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This paper concerns the intermediate dimensions, a spectrum of dimensions that interpolate between the Hausdorff and box dimensions. Potential theoretic methods are used to produce dimension bounds for images of sets under H\"older maps and certain stochastic processes. We apply this to compute the almost-sure value of the dimension of Borel sets under index-$\alpha$ fractional Brownian motion in terms of dimension profiles defined using capacities. As a corollary, this establishes continuity of the profiles for Borel sets and allows us to obtain an explicit condition showing how the Hausdorff dimension of a set may influence the typical box dimension of H\"older images such as projections. The methods used propose a general strategy for related problems; dimensional information about a set may be learned from analysing particular fractional Brownian images of that set. To conclude, we obtain bounds on the Hausdorff dimension of exceptional sets, with respect to intermediate dimensions, in the setting of projections., Comment: 16 pages, 0 figures

The multiple T-value, which is a variant of the multiple zeta value of level two, was introduced by Kaneko and Tsumura [‘Zeta functions connecting multiple zeta values and poly-Bernoulli numbers’, in: Various Aspects of Multiple Zeta Functions, Advanced Studies in Pure Mathematics, 84 (Mathematical Society of Japan, Tokyo, 2020), 181–204]. We show that the generating function of a weighted sum of multiple T-values of fixed weight and depth is given in terms of the multiple T-values of depth one by solving a differential equation of Heun type.

Ordinary differential equations (ODE) constitute a significant portion of any engineering or STEM curriculum. However, students often question the relevance to their professional lives of the mathematics they learn ODE courses. This is largely due to the fact that they rarely see real and credible connections to real world phenomena and situations in the math classroom. On the other hand, organizations like the European Society for Engineering Education (SEFI), the Mathematical Association of America (MAA), the American Mathematical Society (AMS), and the Society for Industrial and Applied Mathematics (SIAM) involved with the education of engineering professionals, for decades have regarded modeling as an essential skill to foster in students of engineering and related professions, and have called for including modeling in university mathematics courses. Founded in 2013 by Brian Winkel, Emeritus Professorof Mathematics at the United States Military Academy - West Point, SIMIODE is an open community of teachers and learners committed to a modeling first approach to teaching differential equations. This pedagogical innovation is starting to be known and used in several Latin-American universities, though not yet in Panama. This article informs of a mathematical modeling workshop conducted by Dr. Winkel at the UTP in February 2020. The workshop was directed to UTP professors who regularly teach the ordinary differential equations course, in the hopes of motivating them to incorporate mathematical modeling in their teaching. Mathematics professors from other higher ed institutions, high school teachers, as well as graduate students who needed to hone their mathematical modeling skills to carry out their research, also participated. Subsequently, several teachers implemented modeling scenarios with their students during the fall semester of the 2020-2021 school year. Student response to this pedagogical innovation is briefly described., Las ecuaciones diferenciales ordinarias (EDO) constituyen una parte significativa de cualquier currículo de ingeniería o CTIM. No obstante, los estudiantes a menudo cuestionan la relevancia para su vida profesional de las matemáticas que aprenden en los cursos de EDO. En buena medida esto se debe a que pocas veces se establecen nexos reales y creíbles entre los conceptos estudiados en clase y fenómenos y situaciones de la vida real. Por otra parte, organizaciones vinculadas a la formación de profesionales de la ingeniería, como la Sociedad Europea de Formación de Ingenieros (SEFI), la Asociación Matemática de América (MAA), la Sociedad Matemática Americana (AMS), y la Sociedad para Matemática Aplicada e Industrial (SIAM) por décadas han destacado la capacidad de modelación como una competencia esencial a desarrollar en los estudiantes de ingeniería y carreras afines, y han hecho un llamado para incluir la modelación en los cursos básicos de matemáticas a nivel de pregrado. SIMIODE es una comunidad abierta de enseñantes y aprendientes para enseñar y aprender sobre ecuaciones diferenciales a nivel de pregrado fundada en el 2013 por Brian Winkel, profesor emérito del United States Military Academy, West Point. La propuesta pedagógica de SIMIODE, denominada modelado primero, ya empieza a conocerse y ponerse práctica en algunas universidades latinoamericanas, aunque todavía no en Panamá. Este artículo da cuenta de un taller de modelación matemática realizado por el Dr. Winkel en la UTP en febrero de 2020. El taller estaba dirigido a docentes de la UTP que regularmente imparten el curso de ecuaciones diferenciales ordinarias, con el objetivo de motivarlos a incorporar la modelación matemática en su quehacer docente. Participaron también profesores de matemáticas de otras instituciones de educación superior, docentes de secundaria, así como estudiantes de posgrado que requerían afinar sus habilidades de modelación matemática para sus trabajos de investigación. Posteriormente, varios docentes implementaron escenarios de modelación con sus estudiantes durante el primer semestre del año académico 2020-2021. Se describe brevemente la respuesta de los estudiantes a esta innovación pedagógica.

W artykule przedstawiamy sprawozdanie z Sesji wspomnieniowej pamięci prof. Andrzeja Pelczara (1937–2010), zorganizowanej online 2 czerwca 2020 przez Zarząd Oddziału Krakowskiego Polskiego Towarzystwa Matematycznego. Przybliżamy sylwetkę A. Pelczara (1937–2010) i niektóre z Jego osiągnięć wspomnianych podczas tej Sesji. Przywołujemy także fragmenty wypowiedzi uczestników Sesji na temat A. Pelczara. Andrzej Pelczar (1937–2010). „A righteous man of exceptional moral principles”. Online memorial session (2 June 2020, 17.00–20.00) In the article we present the report from the memorial session of prof. Andrzej Pelczar (1937–2010), organized online on June 2, 2020 by the Board of the Krakow Branch of the Polish Mathematical Society. We familiarize the reader with the profile of A. Pelczar (1937–2010) and some of his achievements recalled during the session. We invoke also fragments of statements made by participants of the session.

Perhaps it should not be a surprise that A Course in Cryptography, which is published by the American Mathematical Society, is a textbook that is written for a mathematically sophisticated student....

Let g be a finite-dimensional semisimple complex Lie algebra and θ an involutive automorphism of g. According to G. Letzter, S. Kolb and M. Balagović the fixed-point subalgebra k=gθ has a quantum counterpart B, a coideal subalgebra of the Drinfeld-Jimbo quantum group Uq(g) possessing a universal K-matrix K. The objects θ, k, B and K can all be described in terms of Satake diagrams. In the present work we extend this construction to generalized Satake diagrams, combinatorial data first considered by A. Heck. A generalized Satake diagram naturally defines a semisimple automorphism θ of g restricting to the standard Cartan subalgebra h as an involution. It also defines a subalgebra k⊂g satisfying k∩h=hθ, but not necessarily a fixed-point subalgebra. The subalgebra k can be quantized to a coideal subalgebra of Uq(g) endowed with a universal K-matrix in the sense of Kolb and Balagović. We conjecture that all such coideal subalgebras of Uq(g) arise from generalized Satake diagrams in this way.

We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several theorems are proved using martingale and combinatorics techniques. In particular, the empirical observation of the stability of the Bitcoin protocol is proved. This survey article on the mathematics of Bitcoin is published by the Newsletter of the European Mathematical Society, vol.115, 2020, p.31-37. Continuation of arXiv:1601.05254 (EMS Newsletter, 100, 2016 p.32).

The importance of encouraging and supporting young people from underrepresented populations to study science, mathematics, technology, and engineering (STEM) is perhaps as great today as at any tim...

This is a slightly revised version of the Presidential address (General) delivered at the 84th Annual Conference of the Indian Mathematical Society held at Jammu, India during November 2018., 7 pages

The role of mathematics in the education of Dutch army officers changed dramatically in the early 19th century. This shift became visible with the founding of the Dutch Royal Military Academy in 1828, which shows the role of mathematics in military education shifting toward a purely pedagogical function. This change in approach, which primarily occurred in 1860’s, affected the standing and perception of an academy once highly respected in the field of mathematics. In the present work, I examine both the curricula at the Academy and the crucial role of the Academy’s mathematics instructors in the Dutch Mathematical Society and the Royal Academy of Sciences. Importantly, these two institutions managed to successfully adapt to the changing character of mathematical sciences that occurred around 185 Mathematicians at the Royal Military Academy, however, appeared to cling to an outdated view of mathematics. Failing to update their approach ultimately caused the Academy to lose its once prominent place in the Dutch mathematical community.

We give a general overview of the influence of William Thurston on the French mathematical school and we show how some of the major problems he solved are rooted in the French mathematical tradition. At the same time, we survey some of Thurston's major results and their impact. The final version of this paper will appear in the Surveys of the European Mathematical Society.

James Fairley McKenzie, who was a professor of applied mathematics at the University of Natal from 1981 to 1998, would have been 80 in May 2018. A Special Session was held in his honour at the Annu...

Generalization of the paper [Y. B. Jun and S. Z. Song, Semidetached subalgebras in [Formula: see text]-algebras, to appear in Bulletin of the Korean Mathematical Society] is discussed. Several conditions for a semidetached structure in [Formula: see text]-algebras to be a semidetached subalgebra are provided. The concepts of ([Formula: see text])-fuzzy subalgebra, [Formula: see text]-left ([Formula: see text]-right) [Formula: see text]-fuzzy subalgebra, ([Formula: see text])-fuzzy subalgebra and ([Formula: see text])-fuzzy subalgebra are introduced, and relative relations and properties are discussed.

We define the relative Dolbeault homology of a complex manifold with currents via a Cech approach, and we prove its equivalence with the relative Cech–Dolbeault cohomology as defined by Suwa (in: Singularities–Niigata–Toyama 2007. Advanced studies in pure mathematics, vol 56. Mathematical Society of Japan, Tokyo, pp 321–340, 2009). This definition is then used to compare the relative Dolbeault cohomology groups of two complex manifolds of the same dimension related by a suitable proper surjective holomorphic map. Finally, an application to blow-ups is considered and a blow-up formula for the Dolbeault cohomology in terms of relative cohomology is presented.

We resolve parts (A) and (B) of Problem 1.100 from Kirby's list by showing that many nontrivial links arise as cross-sections of unknotted holomorphic disks in the four-ball. The techniques can be used to produce unknotted ribbon surfaces with prescribed cross-sections, including unknotted Lagrangian disks with nontrivial cross-sections., 12 pages, 9 figures. v2: Major revision; changes reflected in abstract

Resume. Des quelques articles publies par Robert P. Langlands en physique mathematique, c'est celui publie dans le {\it Bulletin of the American Mathematical Society} sous le titre {\it Conformal invariance in two-dimensional percolation} qui a eu, a ce jour, le plus d'impact : les idees d'Oded Schramm ayant mene a l'equation de Loewner stochastique et les preuves de l'invariance conforme de modeles de physique statistique par Stanislav Smirnov ont ete suscitees, au moins en partie, par cet article. Ce chapitre rappelle sommairement quelques idees de l'article original ainsi que celles issues des travaux de Schramm et Smirnov. Il est aussi l'occasion pour moi de decrire la naissance de ma collaboration avec Robert Langlands et d'exprimer ma profonde gratitude pour cette fantastique experience scientifique et humaine. Abstract. Of all mathematical physics contributions by Robert P. Langlands, the paper {\it Conformal invariance in two-dimensional percolation} published in the {\it Bulletin of the American Mathematical Society} is the one that has had, up to now, the most significant impact: Oded Schramm's ideas leading to the stocastic Loewner equation and Stanislav Smirnov's proof in two dimensions were at least partially inspired by it. This chapter reviews briefly some ideas of the original paper and some of those by Schramm and Smirnov.

Wefelscheid (Untersuchungen über Fastkörper und Fastbereiche, Habilitationsschrift, Hamburg, 1971) generalised the well-known Theorem of Artin/Schreier about the characterization of formally real fields and the fundamental result of Baer/Krull to near-fields. In the last fifty years arose from the Theorem of Baer/Krull a theory, which analyses the entirety of the orderings of a field (E. Becker, L. Bröcker, M. Marshall et al.), as presented e.g. in the book by Lam (Orderings, valuations and quadratic forms, American Mathematical Society, Providence, 1983). At the centre of this theory are preorders and their compatibility with valuations or places. We develop some essential results of this theory for the near-field case. In particular, we derive the Brown/Marshall’s inequalities and Bröcker’s Theorem on the trivialisation of fans in the near-field case.

Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical Society}, notebooks, Quarterly Reports to the University of Madras, letters to Hardy, published papers and the Lost Notebook. His evaluations are often surprising, beautiful, elegant, and useful in other mathematical contexts. He also discovered general methods for evaluating and approximating integrals. A survey of Ramanujan's contributions to the evaluation of integrals is given, with examples provided from each of the above-mentioned sources., Comment: 14 pages, to appear in the first special volume of the Hardy-Ramanujan Journal dedicated to the memory of Srinivasa Ramanujan

Under the influence of a new mathematical society founded in Cracow in 1917 gathering Banach, Leja, Nikodym, Steinhaus and Zaremba, a new era opened for Polish mathematics. New mathematical journals were set up: Fundamenta Mathematicae (1920) in Warsaw, Studia Mathematica (1929) in Lwow. The involvement of Polish mathematicians was very important in these journals and Banach in particular would publish there a large amount of his work. Through the presentation of this intense publication activity, we examine a few research topics that played a central role in the revival of Polish mathematics at the beginning of the 20th century.

In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic varieties, and discuss some of its applications to problems in Number Theory. This is an extended version of a talk at the Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Krak\'ow, 2019., Comment: Comments are welcome !

Ramanujan wrote a few articles soon after he reached Cambridge and in June 1914, Hardy presented some of the Entries (Theorems) from the Notebooks of Ramanujan at a meeting of the London Mathematical Society.

The Unione Matematica Italiana (Italian Mathematical Union, UMI) was created according to a motion approved in Brussels in July 1919 by the International Research Council, which promoted the creation of national scientific committees. The recent reorganization of the UMI Archive has made significant documents available to science historians. By using some of these unpublished letters and documents, we focus on the following issues: (i) The foundation and early years of the UMI and its journal, the Bollettino della Unione Matematica Italiana (BUMI); (ii) The international models for the new society, in particular the Deutsche Mathematiker-Vereinigung, the Societe mathematique de France and the American Mathematical Society; (iii) The impact of national and international events on the UMI, including the International Congresses of Mathematicians (ICM).

Funding Information: Acknowledgments. The authors would like to thank the Hausdorff Research Institute for Mathematics in Bonn for their hospitality during the Junior Trimester Program in Topology in 2016. Much of the work on this paper was carried out during that program. The authors also acknowledge the support of the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The second author was supported by the Max Planck institute for Mathematics and thanks the Mittag-Leffler Institute for their hospitality. The third author was supported by the German Research Foundation Schwerpunktprogramm 1786. The fourth author was supported by Independent Research Fund Denmark’s Sapere Aude program (DFF–4002-00224) and by the Max Planck Institute for Mathematics. Publisher Copyright: © European Mathematical Society 2021 Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

The earliest contributions of Ramanujan to Mathematics were in the form of Questions and/or Answers to questions in the Journal of the Indian Mathematical Society.

Polish scientists, the hematologist Maria Wazewska-Czyzewska and the mathematician Andrzej Lasota, formulated a mathematical model of the red blood cell system dynamics, known today as the Lasota–Wazewska equation, in an article published in Applied Mathematics (annals of the Polish Mathematical Society) in the year 1976. Their main goal was to provide a model that, with the possible low number of constants having a specified biological meaning, would allow to predict changes in the number of blood cells in the bloodstream. The basic idea was to associate some known equation of population dynamics taking into account the age structure of the population, with a properly constructed feedback in the form of an integral equation with a delayed argument.

When Ramanujan’s lost notebook (Ramanujan, The lost notebook and other unpublished papers, Narosa, New Delhi, 1988) was published in 1988, accompanying it were other unpublished notes and partial manuscripts by Ramanujan. In one of these previously unpublished partial manuscripts, Ramanujan offered two elegant identities, associated, respectively, with the classical circle and divisor problems. In fact, they are two-variable analogues, but not generalizations, of classical identities associated with these two famous problems. The origin and history of this partial manuscript is unclear. We do know that after Ramanujan died in 1920, the University of Madras on 30 August, 1923 sent to G.H. Hardy a parcel of Ramanujan’s unpublished work, probably containing the lost notebook and the previously mentioned fragment (Berndt and Rankin, Ramanujan: essays and surveys, American Mathematical Society, Providence, 2001; London Mathematical Society, London, 2001, p. 266). Unfortunately, we do not have any record of what was included in this package. If this fragment was included in the mailing, then it is possible that Ramanujan wrote it at the end of his life in either 1919 or 1920. On the other hand, from Hardy’s paper (Hardy, Q J Math, 46:263–283, 1915) on the circle problem published in 1915, it is evident that by early in his stay in England, Ramanujan had a strong interest in the circle and divisor problems, and so the fragment may emanate from this period. In 2013, the first and third present authors and S. Kim published a proof (Berndt et al., Adv Math, 236:24–59, 2013) of the identity from the fragment connected with the circle problem. In this paper, a proof of the second identity is briefly sketched.

Peer review and citation metrics are two means of gauging the value of scientific research, but the lack of publicly available peer review data makes the comparison of these methods difficult. Mathematics can serve as a useful laboratory for considering these questions because as an exact science, there is a narrow range of reasons for citations. In mathematics, virtually all published articles are post-publication reviewed by mathematicians in Mathematical Reviews (MathSciNet) and so the data set was essentially the Web of Science mathematics publications from 1993 to 2004. For a decade, especially important articles were singled out in Mathematical Reviews for featured reviews. In this study, we analyze the bibliometrics of elite articles selected by peer review and by citation count. We conclude that the two notions of significance described by being a featured review article and being highly cited are distinct. This indicates that peer review and citation counts give largely independent determinations of highly distinguished articles. We also consider whether hiring patterns of subfields and mathematicians' interest in subfields reflect subfields of featured review or highly cited articles. We reexamine data from two earlier studies in light of our methods for implications on the peer review/citation count relationship to a diversity of disciplines., 21 pages, 3 figures, 4 tables

This research identifies the similarities and differences between the MathSciNet search features and functions of the American Mathematical Society (AMS) and EBSCOhost platforms. A series of iterat...

Let $$(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times \cdots \times S_{r_k}^1, dt_1^2+dt_2^2+\cdots +dt_k^2)$$ be flat tori, $$r_k\ge \cdots \ge r_2\ge r_1>0$$ and $$({\mathbb {R}}^n,g_E)$$ the Euclidean space with the flat metric. We compute the isoperimetric profile of $$(T^2\times {\mathbb {R}}^n, h_2+g_E)$$ , $$2\le n\le 5$$ , for small and big values of the volume. These computations give explicit lower bounds for the isoperimetric profile of $$T^2\times {\mathbb {R}}^n$$ . We also note that similar estimates for $$(T^k\times {\mathbb {R}}^n, h_k+g_E)$$ , $$2\le k\le 5$$ , $$2\le n\le 7-k$$ , may be computed, provided estimates for $$(T^{k-1}\times {\mathbb {R}}^{n}, h_{k-1}+g_E)$$ exist. We compute this explicitly for $$k=3$$ . We use symmetrization techniques for product manifolds, based on work of Ros (Global theory of minimal surfaces (Proc. Clay Mathematics Institute Summer School, 2001). American Mathematical Society, Providence, 2005) and Morgan (Ann Glob Anal Geom 30:73–79, 2006).

Review of the book "Mathematical Petersburg: History, Science, Sights: Guidebook-Directory / Ed. G.I. Sinkevich, Scientific Editor A.I. Nazarov.- St. Petersburg: Educational projects, 2018. - 336 p.". The book is devoted to the historical development and the modern state of the mathematical life of St. Petersburg from the XVIII century to the present. The book reviews the scientific and educational activities in academic institutions, university and other universities in St. Petersburg. The book also reviews the work of the Mathematical Society, archives and libraries, the creation of special schools for talented children, the organization of mathematical olympiads.

We investigate the relationship between solitonic metrics $$g_u = - (\sin ^2 \frac{u}{2}) c^2 d t^2 + (\cos ^2 \frac{u}{2}) \sum _{i=1}^n (d x^i )^2$$ with $$u \in C^\infty ({{\mathbb {R}}}^{n+1})$$ and stationary points of the functional $$E_\Omega (\Phi ) = \frac{1}{2} \int _\Omega \Vert d \Phi \Vert ^2 d^{n+1} \mathbf{x}$$ with $$\Phi \in C^\infty ({{\mathbb {R}}}^{n+1}, S^2 )$$. Building on work by F.L. Williams (cf. Williams, in: Milton (ed) Quantum field theory under the influence of external conditions, Rinton Press, Princeton, pp 370–372, 2004; in: 4th international winter conference on mathematical methods in physics, Rio de Janeiro, http://pos.sissa.it/archive/conferences/013/003/wc2004_003.pdf, 2004; in: Chen (ed) Trends in soliton research, Nova Science Publications, Hauppauge, pp 1–14, 2006; in: Maraver, Kevrekidis, Williams (eds) The sine-gordon modeland its applications, Springer, Berlin, pp 177–205, 2014) we show that a map $$\Phi = (\cos \beta \sin \frac{u}{2}, \sin \beta \sin \frac{u}{2}, \cos \frac{u}{2} )$$ with $$\beta (\mathbf{x}, t) = m \big ( 1 + | \mathbf{v} |^2 \big )^{-1/2} (t + \mathbf{v} \cdot \mathbf{x})$$ is harmonic if and only if $$u_{tt} + \Delta u = m^2 \sin u$$ (the sine-Gordon equation) and $$u_t + \mathbf{v} \cdot \nabla u = 0$$ (the convection equation). In the spirit of work by B. Solomon (cf. Solomon in J Differ Geom 21:151–162, 1985) we build a 1-parameter variation of $$\Phi $$ which singles out [from the full Euler–Lagrange system of the variational principle $$\delta E_\Omega (\Phi ) = 0$$] the convection equation. Williams’ harmonic maps $$\Phi ^\pm = (1 + v^2 )^{-1/2} (\tau \cos \beta , \tau \sin \beta , \pm (1 + v^2 )^{1/2}\tanh \rho )$$ are shown to be harmonic morphisms of dilation $$\lambda = m(1 + v^2 )^{-1/2}\tau $$, further explaining the relationship between Jackiw–Teitelboim 2-dimensional dilation-gravity theory (cf. Jackiw, in: Christensen (ed) Quantum theory of gravity, MIT, Cambridge, pp 403–420, 1982; Teitelboim, in: Christensen (ed) Quantum theory of gravity, Adam Hilger Ltd, Bristol, pp 403–420, 1984) and harmonic map theory (cf. Baird and Wood Harmonic morphisms between Riemannian manifolds, London mathematical society monographs, new series, 29, The Clarendon Press, Oxford University Press, Oxford, ISBN 0-19-850362-8, 2003). We show that geodesic motion in a weak solitonic gravitational field $$g_{u_\epsilon }$$ [$$u_\epsilon = u_0 + 2 \epsilon \rho $$ with $$\rho \in C^\infty ({{\mathbb {R}}}^{n+1})$$ bounded and $$\epsilon<< 1$$] in the Newtonian velocity limit ($$\Vert \mathbf{u}\Vert /c<< 1$$) obeys to the law of motion $$d^2 \mathbf{r}/d t^2 = - \nabla \phi $$ in a central force field of potential $$\phi \equiv \epsilon c^2 \tan \frac{u_0}{2} \, \rho $$. To justify the use of geodesic equations as equations of motion we address a relativistic mechanics problem i.e. the rotation of a disc in a solitonic gravitational field and exhibit a class of metrics $$g_u$$ one of whose geodesic equations yields a relativistic generalization $$d^2 r/d s^2 = (r w^2 )/c^2$$ of centrifugal accelerations in classical mechanics.

The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet M...

This is the author accepted manuscript. The final version is available from American Mathematical Society via the DOI in this record

In October 1946, mathematicians and physicists founded the Korean Society of Mathematics and Physics, which was relaunched as the Korean Mathematical Society (KMS) in March 1952. This article presents the history of three journals published by the KMS. Volume 1 of the first journal, Mathematics Education, was published in 1955, but it was discontinued after publication of volume 3. After that, as the KMS was reorganized in the 1960s, it began once more to publish a journal in 1964, with the title Mathematics. Later, Mathematics was divided into the Journal of the Korean Mathematical Society and the Bulletin of the Korean Mathematical Society. A third journal, Communications of the Korean Mathematical Society, was first published in 1986. Since then, a total of three journals have been published by the KMS. We can conceive of the years before 1980 as an era focused on education, while the subsequent years have constituted a research era. In this period, mathematics in Korea achieved remarkable growth through extensive international collaboration in research and the internationalization of journals of the KMS. In particular, the Journal of the Korean Mathematical Society and Bulletin of the Korean Mathematical Society achieved being indexed in SCIE, while Communications of the Korean Mathematical Society achieved being indexed in ESCI, a stage that precedes being indexed in SCIE. The journals published by the KMS will continue to serve as a venue for outstanding research results from throughout the world to be published and contribute greatly to the international growth of Korean mathematical capabilities.

This paper surveys the similarities and differences between the game of cops and robbers and classes of related games. The game of cops and robbers is a class of pursuit–evasion games played on a finite graph. The players comprise a set of cops and a robber located on vertices of the graph, and they move alternately along edges of the graph. The cops win the game if at least one cop occupies the same vertex of the robber in finite time; otherwise, the robber wins. Quilliot (Jeux de points fixes sur les graphes, These de 3ieme Cycle, Universite de Paris VI, Paris, pp 131–145, 1978) and Nowakowski and Winkler (Discrete Math 43:235–239, 1983) were among the first to study this class of games. The main questions studied in the literature of cops and robbers games are on the class of graphs that characterize cop-win games, on the minimum number of cops needed for classes of graphs to be cop-win, on a conjecture due Meyniel (Personal communication, 1985) about the cop number of a graph and more recently on the game played on random and/or infinite graphs (Bonato and Nowakowski in The game of cops and robbers, Student mathematical library, vol 61, American Mathematical Society, Providence, 2010; Bonato and Pralat in Graph searching games and probabilistic methods, CRC Press, Boca Raton, 2017). While the game of cops and robbers is not traditionally modeled in the language of extensive game theory (Kuhn, in: Kuhn, Tucker (eds) Contributions to the theory of games II, Princeton University Press, Princeton, 1953), Kehagias et al. (The role of visibility in pursuit/evasion games, 2014) give a general framework for the game of cops and robbers that relate to extensive games. By using the notion of “capture time,” they are able to represent the game using a standard discrete dynamic game model with explicit payoff functions for the cops and the robber. More recently, the game of cops and robbers has also been related to dynamic games with state variables (Bonato and Macgillivray in Contrib Discrete Math, 2017) and discounted stochastic games (Konstantinidis and Kehagias in Selfish cops and adversarial robber: multi-player pursuit evasion on graphs, 2017a, arXiv:1703.07695 ; Theor Comput Sci 680:25–35, 2017b). In this survey, we study these connections.