicit projected dynamical system and extended general implicit Wiener-Hopf dynamical system. We prove that these new dynamical systems converge globally exponentially to a unique solution of the extended general quasi variational inequalities under some suitable conditions. Some special cases are also discussed. The ideas and technique of this paper may stimulate further research. [ABSTRACT FROM AUTHOR]

In this paper, the $$H_{\infty }$$ filtering problem is considered for Markovian switching genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays along intrinsic molecular fluctuations and extrinsic molecular noises. The aim of this paper is to design a filter to estimate the true concentrations of mRNAs and proteins. By choosing suitable Lyapunov-Krasovskii functionals and reciprocally convex combination approach, sufficient conditions are obtained to ensure that the filtering error system is globally stochastically stable in the mean-square sense with the prescribed $$H_{\infty }$$ disturbance attenuation levels. The existence of the designed $$H_{\infty }$$ filters is expressed in terms of linear matrix inequalities (LMIs), which can be easily solved by using Matlab LMI toolbox. Also the corresponding results are obtained for the GRNs without leakage delays. Finally, two numerical examples are given, which include a repressilator model of Escherichia coli to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the boundary blow-up solutions to the nonlocal elliptic systems of cooperative type. By introducing the boundary measure, the boundary blow-up problem becomes a Cauchy problem. Then using the super-subsolution method, we obtain the existence and nonexistence of positive solutions. Moreover, we study the stability of the minimal solution to the Cauchy problem. [ABSTRACT FROM AUTHOR]

The authors consider a typical model used in many fields of applied mathematics regarding selection of optimal decisions in stochastic systems. The multidimensional death process controlled on an interval of random length, which is analyzed in the paper, can be used to describe phenomena that appear in economical, biological, medical, engineering, and other applications. Several approaches are proposed to determine the optimality criteria, the properties of corresponding risk function are investigated, and a computing algorithm is developed for construction of optimal stationary strategies. [ABSTRACT FROM AUTHOR]

Huang et al. (J Bus Econ Stat 32:237-244, 2014) first proposed a Pearson Chi-Square based feature screening procedure tailored to multi-classification problem with ultrahigh dimensional categorical covariates, which is a common problem in practice but has seldom been discussed in the literature. However, their work establishes the sure screening property only in a limited setting. Moreover, the p value based adjustments when the number of categories involved by each covariate is different do not work well in several practical situations. In this paper, we propose an adjusted Pearson Chi-Square feature screening procedure and a modified method for tuning parameter selection. Theoretically, we establish the sure screening property of the proposed method in general settings. Empirically, the proposed method is more successful than Pearson Chi-Square feature screening in handling non-equal numbers of covariate categories in finite samples. Results of three simulation studies and one real data analysis are presented. Our work together with Huang et al. (J Bus Econ Stat 32:237-244, 2014) establishes a solid theoretical foundation and empirical evidence for the family of Pearson Chi-Square based feature screening methods. [ABSTRACT FROM AUTHOR]

The current work presents analytical solutions of a nonlinear conformable time-fractional equation by using two different techniques. These are the modified simple equation method and the exponential rational function method. Based on the conformable fractional derivative and traveling wave transformation, the fractional partial differential equation is turned into the nonlinear non-fractional ordinary differential equation. Therefore, we implement the algorithms to this nonlinear non-fractional ordinary differential equation. To the best of our knowledge, the exact solutions obtained in this paper might be very useful in various areas of applied mathematics in interpreting some physical phenomena. [ABSTRACT FROM AUTHOR]

Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this order-theoretic structure, we develop a new perspective on quantum observables. In this first paper (of two), we show that self-adjoint operators affiliated with a von Neumann algebra $${\mathcal{N}}$$ can equivalently be described as certain real-valued functions on the projection lattice $${\mathcal{P}(\mathcal{N}})$$ of the algebra, which we call q-observable functions. Bounded self-adjoint operators correspond to q-observable functions with compact image on non-zero projections. These functions, originally defined in a similar form by de Groote (Observables II: quantum observables, ), are most naturally seen as adjoints (in the categorical sense) of spectral families. We show how they relate to the daseinisation mapping from the topos approach to quantum theory (Döring and Isham , New Structures for Physics, Springer, Heidelberg, ). Moreover, the q-observable functions form a conditionally complete lattice which is shown to be order-isomorphic to the lattice of self-adjoint operators with respect to the spectral order. In a subsequent paper (Döring and Dewitt, , preprint), we will give an interpretation of q-observable functions in terms of quantum probability theory, and using results from the topos approach to quantum theory, we will provide a joint sample space for all quantum observables. [ABSTRACT FROM AUTHOR]

In a recent paper, Bakalov and Milanov (Compositio. Math. 149: 840-888, 2013) proved that the total descendant potential of a simple singularity satisfies the $${\mathcal{W}}$$ -constraints, which come from the $${\mathcal{W}}$$ -algebra of the lattice vertex algebra associated with the root lattice of this singularity and a twisted module of the vertex algebra. In the present paper, we prove that the solution of these $${\mathcal{W}}$$ -constraints is unique up to a constant factor, as conjectured by Bakalov and Milanov in their paper. [ABSTRACT FROM AUTHOR]

Recently, Kim and Kim introduced some identities of degenerate Daehee numbers which are derived from nonlinear differential equations (see (Kim and Kim in J. Nonlinear Sci. Appl. 10:744-751, 2017)). From the viewpoint of inversion formula, we study the degenerate Daehee number arising from a nonlinear differential equation. In this paper, we obtain the explicit expression of degenerate Daehee numbers from the inversion formula of (Kim and Kim in J. Nonlinear Sci. Appl. 10:744-751, 2017) using the generating function and nonlinear differential equations. [ABSTRACT FROM AUTHOR]

Kaluza-Klein theory, as a topic of great interest in theoretical physics, applied mathematics and differential geometry, represents the framework in which we develop our study. Based on Bejancu's results from Bejancu (Prog Theor Phys 128(3):541-585, 2012), we continue here our previous paper Bejan and Chiriac (Int J Geom Methods Mod Phys 10:1, 2013), by dealing with a natural almost paracontact structure on a general Kaluza-Klein space. Such a structure is analogous to the almost contact structure, [see Blair (Contact manifolds in Riemannian geometry. LNM, vol 509. Springer, Berlin, 1976)], which is related to thermodynamics, Mrugala (RIMS Kokyuroku 1142:167-181, 2000), Mrugala (Rep Math Phys 38(3):339-348, 1996). Also, some necessary and sufficient conditions for the existence of Ricci solitons on Kaluza-Klein spaces are provided here. [ABSTRACT FROM AUTHOR]

In this paper, we present families of piecewise linear systems which are controlled by a continuous piecewise monoparametric control function for the generation of monoparametric families of multi-scroll attractors. Thus, the maximum range of values that the parameter set can take in order to preserve the useful dynamics for generating of multi-scroll attractors is found and it will be called maximal robust dynamics interval. This class of dynamical systems is the result of combining two or more unstable 'one-spiral' trajectories. We give necessary and sufficient conditions in order to preserve multi-scroll attractors in terms of a parameter, i.e., a family of multi-scroll attractors is generated by means of a family of switching systems with multiple monoparametric companion matrices. Lastly, we provide an example to show how the developed theory works. [ABSTRACT FROM AUTHOR]

In this paper, by using four functionals fixed point theorem, we obtain sufficient conditions for the existence of at least one positive solution of an nth-order m-point boundary value problem. As an application, we give an example to demonstrate our main result. [ABSTRACT FROM AUTHOR]

In recent years, nonhomogeneous wavelet frames have attracted some mathematicians' interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained. .. [ABSTRACT FROM AUTHOR]