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The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00283-016-9700-z Byline: Tinne Hoff Kjeldsen (1) Author Affiliation: (1) Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark Article History: Registration Date: 24/12/2016 Online Date: 10/05/2017

Byline: Marc Chamberland (1), Eugene A. Herman (1) Author Affiliation: (1) Department of Mathematics and Statistics, Grinnell College, Grinnell, IA, 50112, USA Article History: Registration Date: 28/08/2014 Received Date: 16/12/2013 Accepted Date: 28/08/2014 Online Date: 25/12/2014 Article note: An erratum to this article can be found at http://dx.doi.org/10.1007/s00283-015-9536-y.

Byline: John J. Watkins (1) Author Affiliation: (1) 0000 0001 0657 7781, grid.254544.6, Department of Mathematics and Computer Science, Colorado College, Colorado Springs, CO, 80903, USA Article History: Registration Date: 05/06/2018 Online Date: 17/08/2018 Article note: Feel like writing a review for The Mathematical Intelligencer? Contact the column editor if you wish to submit an unsolicited review, or if you would welcome being assigned a book to review.

Byline: L.L. Stacho (1), Gy. Domotor (2), M.I. Ban (2) Keywords: Elber--Karplus procedures; reaction path-following; DDRP method Abstract: The flaws in the 'Reply' [1] to our paper [2] have been pointed out. Elber and Karplus (EK) have not disproved our irrefutable global statement that the energy average cannot be minimized which rebuts the theoretical background of EK-type calculations. Another statement of ours has shown that even a curve for which the average energy is locally minimal for all directional perturbations in the sense of classical variational calculus cannot be identical with the reaction path (RP) defined as a steepest descent path (SDP). EK found an error in the early preprint of our theoretical paper [3] and because of this error they qualified our correct variational statement as false for all the SDPs consisting of a straight line each. Mixing global and variational arguments, EK refuted our criticism in a logically incorrect manner. In this Comment we prove that both of our earlier statements invariably remain in force and the criticism included in those has been as well-established and solid as was before. Author Affiliation: (1) Bolyai Institute, JATE University of Szeged, H-6720, Szeged, Aradi Vertanuk tere 1, Hungary (2) Institute of Physical Chemistry, JATE University of Szeged, H-6720, Szeged, POB 105, Hungary Article History: Registration Date: 09/10/2004

Congruences mod p for a prime p and partial products of the numbers 1, ..., p - 1 are obtained. Bibliography: 2 titles., UDC 511 1. FULL FACTORIALS In accordance with the Wilson theorem, for a positive rational prime number p, the factorial of p - 1 satisfies the congruence (p - 1)! [...]

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00283-017-9750-x Byline: Oscar Sheynin (1) Author Affiliation: (1) Berlin, Germany Article History: Registration Date: 28/08/2017 Online Date: 22/11/2017 Article note: This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of 'mathematical community' is the broadest: 'schools' of mathematics, circles of correspondence, mathematical societies, student organizations, extra-curricular educational activities (math camps, math museums, math clubs), and more. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others. Submissions should be uploaded to http://tmin.edmgr.com or sent directly to Marjorie Senechal, mi.editor1@gmail.com

Byline: Marc Chamberland (1), Eugene A. Herman (1) Author Affiliation: (1) Department of Mathematics and Statistics, Grinnell College, Grinnell, IA, 50112, USA Article History: Registration Date: 16/01/2015 Online Date: 23/04/2015 Article note: The online version of the original article can be found under doi: 10.1007/s00283-014-9499-4. The online version of the original article can be found at http://dx.doi.org/10.1007/s00283-014-9499-4.

Over the last 25 years, reforms in undergraduate biology education have transformed the way biology is taught at many institutions of higher education. This has been fueled in part by a burgeoning discipline-based education research community, which has advocated for evidence-based instructional practices based on findings from research. This perspective will review some of the changes to undergraduate biology education that have gained or are currently gaining momentum, becoming increasingly common in undergraduate biology classrooms. However, there are still areas in need of improvement. Although more underrepresented minority students are enrolling in and graduating from biology programs than in the past, there is a need to understand the experiences and broaden participation of other underserved groups in biology and ensure biology classroom learning environments are inclusive. Additionally, although understanding biology relies on understanding concepts from the physical sciences and mathematics, students still rarely connect the concepts they learn from other STEM disciplines to biology. Integrating concepts and practices across the STEM disciplines will be critical for biology graduates as they tackle the biological problems of the twenty-first century.

UDC 515.164 (Journal of Mathematical Sciences, Vol. 159, No. 6, pp. 753-760 (2009)) There is a misprint in the formulation of Lemma 3. Instead of the dimension constraints n-k = [...]

Byline: P. M. Akhmet'ev (1) Author Affiliation: (1) Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia Article History: Registration Date: 06/01/2011 Online Date: 11/01/2011 Article note: The online version of the original article can be found under doi: http://dx.doi.org/10.1007/s10958-009-9467-2. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 5, p. 211, 2009.

The drop of the smoothness of an analytic function compared to the smoothness of its modulus is discussed for the unit ball of [C.sup.n]. The paper is devoted to local aspects of the problem. Bibliography: 11 titles., UDC 517.55 This paper is an announcement; all the proofs of the new results discussed here will be published later elsewhere. The following theorem was first published in the paper [...]

The drop of the smoothness of an analytic function compared to the smoothness of its modulus is discussed for the unit ball of [C.sup.n]. The paper is devoted to local aspects of the problem. Bibliography: 11 titles., UDC 517.55 This paper is an announcement; all the proofs of the new results discussed here will be published later elsewhere. The following theorem was first published in the paper [...]

UDC 51(091) The present collection of papers (in two parts) is dedicated to the memory of our advisor Yuri Petrovich Solovyov--an outstanding mathematician and person, whom we always remember with [...]

Let K be a field with at least 19 elements. It is proved that any subgroup of GL(4, K) generated by a pair of 2-tori contains unipotent elements of rank 1 or 2. Taking into account previous papers of N. A. Vavilov and the author, this result is valid for any general linear group. It is one of the first steps in studying subgroups generated by a pair of microweight tori in Chevalley groups. Bibliography: 12 titles., 1. Introduction In the present paper we prove that in the group GL(4, K) over a field K with at least 19 elements, any subgroup generated by a pair of [...]

The theory of commutative rings of differential operators relating the completely integrable systems with the geometry of algebraic curves was constructed several decades ago. It was especially complete in the case of rings, generated by two operators of the coprime order, usually of order 2 and of some odd order; the theory of such rings turned out to be equivalent to the theory of KdV hierarchy. However, the corresponding algebraic curves were always hyperelliptic. In order to handle the general (canonical curves), one should consider the rings, generated by more than two operators. In the previous paper of 1980, the author considered the simplest possible case of this kind-that of generators of orders 3, 4, 5. The goal of the present paper is to give the details of the calculations in that paper and to explain the conjectural geometry underlying some enigmatic phenomena that were used in 1980 to complete the calculations and give some algebro-geometric applications., Author(s): George B. Shabat [sup.1] Author Affiliations: (1) https://ror.org/0473ch268, grid.446275.6, 0000 0001 2162 6510, Russian State University for the Humanities, , Moskow, Russia Introduction and history The theory of commuting [...]

This paper proposes new asymptotic expansions in the central limit theorem which permit us to approximate distributions of normalized sums of independent symmetric random variables with explicit estimates of the remainder. These expansions contain the last known moment of the original random variables in their main part., Author(s): V. N. Sobolev [sup.1], A. E. Condratenko [sup.1] Author Affiliations: (1) grid.14476.30, 0000 0001 2342 9668, MSU, , Moscow, Russia Introduction and notation Let [Formula omitted] be independent identically [...]

The paper extends an earlier result of G.V. Kalachev et al. (Sb. Math. 210(8):1129-1147, 2019) on the existence of a maximizer of convolution operator acting between two Lebesgue spaces on [Formula omitted] with kernel from some [Formula omitted], [Formula omitted]. On the other hand, E. Lieb (Ann. of Math. 118:(2):349-374, 1983) proved the existence of a maximizer for the Hardy-Littlewood-Sobolev inequality and remarked that in general a convolution maximizer for a kernel from weak [Formula omitted] may not exist. In this paper we axiomatize some properties used in the proof of the Kalachev-Sadov 2019 theorem and obtain a more general result. As a consequence, we prove that the convolution maximizer always exists for kernels from a slightly more narrow class than weak [Formula omitted], which contains all Lorentz spaces [Formula omitted] with [Formula omitted]., Author(s): Sergey Sadov [sup.1] Author Affiliations: (1) Moscow, Russia Introduction In this paper we extend the main result of [1]. We will mostly follow [1] in notation and terminology. Following [...]

This text cites a letter of M. I. Gordin to I. A. Ibragimov (November of 2014) and letters to M. A. Livshits and B. A. Lifshits (May of 2009). The [...]

The present volume mostly consists of papers written by participants of the seminar Graphs on Surfaces and Curves over Number Fields, which I have been running at Moscow State University [...]

The paper proves that an indecomposable nonnegative matrix is chainable if and only if it satisfies Kolmogorov's condition, under which the Markov chain determined by a stochastic matrix obeys the multidimensional local limit theorem. Bibliography: 8 titles., 1. Introduction This paper continues the study of nonnegative chainable matrices initiated in [1]. Familiarity with [1] is desirable, but all the necessary definitions and facts are provided below. Additional [...]

Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and [F.sub.c](X, Y) = X + Y + cXY be a polynomial formal group, which defines the formal module [F.sub.c](M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [[[p.sup.m]].sub.c](X), which we denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Let H be the multiplicative group of Cartier curves and [H.sub.c] be the formal analog of the module [F.sub.c](M). In the present paper, the formal symbol [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol. Bibliography: 10 titles., UDC 512.741 1. Introduction The present paper is a continuation of paper [10], in which an explicit formula of the Hilbert symbol for polynomial formal groups was given. We generalize [...]

The results of a recent paper by A. V. Vasin, S. V. Kislyakov, and the author on the relationship between the local boundary smoothness of an analytic function and local boundary smoothness of its modulus are extended to the case of generalized pointwise Holder type conditions of order between one and two. Bibliography: 8 titles., UDC 517.547.3 This note announces a generalization of some particular results from the paper [8]. Their proofs and a significant amount of details can be found in the preprint [5]. [...]

In the paper, we obtain lower estimates for decreasing rearrangements of the convolutions through decreasing rearrangements of kernels and functions to be convolved. These estimates show the exactness of some corollaries of O'Neil's upper estimates for convolutions. The results are applied for equivalent descriptions of the cones of decreasing rearrangements for generalized Bessel and Riesz potentials. These are the key results for study of integral properties of potentials., Author(s): Mikhail L. Goldman [sup.1] Author Affiliations: (1) grid.77642.30, 0000 0004 0645 517X, People's Friendship University of Russia, , Moscow, Russia Introduction In this paper, decreasing rearrangements of generalized Bessel-Riesz [...]

In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far. These are integro-differential operators defined as compositions of the first order derivative and an integral operator of convolution type. Depending on succession of these operators, the general fractional derivatives of the Riemann-Liouville and of the Caputo types were defined and studied. The main objective of this paper is a construction of the 1st level general fractional derivatives that comprise both the general fractional derivative of the Riemann-Liouville type and the general fractional derivative of the Caputo type. We also provide some of their properties including the 1st and the 2nd fundamental theorems of Fractional Calculus for these derivatives and the suitably defined general fractional integrals., Author(s): Yuri Luchko [sup.1] Author Affiliations: (1) Department of Mathematics, Physics, and Chemistry, Berlin University of Applied Sciences and Technology, , Luxemburger Str. 10, 13353, Berlin, Germany Introduction In the [...]

In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the case when, for the two boundary value problems, some coefficients of the differential expressions and of the boundary conditions coincide. We estimate the difference of their spectral data in this case. Although the asymptotic behaviour of spectral data is well-studied for differential operators with regular (integrable) coefficients, to the best of the author's knowledge, there were no results in this direction for the higher-order differential operators with distribution coefficients (generalized functions) in a general form. The technique of this paper relies on the recently obtained regularization and the Birkhoff-type solutions for differential operators with distribution coefficients. Our results have applications to the theory of inverse spectral problems as well as a separate significance., Author(s): Natalia P. Bondarenko [sup.1] [sup.2] Author Affiliations: (1) grid.79011.3e, 0000 0004 0646 1422, Department of Applied Mathematics and Physics, Samara National Research University, , Moskovskoye Shosse 34, 443086, Samara, [...]

The present paper is devoted to the investigation of uniform stabilities of positive [Formula omitted]-semigroups defined on abstract state spaces by means of a generalized Dobrushin ergodicity coefficient. The most known results in the literature were obtained for Markov semigroups acting on Banach lattices having unique invariant states. The essence of the present paper is that the considered Markov semigroups (acting on abstract state spaces) do not generally have invariant states and, moreover, abstract state spaces need not necessarily be lattices, implying that the results of the paper are principal in this direction., Author(s): Nazife Erkursun-Özcan [sup.1], Farrukh Mukhamedov [sup.2] [sup.3] Author Affiliations: (1) https://ror.org/04kwvgz42, grid.14442.37, 0000 0001 2342 7339, Department of Mathematics, Faculty of Science, Hacettepe University, , 06800, Ankara, Turkey (2) [...]

This review article is dedicated to Professor Nikolai Karapetiants on the occasion of the 80th anniversary of his birthday. This article contains a biography of Nikolai Karapetiants, as well as a brief overview of his research., Author(s): Oleg G. Avsyankin [sup.1], Stefan G. Samko [sup.2] [sup.3] Author Affiliations: (1) https://ror.org/01tv9ph92, grid.182798.d, 0000 0001 2172 8170, Institute of Mathematics, Mechanics and Computer Sciences, Regional Mathematical Center, Southern [...]

The paper is devoted to the master thesis on "information theory" which was written by the author in 1956-57. The topic was suggested by his advisor A. A. Bobrov (a student of A. Ya. Khinchin and A. N. Kolmogorov), and the thesis was written under the influence of lectures by N. I. Gavrilov (a student of I. G. Petrovskii) on the qualitative theory of differential equations, which included the statement of Birkhoff's theorem for ergodic dynamical systems. In the thesis, the author used the concept of Shannon entropy in the study of ergodic dynamical systems f (p, t) in a separable compact metric space R with an invariant measure [mu] (where [mu](R) = 1) and introduced the notion of the ([epsilon],T)-entropy of a system as a quantitative characteristic of the degree of mixing. In the work, not only partitions of R were considered, but also partitions of the interval (-[infinity], [infinity]) into subintervals of length T > 0. In particular, f (p, T) was regarded as an aiutomorphism S of X = R, and the ([epsilon],T)-entropy is essentially the [epsilon]-entropy of S. But, despite some "oversights" in the definition of the ([epsilon],T)-entropy and many years that have passed, the author decided to publish the corresponding chapter of the thesis in connection with the following: 1) There is a number of pampers that refer to this work in the explanation of the history of the concept of Kolmogorov's entropy. 2) Recently, B. M. Gurevich obtained new results on the [epsilon]-entropy [h.sub.[epsilon]] (S), which show that for two ergodic automorphisms with equal finite entropies their [epsilon]-entropies also coincide for all e, but, on the other hand, there are unexpected nonergodic automorphisms with equal finite entropies, but different [epsilon]-entropies for some e. This shows that the concept of e-entropy is of scientific value. Bibliography: 25 + 8 titles., UDC 917.987 COMMENTARY BY A. M. VERSHIK We publish a paper by Professor D. Z. Arov on the notion of [epsilon]entropy, which was introduced in his master thesis in 1957 [...]

In this paper, the structural properties of a function are characterized by moduli of continuity. The classical Hardy-Littlewood theorem describes a relation between the smoothness of the analytic function boundary values at the boundary of its analyticity and the growth rate of the modulus of its higher-order derivatives. An analogue of the Hardy-Littlewood theorem has been obtained for functions from the class [H.sub.p] and higher-order moduli of continuity. Keywords. Class [H.sub.p], modules of continuity, theory of functions, boundary properties., 1. Introduction The classes [H.sub.p](0 < p < [infinity]) consisting of functions / that are analytic in the interior D of the unit circle and for which [Please download the [...]

This paper presents a methodology to study non-twist invariant circles and their bifurcations for area preserving maps, which is supported on the theoretical framework developed in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014). We recall that non-twist invariant circles are characterized not only by being invariant, but also by having some specified normal behavior. The normal behavior may endow them with extra stability properties (e.g., against external noise), and hence, they appear as design goals in some applications, e.g., in plasma physics, astrodynamics and oceanography. The methodology leads to efficient algorithms to compute and continue, with respect to parameters, non-twist invariant circles. The algorithms are quadratically convergent and, when implemented using FFT, have low storage requirement and low operations count per step. Furthermore, the algorithms are backed up by rigorous a posteriori theorems, proved and discussed in detail in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014), which give sufficient conditions guaranteeing the existence of a true non-twist invariant circle, provided an approximate invariant circle is known. Hence, one can compute confidently even very close to breakdown. With some extra effort, the calculations could be turned into computer-assisted proofs, see Figueras et al. (Found. Comput. Math. 17:1123-1193, 2017) for examples of the latter. The algorithms are also guaranteed to converge up to the breakdown of the invariant circles, and then, they are suitable to compute regions of parameters where the non-twist invariant circles exist. The calculations involved in the computation of the boundary of these regions are very robust, and they do not require symmetries and can run without continuous manual adjustments, largely improving methods based on the computation of very long period periodic orbits to approximate invariant circles. This paper contains a detailed description of our algorithms, the corresponding implementation and some numerical results, obtained by running the computer programs. In particular, we include calculations for two-dimensional parameter regions where non-twist invariant circles (with a prescribed frequency) exist. Indeed, we present systematic results in systems that do not contain symmetry lines, which seem to be unaccessible for previous methods. These numerical explorations lead to some open questions, also included here., Author(s): Alejandra González [sup.1], Àlex Haro [sup.2], Rafael de la Llave [sup.3] Author Affiliations: (1) Foundations of Learning, Zurich, , Schwäntenmos 4, 8126, Zumikon, Switzerland (2) grid.5841.8, 0000 0004 1937 [...]

The paper tells about the main features and events of the ergodic seminar organized and headed by V. A. Rokhlin at the Leningrad State University. The seminar was active in 1960-1970., 1. V. A. ROKHLIN'S MOVING TO LENINGRAD Vladimir Abramovich Rokhlin, with his wife Anna Alexandrovna Gurevich, his son Volodya (born in 1952), and his daughter Lisa (born in 1955), moved [...]

In this paper, we obtain a stochastic criterion for the k-motion of a regular two-dimensional surface in three-dimensional Euclidean space--a stochastic analog of the main theorem of bending theory . Keywords and phrases: surface bending, stochastic process. AMS Subject Classification: 31A10, 60J60 Dedicated to the 80th Anniversary of Professor V. T. Fomenko, In this paper, we obtain a stochastic criterion for the k-motion of a regular surface of nonzero mean curvature and constant-sign Gaussian curvature in three-dimensional Euclidean space. This paper continues [...]

In the present paper, we consider the problem of probability density function estimation. Our data has multiplicative noise; therefore, we cannot use direct methods. Our method is based on estimation of coefficients of the Fourier transform for the density function., 1. Introduction In the present paper, we consider the problem of detecting impurities in liquids. During the experiment, liquid is illuminated by the laser light and impurity particles are captured [...]

The present paper is devoted to the study of the dimension of the space of all derivations on homogeneous commutative regular algebras. We shall show that if [Formula omitted] is a Maharam homogeneous measure space with a finite countable-additive measure [Formula omitted] and [Formula omitted] is a homogeneous regular unital subalgebra in [Formula omitted] with the homogeneous Boolean algebra of idempotents [Formula omitted] then [Formula omitted] where [Formula omitted] is the weight of the Boolean algebra [Formula omitted] and [Formula omitted] is the transcendence degree of [Formula omitted]., Author(s): Shavkat Ayupov [sup.1] [sup.2], Karimbergen Kudaybergenov [sup.1] [sup.3], Khakimbek Karimov [sup.1] [sup.4] Author Affiliations: (1) grid.419209.7, 0000 0001 2110 259X, V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, , [...]

In the paper it is shown that there exist a set [Formula omitted] with the measure being arbitrarily close to 1 and a weighted function [Formula omitted] with [Formula omitted] on E, so that with a proper modification of an arbitrary function [Formula omitted] outside E one can obtain a function [Formula omitted] being universal for the weighted space [Formula omitted] with respect to Walsh system in the sense of signs., Author(s): M. G. Grigoryan [sup.1], A.A. Sargsyan [sup.1] Author Affiliations: (1) https://ror.org/00s8vne50, grid.21072.36, 0000 0004 0640 687X, Yerevan State University, Alex Manoogian 1, , 0025, Yerevan, Armenia Introduction In this [...]

In the present paper, we study the generalized Cauchy problem of the incompressible micropolar fluid system in [Formula omitted] By using the Fourier localization argument and the Littlewood-Paley theory, we establish the local existence for large initial data and the global existence for small initial data in critical Fourier-Besov-Morrey spaces., Author(s): Fatima Ouidirne [sup.1], Achraf Azanzal [sup.1], Chakir Allalou [sup.1], Mohamed Oukessou [sup.1] Author Affiliations: (1) https://ror.org/02m8tb249, grid.460100.3, 0000 0004 0451 2935, Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane [...]

For a rational function [Formula omitted], Wali and Shah (The Journal of Anal., 25(1):(2017), 43-53) proved the following: |r'(z)|[greater than or equal to]12|B'(z)|+|cn|-|c0||cn|+|c0||r(z)|.In this paper, we prove Bernstein-type inequalities for rational functions with prescribed poles. The obtained results refine some inequalities on rational functions and strengthen known polynomial inequalities., Author(s): M. Y. Mir [sup.1], S. L. Wali [sup.1], W. M. Shah [sup.1] Author Affiliations: (1) https://ror.org/03asvq815, grid.462329.8, 0000 0004 1764 7505, Department of Mathematics, Central University of Kashmir, , [...]

In the paper, we prove probabilistic analogs of the universal approximation theorems and link continuous random variables of a certain type and monotonic feedforward artificial neural networks with one-dimensional input, output and one hidden layer. In particular, we show that any continuous infinitely divisible random variable can be successfully approximated with a mix of logistic distributions. Based on the theorems proved in the current paper, we develop a new approach for developing Monte Carlo methods combined with artificial neural networks for pricing options in Lévy models. In contrast to straightforward incorporation of neural networks into Monte Carlo methods, we approximate the cumulative distribution function, but not its inverse. Moreover, we give a clear probabilistic interpretation of the constructed approximator that helps us simulate the Lévy process by using only separate components of our neural network., Author(s): Oleg Kudryavtsev [sup.1] [sup.2], Natalia Danilova [sup.1] [sup.2] Author Affiliations: (1) InWise Systems, LLC, , Rostov-on-Don, Russia (2) https://ror.org/01tv9ph92, grid.182798.d, 0000 0001 2172 8170, I.I.Vorovich Institute of Mathematics, Mechanics [...]

Scattering of time-harmonic electromagnetic waves by penetrable, anisotropic dielectric obstacles admits an equivalent formulation in terms of a strongly singular volume integral equation (VIE). The aim of this study is to analyse the essential spectrum of the integral operator that describes this equation in the case where the dielectric permittivity is a piecewise constant symmetric [Formula omitted] matrix with some bounds on the eigenvalues. For Lipschitz interfaces, we show that the spectrum is contained in some finite interval which depends on the spectral properties of the above matrix. The results on the spectrum will then be used to derive sufficient conditions to ensure that the integral operator of the VIE is Fredholm of index zero., Author(s): H. Sakly [sup.1], G. Matoussi [sup.1] Author Affiliations: (1) https://ror.org/057x6za15, grid.419508.1, 0000 0001 2295 3249, Department of Mathematics, GAMA Laboratory LR21ES10, Faculty of Sciences of Bizerte, University of Carthage, [...]

In this paper we propose a mixture global vector autoregressive model with exogenous variables to study country/region interdependencies that exist between national and international variables in the world economy. This model generalizes the linear one introduced by Pesaran et al. (Journal of Business & Economic Statistics 22(2):129-162, 2004) taking into account the possibility of contagion effects. Then, we give a complete solution of the above mixture global model, discuss its stability properties, and provide a likelihood-based analysis of the country/region specific models. Finally, a simulation experiment is presented to demonstrate the utility of the proposed algorithm and the nature of the problems under consideration., Author(s): Maddalena Cavicchioli [sup.1] Author Affiliations: (1) https://ror.org/02d4c4y02, grid.7548.e, 0000 0001 2169 7570, Department of Economics Marco Biagi, University of Modena and Reggio Emilia, , Modena, Italy Introduction It is [...]

We consider the Dirac operators on [Formula omitted] with singular potentials 1DA,[Phi],m,[GAMMA][delta][Sigma]=DA,[Phi],m+[GAMMA][delta][Sigma]where 2DA,[Phi],m=[summation]j=1n[alpha]j-i[partial differential]xj+Aj+[alpha]n+1m+[Phi]INis a Dirac operator on [Formula omitted] with the variable magnetic and electrostatic potentials [Formula omitted] and [Formula omitted], and the variable mass m. In formula (2) [Formula omitted] are the [Formula omitted] Dirac matrices, that is [Formula omitted], [Formula omitted] is the unit [Formula omitted] matrix, [Formula omitted] [Formula omitted] is a singular delta-type potential supported on a uniformly regular unbounded [Formula omitted]hypersurface [Formula omitted] being the common boundary of the open sets [Formula omitted]. Let [Formula omitted] be the Sobolev spaces of [Formula omitted]dimensional vector-valued distributions [Formula omitted] on [Formula omitted] and H1(Rnâ²[Sigma],CN)=H1([Omega]+,CN)âH1([Omega]-,CN).We associate with the formal Dirac operator [Formula omitted] the interaction (transmission) operator [Formula omitted] defined by the Dirac operator [Formula omitted] on [Formula omitted] and the interaction condition [Formula omitted] [Formula omitted] associated with the singular potential. The main goal of the paper is to study the Fredholm property of the operators [Formula omitted] for some non-compact [Formula omitted]-hypersurfaces., Author(s): Vladimir S. Rabinovich [sup.1] Author Affiliations: (1) https://ror.org/059sp8j34, grid.418275.d, 0000 0001 2165 8782, Instituto Politécnico Nacional, ESIME Zacatenco, , Ciudad de México, Mexico Introduction [Formula omitted] The Dirac operators [...]

In this paper, we try to apply the advantages of principal component analysis (PCA) and online learning to the calculation of optimal portfolio investments. Each of these methods is widely used separately. This is done in order to make it possible to use online learning algorithms for high-dimension portfolios., Author(s): G. Beliavsky [sup.1], N. Danilova [sup.1], K. Yao [sup.1] Author Affiliations: (1) https://ror.org/01tv9ph92, grid.182798.d, 0000 0001 2172 8170, Operations Research, Mathematics, Mechanics and Computer Sciences Institute of Southern Federal [...]

The present paper is a survey of some of the authors' results on the asymptotic behavior of individual eigenvalues and eigenvectors of sequences of Toeplitz matrices when their size tends to infinity. The symbols of the matrices are supposed to have power singularities and are special cases of so-called Fisher-Hartwig symbols., Author(s): M. Bogoya [sup.1], A. Böttcher [sup.2], S. M. Grudsky [sup.3] [sup.4] Author Affiliations: (1) https://ror.org/00jb9vg53, grid.8271.c, 0000 0001 2295 7397, Departamento de Matemáticas, Universidad del Valle, , Cali, Colombia [...]

We consider the discrete Dirichlet boundary value problem for a discrete elliptic pseudodifferential equation in the quadrant and study its solvability in discrete counterparts of the Sobolev-Slobodetskii space. The study is based on a special factorization of the elliptic symbol. We compare the solutions to the discrete Dirichlet problem and its continuous counterpart. Bibliography: 10 titles. In this paper, based on the ideas and methods of [1, 2] (cf. also [3] [7]), we compare discrete and continuous elliptic boundary value problems in the quadrant for the simplest pseudodifferential operators. We emphasize that, in the case of a quadrant, there are principal differences from the case of a half-space, and new analytic tools are required., 1 Preliminaries We recall the main notions and results which will be used throughout the paper (we refer to [5] for details). Let 1? be an integer lattice in the [...]

Author(s): Sergei Grudsky [sup.1], Helmuth R. Malonek [sup.2], Vladimir Rabinovich [sup.3], Ioannis Stratis [sup.4] Author Affiliations: (1) grid.512574.0, Departamento de Matemáticas, CINVESTAV del I.P.N., , Apartado Postal 14-740, C.P. 07360, [...]

We study the optimal control problem for nonlinear mathematical models describing the equilibrium state of an inhomogeneous body, where the nonlinearity is caused by the Signorini contact condition. We establish the solvability of the optimal control problem and prove that the equilibrium problem for an elastic body with two joined rigid inclusions is the limit for a family of equilibrium problems for bodies with two separate inclusions. Bibliography: 7 titles., In this paper, we study the optimal control problem for nonlinear mathematical models describing possible contacts of an inhomogeneous body with a fixed undeformable obstacle, where the body consists of [...]

The aim of the paper is to improve previously obtained estimate of the constant in the inequality for the uniform distance between n- and (n + 1)-fold convolutions of one-dimensional probability distributions in the case where 0 is the q-quantile of a distribution F. Bibliography: 6 titles., In the present paper, we give an estimate from above for the absolute constant in a special case of the Kolmogorov-Rogozin inequality and improve an estimate for the constant in [...]

It is proved that the free boundary problem for two phase viscous compressible and incompressible fluids in the spaces [W.sub.p.sup.+l,1+l/2]([Q.sub.T]) with p > 2, 1 [member of] (1/p, 2/p), is solvable locally in time. Bibliography: 5 titles., 1. INTRODUCTION The present paper is a continuation of papers [1, 2], where the evolutionary free boundary problem for two phase viscous fluids of different types was studied in the [...]