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Search RSS2015 interdyscyplinarne centrum modelowania matematycznego i komputerowego60XLVII National Conference on Applications of Mathematics, September 4-11, 2018, Zakopane-Kościelisko, Poland
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The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville, USA and Łódź University of Technology) and Heinz Schättler (Washington University, St. Louis, USA) with optimal control in biomedical problems./resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6439Mathematical Days at WUST
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Polish Nationwide Mathematical Student Conference OMatKo!!! was set up by students from all four mathematical scientific clubs at Wroclaw University of Science and Technology. The fifth edition of our conference took place from 13th to 15th of April 2018 and it has become the biggest mathematical student conference in the whole country, attracting more than 200 students. There are both Polish and foreign students among our participants. This event is dedicated not only to mathematics and informatics but also scientific related students. Our project gives an opportunity to gain knowledge and share experience, as well as to develop soft skills and public appearance among both participants and the organizing team. These actions contribute to young people self-development and push to cooperate with others - the conference enables participants to establish cooperation between active students and we encourage the most outstanding individuals to constant improvement./resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6414Nauki społeczne-matematyczne czy matematyzowalne? 27 -- 28 września 2018, Kraków
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W dniach 27 i 28 września 2018 roku na Uniwersytecie Ekonomicznym w Krakowie odbyła się konferencja {\it Nauki społeczne - matematyczne czy matematyzowalne?} poświęcona pamięci prof. dr. hab. Andrzeja Malawskiego, matematyka, filozofa i ekonomisty, wielkiego entuzjasty zastosowań matematyki w naukach społecznych, a zwłaszcza w teorii ekonomii. Andrzej Malawski ukończył dwa kierunki studiów na Uniwersytecie Jagiellońskim: matematykę oraz filozofię. Te dwie dyscypliny wywarły ogromny wpływ na Jego późniejszą działalność naukową. Po ukończeniu studiów matematycznych podjął pracę w~Wyższej Szkole Ekonomicznej w Krakowie, obecnie Uniwersytet Ekonomiczny, gdzie uzyskiwał kolejne stopnie i tytuły naukowe oraz gdzie pracował do końca swoich dni. Profesor Andrzej Malawski był uznanym w kraju i~za granicą specjalistą w zakresie teoretycznych podstaw ekonomii. Jego zainteresowania naukowe koncentrowały się wokół matematycznych podstaw ekonomii -- ogólnej teorii równowagi gospodarczej, ekonomii ewolucyjnej, teorii systemów, a~także metodologii ekonomii. Czynnie uczestniczył w pracach Komisji Ekonomicznej Polskiej Akademii Umiejętności i Komitetu Statystyki i~Ekonometrii Polskiej Akademii Nauk, był członkiem Polskiego Towarzystwa Matematycznego, International Joseph A. Schumpeter Society, oraz Society for Economic Design./resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6443De Vylder type approximation of the ruin probability for the insurer-reinsurer model
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In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer - reinsurer model. Applying De Vylder’s idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution only assuming that the third moment exists. We check performance of the approximation by means of the Monte Carlo simulations studying several typical claim amount distributions. All results show that the proposed approximation yields very small relative errors. Finally, we illustrate the approximation by considering real-world loss data obtained from a Polish insurance company./resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6417XLIV Conference "Mathematical Statistics", Będlewo 2018
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On December 2--7, 2018, in Będlewo, the XLIV Conference "Mathematical Statistics" was held, organized by the Banach Center of Institute of Mathematics Polish Accademy of Science, the Committee on Statistics of the Committee of Mathematics of the Polish Academy of Sciences, and the Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Toruń. During the 19 sessions, a total of 46 lectures and a series of lectures on "Bayesian Inference in Intractable Likelihood Models", i.e. on Bayesian modeling with a difficult likelihood function, were given. The lecture was delivered by Krzysztof Łatuszyński from the University of Warwick in Great Britain./resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6448Polish Nationwide Mathematical Student Conference OMatKo!!!
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Polish Nationwide Mathematical Student Conference OMatKo!!! was set up by students from all four mathematical scientific clubs at Wroclaw University of Science and Technology. The fifth edition of our conference took place from 13th to 15th of April 2018 and it has become the biggest mathematical student conference in the whole country, attracting more than 200 students. There are both polish and foreign students among our participants. This event is dedicated not only to mathematics and informatics, but also scientific related students. Our project gives opportunity to gain knowledge and share experience, as well as to develop soft skills and public appearance among both participants and the organizing team. These actions contribute to young people self-development and push to cooperate with others - the conference enables participants to establish cooperation between active students and we encourage the most outstanding individuals to constant improvement. /resource/bwmeta1.element.ojs-doi-10_14708_ma_v47i0_6413The phenomenon of the Steinhaus Seminar on Applied Mathematics: Topics
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This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are well-founded in mathematical journals./resource/bwmeta1.element.ojs-doi-10_14708_am_v13i0_6446Russian Translations and Translators of Western European works (XVIII - early twentieth century) devoted to the history of mathematics
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This work is a continuation of the author's presentation of the history of mathematics in Russia as a research area within the history of science (v. Lokot (2018)). The elements of the history of mathematics began to intensively emerge in the epoch of Peter the Great and have undergone several stages of development. There are five stages that Russian scientists have gone through, shaping the elements of research in the history of mathematics into the research area with its own subject, objectives and methods. This article continues the analysis of the first period, ie the stage of historical and scientific translations in the field of history of science. Chronologically, the translations of Western European works devoted to the history of mathematics have been analyzed, taking into account the personality of translators, who have relatively little space devoted to works on the history of mathematics./resource/bwmeta1.element.ojs-doi-10_14708_am_v13i0_6460On the hypersurfaces contained in their Hessian
/resource/bwmeta1.element.ojs-issn-2300-133X-year-2019-volume-18-article-314
/resource/bwmeta1.element.ojs-issn-2300-133X-year-2019-volume-18-article-314Local convergence comparison between two novel sixth order methods for solving equations
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/resource/bwmeta1.element.ojs-issn-2300-133X-year-2019-volume-18-article-296Domination Parameters of a Graph and its Complement
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A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement./resource/bwmeta1.element.doi-10_7151_dmgt_2002Inverse Problem on the Steiner Wiener Index
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The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) =∑u,v∈V (G) dG(u, v), where dG(u, v) is the distance (the length a shortest path) between the vertices u and v in G. For S ⊆ V (G), the Steiner distance d(S) of the vertices of S, introduced by Chartrand et al. in 1989, is the minimum size of a connected subgraph of G whose vertex set contains S. The k-th Steiner Wiener index SWk(G) of G is defined as [...] SWk(G)=∑S⊆V(G)|S|=kd(S) $SW_k (G) = \sum\nolimits_{\mathop {S \subseteq V(G)}\limits_{|S| = k} } {d(S)}$ . We investigate the following problem: Fixed a positive integer k, for what kind of positive integer w does there exist a connected graph G (or a tree T) of order n ≥ k such that SWk(G) = w (or SWk(T) = w)? In this paper, we give some solutions to this problem./resource/bwmeta1.element.doi-10_7151_dmgt_2000The Distance Magic Index of a Graph
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Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection ϕ : V (G) → S satisfying ∑x∈N(u) ϕ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeling. Then i(G) − n is called the distance magic index of the graph G. In this paper we determine the distance magic index of trees and complete bipartite graphs./resource/bwmeta1.element.doi-10_7151_dmgt_1998Upper Bounds for the Strong Chromatic Index of Halin Graphs
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The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph G by drawing T on the plane and then drawing a cycle C connecting all its leaves in such a way that C forms the boundary of the unbounded face. We call T the characteristic tree of G. Let G denote a Halin graph with maximum degree Δ and characteristic tree T. We prove that χ′s(G) ⩽ 2Δ + 1 when Δ ⩾ 4. In addition, we show that if Δ = 4 and G is not a wheel, then χ′s(G) ⩽ χ′s(T) + 2. A similar result for Δ = 3 was established by Lih and Liu [21]./resource/bwmeta1.element.doi-10_7151_dmgt_2003Cubic Graphs with Total Domatic Number at Least Two
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Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two./resource/bwmeta1.element.doi-10_7151_dmgt_1996Core Index of Perfect Matching Polytope for a 2-Connected Cubic Graph
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For a 2-connected cubic graph G, the perfect matching polytope P(G) of G contains a special point [...] xc=(13,13,…,13) $x^c = \left( {{1 \over 3},{1 \over 3}, \ldots ,{1 \over 3}} \right)$ . The core index ϕ(P(G)) of the polytope P(G) is the minimum number of vertices of P(G) whose convex hull contains xc. The Fulkerson’s conjecture asserts that every 2-connected cubic graph G has six perfect matchings such that each edge appears in exactly two of them, namely, there are six vertices of P(G) such that xc is the convex combination of them, which implies that ϕ(P(G)) ≤ 6. It turns out that the latter assertion in turn implies the Fan-Raspaud conjecture: In every 2-connected cubic graph G, there are three perfect matchings M1, M2, and M3 such that M1 ∩ M2 ∩ M3 = ∅. In this paper we prove the Fan-Raspaud conjecture for ϕ(P(G)) ≤ 12 with certain dimensional conditions./resource/bwmeta1.element.doi-10_7151_dmgt_2001Fibonacci and Telephone Numbers in Extremal Trees
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In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers./resource/bwmeta1.element.doi-10_7151_dmgt_1997Hereditary Equality of Domination and Exponential Domination
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We characterize a large subclass of the class of those graphs G for which the exponential domination number of H equals the domination number of H for every induced subgraph H of G./resource/bwmeta1.element.doi-10_7151_dmgt_2006Rainbow Vertex-Connection and Forbidden Subgraphs
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A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them. For a connected graph G, the rainbow vertex-connection number of G, denoted by rvc(G), is defined as the minimum number of colors that are required to make G rainbow vertex-connected. In this paper, we find all the families ℱ of connected graphs with |ℱ| ∈ {1, 2}, for which there is a constant kℱ such that, for every connected ℱ-free graph G, rvc(G) ≤ diam(G) + kℱ, where diam(G) is the diameter of G./resource/bwmeta1.element.doi-10_7151_dmgt_2004Cores, Joins and the Fano-Flow Conjectures
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The Fan-Raspaud Conjecture states that every bridgeless cubic graph has three 1-factors with empty intersection. A weaker one than this conjecture is that every bridgeless cubic graph has two 1-factors and one join with empty intersection. Both of these two conjectures can be related to conjectures on Fano-flows. In this paper, we show that these two conjectures are equivalent to some statements on cores and weak cores of a bridgeless cubic graph. In particular, we prove that the Fan-Raspaud Conjecture is equivalent to a conjecture proposed in [E. Steffen, 1-factor and cycle covers of cubic graphs, J. Graph Theory 78 (2015) 195–206]. Furthermore, we disprove a conjecture proposed in [G. Mazzuoccolo, New conjectures on perfect matchings in cubic graphs, Electron. Notes Discrete Math. 40 (2013) 235–238] and we propose a new version of it under a stronger connectivity assumption. The weak oddness of a cubic graph G is the minimum number of odd components (i.e., with an odd number of vertices) in the complement of a join of G. We obtain an upper bound of weak oddness in terms of weak cores, and thus an upper bound of oddness in terms of cores as a by-product./resource/bwmeta1.element.doi-10_7151_dmgt_1999On the Total<i>k</i>-Domination in Graphs
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Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph./resource/bwmeta1.element.doi-10_7151_dmgt_2016Bounding the Open<i>k</i>-Monopoly Number of Strong Product Graphs
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Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ {1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋} be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if [...] δM(v)≥δG(v)2+k $\delta _M (v) \ge {{\delta _G (v)} \over 2} + k$ , where δM(v) represents the number of neighbors of v in M and δG(v) the degree of v in G. A set M is called an open k-monopoly if every vertex v of G is k-controlled by M. The minimum cardinality of any open k-monopoly is the open k-monopoly number of G. In this article we study the open k-monopoly number of strong product graphs. We present general lower and upper bounds for the open k-monopoly number of strong product graphs. Moreover, we study in addition the open 0-monopolies of several specific families of strong product graphs./resource/bwmeta1.element.doi-10_7151_dmgt_2017Matchings Extend to Hamiltonian Cycles in 5-Cube
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Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5./resource/bwmeta1.element.doi-10_7151_dmgt_2010Sharp Upper Bounds on the Clar Number of Fullerene Graphs
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The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n ≥ 20 except n = 22 and n = 30./resource/bwmeta1.element.doi-10_7151_dmgt_2013A Note on the Interval Function of a Disconnected Graph
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In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition./resource/bwmeta1.element.doi-10_7151_dmgt_1990Requiring that Minimal Separators Induce Complete Multipartite Subgraphs
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Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums of complete, cycle, wheel, and octahedron graphs./resource/bwmeta1.element.doi-10_7151_dmgt_1988The Graphs Whose Permanental Polynomials Are Symmetric
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The permanental polynomial [...] π(G,x)=∑i=0nbixn−i $\pi (G,x) = \sum\nolimits_{i = 0}^n {b_i x^{n - i} }$ of a graph G is symmetric if bi = bn−i for each i. In this paper, we characterize the graphs with symmetric permanental polynomials. Firstly, we introduce the rooted product H(K) of a graph H by a graph K, and provide a way to compute the permanental polynomial of the rooted product H(K). Then we give a sufficient and necessary condition for the symmetric polynomial, and we prove that the permanental polynomial of a graph G is symmetric if and only if G is the rooted product of a graph by a path of length one./resource/bwmeta1.element.doi-10_7151_dmgt_1986Power Domination in Knödel Graphs and Hanoi Graphs
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In this paper, we study the power domination problem in Knödel graphs WΔ,2ν and Hanoi graphs [...] Hpn $H_p^n $ . We determine the power domination number of W3,2ν and provide an upper bound for the power domination number of Wr+1,2r+1 for r ≥ 3. We also compute the k-power domination number and the k-propagation radius of [...] Hp2 $H_p^2$ ./resource/bwmeta1.element.doi-10_7151_dmgt_1993Bounds on the Locating Roman Domination Number in Trees
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A Roman dominating function (or just RDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is the value f(V (G)) = ∑u∈V(G) f(u). An RDF f can be represented as f = (V0, V1, V2), where Vi = {v ∈ V : f(v) = i} for i = 0, 1, 2. An RDF f = (V0, V1, V2) is called a locating Roman dominating function (or just LRDF) if N(u) ∩ V2 ≠ N(v) ∩ V2 for any pair u, v of distinct vertices of V0. The locating Roman domination number [...] γRL(G) $\gamma _R^L (G)$ is the minimum weight of an LRDF of G. In this paper, we study the locating Roman domination number in trees. We obtain lower and upper bounds for the locating Roman domination number of a tree in terms of its order and the number of leaves and support vertices, and characterize trees achieving equality for the bounds./resource/bwmeta1.element.doi-10_7151_dmgt_1989On Two Generalized Connectivities of Graphs
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The concept of generalized k-connectivity κk(G), mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. The pendant tree-connectivity τk(G) was also introduced by Hager in 1985, which is a specialization of generalized k-connectivity but a generalization of the classical connectivity. Another generalized connectivity of a graph G, named k-connectivity κ′k(G), introduced by Chartrand et al. in 1984, is a generalization of the cut-version of the classical connectivity. In this paper, we get the lower and upper bounds for the difference of κ′k(G) and τk(G) by showing that for a connected graph G of order n, if κ′k(G) ≠ n − k + 1 where k ≥ 3, then 1 ≤ κ′k(G) − τk(G) ≤ n − k; otherwise, 1 ≤ κ′k(G) ‘− τk(G) ≤ n − k + 1. Moreover, all of these bounds are sharp. We get a sharp upper bound for the 3-connectivity of the Cartesian product of any two connected graphs with orders at least 5. Especially, the exact values for some special cases are determined. Among our results, we also study the pendant tree-connectivity of Cayley graphs on Abelian groups of small degrees and obtain the exact values for τk(G), where G is a cubic or 4-regular Cayley graph on Abelian groups, 3 ≤ k ≤ n./resource/bwmeta1.element.doi-10_7151_dmgt_1987A Characterization for 2-Self-Centered Graphs
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A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG). Then, we complete characterization by characterizing edge-minimal 2-self-centered graphs with some triangles. Hence, the main characterization is done since a graph is 2-self-centered if and only if it is a spanning subgraph of some edge-maximal 2-self-centered graphs and, at the same time, it is a spanning supergraph of some edge-minimal 2-self-centered graphs./resource/bwmeta1.element.doi-10_7151_dmgt_1994On Incidence Coloring of Complete Multipartite and Semicubic Bipartite Graphs
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In the paper, we show that the incidence chromatic number χi of a complete k-partite graph is at most Δ + 2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to Δ + 1 if and only if the smallest part has only one vertex (i.e., Δ = n − 1). Formally, for a complete k-partite graph G = Kr1,r2,...,rk with the size of the smallest part equal to r1 ≥ 1 we have χi(G)={Δ(G)+1if r1=1,Δ(G)+2if r1>1. $$\chi _i (G) = \left\{ {\matrix{{\Delta (G) + 1} & {{\rm{if}}\;r_1 = 1,} \cr {\Delta (G) + 2} & {{\rm{if}}\;r_1 > 1.} \cr } } \right.$$ In the paper we prove that the incidence 4-coloring problem for semicubic bipartite graphs is 𝒩𝒫-complete, thus we prove also the 𝒩𝒫-completeness of L(1, 1)-labeling problem for semicubic bipartite graphs. Moreover, we observe that the incidence 4-coloring problem is 𝒩𝒫-complete for cubic graphs, which was proved in the paper [12] (in terms of generalized dominating sets)./resource/bwmeta1.element.doi-10_7151_dmgt_1995Constant Sum Partition of Sets of Integers and Distance Magic Graphs
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Let A = {1, 2, . . . , tm+tn}. We shall say that A has the (m, n, t)-balanced constant-sum-partition property ((m, n, t)-BCSP-property) if there exists a partition of A into 2t pairwise disjoint subsets A1, A2, . . . , At, B1, B2, . . . , Bt such that |Ai| = m and |Bi| = n, and ∑a∈Ai a = ∑b∈Bj b for 1 ≤ i ≤ t and 1 ≤ j ≤ t. In this paper we give sufficient and necessary conditions for a set A to have the (m, n, t)-BCSP-property in the case when m and n are both even. We use this result to show some families of distance magic graphs./resource/bwmeta1.element.doi-10_7151_dmgt_1991On the Number of<i>α</i>-Labeled Graphs
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When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an α-labeling. This is the most restrictive type of difference-vertex labeling and it is located at the very core of this research area. Here we use an extension of the adjacency matrix to count and classify α-labeled graphs according to their size, order, and boundary value./resource/bwmeta1.element.doi-10_7151_dmgt_1985Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4
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We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity./resource/bwmeta1.element.doi-10_1515_spma-2018-0001Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113
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We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices of order 4v for v = 47, 73, 113./resource/bwmeta1.element.doi-10_1515_spma-2018-0002On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix
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Consider the recursion g0 = a, g1 = b, gn = gn−1 + gn−2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn−1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general./resource/bwmeta1.element.doi-10_1515_spma-2018-0003Elastic, plastic, fracture analysis of masonry arches: A multi-span bridge case study
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In this work a comparison is presented between elastic, plastic, and fracture analysis of the monumental arch bridge of Porta Napoli, Taranto (Italy). By means of a FEM model and applying the Mery’s Method, the behavior of the curved structure under service loads is verified, while considering the Safe Theorem approach byHeyman, the ultimate carrying capacity of the structure is investigated. Moreover, by using Fracture Mechanics concepts, the damage process which takes place when the conditions assessed through linear elastic analysis are no longer valid, and before the set-in of the conditions established by means of the plastic limit analysis, is numerically analyzed. The study of these transitions returns an accurate and effective whole service life assessment of the Porta Napoli masonry arch bridge./resource/bwmeta1.element.doi-10_1515_cls-2018-0001The density Turan problem for 3-uniform linear hypertrees. An efficient testing algorithm
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Let \(\mathcal{T}=(V,\mathcal{E})\) be a 3-uniform linear hypertree. We consider a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\). We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\) of the hypertree \(\mathcal{T}\), with hyperedge densities satisfying some conditions, such that the hypertree \(\mathcal{T}\) does not appear in a blow-up hypergraph as a transversal. We present an efficient algorithm to decide whether a given set of hyperedge densities ensures the existence of a 3-uniform linear hypertree \(\mathcal{T}\) in a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\)./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_9Oscillation of third-order delay difference equations with negative damping term
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The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_19-28On almost polynomial structures from classical linear connections
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Let \(\mathcal{M}f_m\) be the category of \(m\)-dimensional manifolds and local diffeomorphisms and let \(T\) be the tangent functor on \(\mathcal{M}f_m\). Let \(\mathcal{V}\) be the category of real vector spaces and linear maps and let \(\mathcal{V}_m\) be the category of \(m\)-dimensional real vector spaces and linear isomorphisms. Let \(w\) be a polynomial in one variable with real coefficients. We describe all regular covariant functors \(F\colon \mathcal{V}_m\to\mathcal{V}\) admitting \(\mathcal{M}f_m\)-natural operators \(\tilde{P}\) transforming classical linear connections \(\nabla\) on \(m\)-dimensional manifolds \(M\) into almost polynomial \(w\)-structures \(\tilde{P}(\nabla)\) on \(F(T)M=\bigcup_{x\in M}F(T_xM)\)./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_13-18Spectral analysis of singular Sturm-Liouville operators on time scales
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In this paper, we consider properties of the spectrum of a Sturm-Liouvilleoperator on time scales. We will prove that the regular symmetricSturm-Liouville operator is semi-bounded from below. We will also give someconditions for the self-adjoint operator associated with the singularSturm-Liouville expression to have a discrete spectrum. Finally, we willinvestigate the continuous spectrum of this operator./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_1-11An existence and approximation theorem for solutions of degenerate nonlinear elliptic equations
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The main result establishes that a weak solution of degenerate nonlinear elliptic equations can be approximated by a sequence of solutions for non-degenerate nonlinear elliptic equations./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_29-43Invo-regular unital rings
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It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo-Khurana (Comm. Algebra, 2001), recently Nielsen and Ster showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_45-53The constructions of general connections on the fibred product of q copies of the first jet prolongation
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We describe all natural operators \(A\) transforming general connections \(\Gamma\) on fibred manifolds \(Y \rightarrow M\) and torsion-free classical linear connections \(\Lambda\) on \(M\) into general connections \(A(\Gamma,\Lambda)\) on the fibred product \(J^{<q>}Y \rightarrow M\) of \(q\) copies of the first jet prolongation \(J^{1}Y \rightarrow M\).</q>/resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_77-90On the Courant bracket on couples of vector fields and \(p\)-forms
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If \(m\geq p+1\geq 2\) (or \(m=p\geq 3\)), all natural bilinear operators \(A\) transforming pairs of couples of vector fields and \(p\)-forms on \(m\)-manifolds \(M\) into couples of vector fields and \(p\)-forms on \(M\) are described. It is observed that any natural skew-symmetric bilinear operator \(A\) as above coincides with the generalized Courant bracket up to three (two, respectively) real constants./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_29On a two-parameter generalization of Jacobsthal numbers and its graph interpretation
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In this paper we introduce a two-parameter generalization of the classical Jacobsthal numbers ((s,p)-Jacobsthal numbers). We present some properties of the presented sequence, among others Binet’s formula, Cassini’s identity, the generating function. Moreover, we give a graph interpretation of (s,p)-Jacobsthal numbers, related to independence in graphs./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_21Products of Toeplitz and Hankel operators on the Bergman space in the polydisk
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In this paper we obtain a condition for analytic square integrable functions \(f,g\) which guarantees the boundedness of products of the Toeplitz operators \(T_fT_{\bar g}\) densely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators \(H_fH^*_g\) is also given./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_57On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields
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Let \(\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}\) be a random field of negatively dependent random variables. The complete convergence results for negatively dependent random fields are refined. To obtain the main theorem several lemmas for convergence of families indexed by \(\mathbb{N}^d\) have been proved. Auxiliary lemmas have wider application to study the random walks on the lattice./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_1On \(\ell_1\)-preduals distant by 1
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For every predual \(X\) of \(\ell_1\) such that the standard basis in \(\ell_1\) is weak\(^*\) convergent, we give explicit models of all Banach spaces \(Y\) for which the Banach-Mazur distance \(d(X,Y)=1\). As a by-product of our considerations, we obtain some new results in metric fixed point theory. First, we show that the space \(\ell_1\), with a predual \(X\) as above, has the stable weak\(^*\) fixed point property if and only if it has almost stable weak\(^*\) fixed point property, i.e. the dual \(Y^*\) of every Banach space \(Y\) has the weak\(^*\) fixed point property (briefly, \(\sigma(Y^*,Y)\)-FPP) whenever \(d(X,Y)=1\). Then, we construct a predual \(X\) of \(\ell_1\) for which \(\ell_1\) lacks the stable \(\sigma(\ell_1,X)\)-FPP but it has almost stable \(\sigma(\ell_1,X)\)-FPP, which in turn is a strictly stronger property than the \(\sigma(\ell_1,X)\)-FPP. Finally, in the general setting of preduals of \(\ell_1\), we give a sufficient condition for almost stable weak\(^*\) fixed point property in \(\ell_1\) and we prove that for a wide class of spaces this condition is also necessary./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_41Generalized trend constants of Lipschitz mappings
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In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_71On the existence of connections with a prescribed skew-symmetric Ricci tensor
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We study the so-called inverse problem. Namely, given a prescribed skew-symmetric Ricci tensor we find (locally) a respective linear connection./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_37On generalized Mersenne numbers, their interpretations and matrix generators
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In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining identities./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_69-76Some new inequalities of Hermite-Hadamard type for GA-convex functions
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Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained./resource/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_55-68XV years of the Center of Applied Mathematics of the Polish Academy of Sciences and the LXV - the founding of Applicationes Mathematicae. March 23, 2018, IM PAN Warsaw
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On March 23, 2018 in Warsaw, at the seat of the Mathematical Institute of the Polish Academy of Sciences, a solemn scientific session was held to commemorate the 15th anniversary of the Center for Applied Mathematics (CZM) IMPAN and the 65th anniversary of the Applicationes Mathematicae scientific journal. The history of CZM and Applicationes was reminded by Łukasz Stettner, CZM manager and editor-in-chief Applicationes. The Application Center for Mathematics was created on the 50th anniversary of the founding of the Applied Mathematics journal, which was founded in 1953 by Hugo Steinhaus together with his associates including Jan Oderfeld as his deputy. From 1968, Hugo Steinhaus ran the Applied Mathematics Seminary in Wrocław, which gathered a wide group of people interested in the mathematical approach to the problems faced with various scientific research, but also in business, medical and veterinary practice./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6447Common-Knowledge and Bayesian Equilibrium in Network Game
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In this paper we investigate equilibriums in the Bayesian routing problem of the network game introduced by Koutsoupias and Papadimitriou [LNCS 1563, pp.404-413. Springer (1999)]. We treat epistemic conditions for Nash equilibrium of social cost function in the network game. It highlights the role of common-knowledge on the users' individual conjectures on the others' selections of channels in the network game.Especially two notions of equilibria are presented in the Bayesian extension of the network game; expected delay equilibrium and rational expectations equilibrium, such as each user maximizes own expectations of delay and social cost respectively. We show that the equilibria have the properties: If all users commonly know them, then the former equilibrium yields a Nash equilibrium in the based KP-model and the latter equilibrium yields a Nash equilibrium for social cost in the network game.Further the notion of price of anarchy is extended for rational expectations equilibriums in the models./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6346K-th Record Values and Their Basic Properties
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In this paper, the k-th record value model is presented. The k-th record values has emerged as an important model of ordered random variables. They appears naturally in real life where one interested in successive k-th maximum observations. The k-th record values are formally defined by Dziubdziela i Kopociński (1976). The paper contains distributional theory for this model./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6367Students Conferences in Applied Mathematics
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1. Student Conference on Applied Mathematics ,,DwuMIan''. 23--25 March 2018, Warsaw, Poland (Łukasz Błaszczyk) On 23--25 March 2018 at the Faculty of Mathematics and Information Science (MIS) of the Warsaw University of Technology, the first edition of the Student Conference on Applied Mathematics ,,DwuMIan'' was organized, together with the Faculty of Mathematics, Informatics and Mechanics (MIM) of the University of Warsaw and with the participation of students’ organizations of these universities: Scientific Club of Mathematical Modeling of WUT, MI^2 DataLab group, Executive Board of the Students’ Union of MIM UW, Scientific Club of Data Science of WUT and Students' Union Faculty Council of MIS WUT. 2. Polish Nationwide Mathematical Student Conference OMatKo!!!. 13 - 15 April, 2018, Wrocław, Poland (Antonina Urbaniak) Polish Nationwide Mathematical Student Conference OMatKo!!! was set up by students from all four mathematical scientific clubs at Wroclaw University of Science and Technology. The fifth edition of our conference took place from 13th to 15th of April 2018 and it has become the biggest mathematical student conference in the whole country, attracting more than 200 students. There are both polish and foreign students among our participants. 3. Mathematical Days at Wrocław University of Science and Technology. 26 - 27 of October, 2018, Wrocław, Poland (Zuzanna Materny) 4. Mathematical Student Conference in Poznań (May 11-13,2018. (Mikołaj Pabiszczak and Jędrzej Garnek) Organizowana jest przez studentów i doktorantów Wydziału Matematyki i Informatyki Uniwersytetu im. Adama Mickiewicza w Poznaniu, zrzeszonych w ramach Koła Naukowego Matematyków oraz Stowarzyszenia Oblicze zgromadziła około 90 studentów z 16 różnych ośrodków akademickich. Podczas tych trzech dni można było wysłuchać 44 referatów w trzech równoległych sesjach. Dotyczyły one zarówno matematyki i informatyki teoretycznej, ale i stosowanej, finansowej i aktuarialnej. he fifth edition of the conference took place at Faculty of Mathematics and Computer Sciences of Adam Mickiewicz University. Organised entirely by students of the faculty, it is one of the oldest and biggest conferences of this type in Poland. Talks (in English and Polish) concerning both applied and theoretical mathematics were delivered in 3 parallel sessions. Moreover, poster session took place./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6387LII competition for the best student work in the theory of probability and applications of mathematics
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The Wrocław Branch of the Polish Mathematical Society organizes in 2019 the 53rd edition of the competition aimed at promoting (dissemination, encouraging practising, showing meaning) among students of the theory of probability and applications of mathematics. At the same time, the competition promotes young mathematicians obtaining original theoretical results from probability studies, or results applied in other disciplines of science than mathematics, such as economy, engineering sciences, science, biology and medicine, sociology and psychology. There are report on the LII Competition and the poster opening the LIII Competition for the Best Student Work in the Theory of Probabiity and Applicantionsof Mathematics in 2019./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6453Remembrance of Andrzej Malawski (1948-2016)
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Professor Andrzej Malawski passed away in 2016. He was an outstanding economist, philosopher and a mathematician. He was fond of mathematics modelling of economic theories. Andrzej Malawski was a founder of the research program of modelling the Schumpeterian vision of innovative development in the framework of the Arrow-Debreu theory of general equilibrium. The results of his research activities were published in papers of the international range. Andrzej Malawski worked at Cracow University of Economics. He was, among others, Deputy Rector of Cracow University of Economics (2008-2012) and Head of Department of Mathematics CUE. In 2000 he was awarded for the monograph \emph{Metoda aksjomatyczna w ekonomii} by Bank Handlowy. Andrzej Malawski was a man of extraordinary mental and character merits. He was characterized by a high personal culture and great modesty. Professor Malawski was very friendly, tactful and, at the same time, exacting and commanding respect. He willingly shared his comprehensive knowledge with others. He was a mentor and unrivalled master for many young scientists. He was well-liked and respected by those with whom he met on his research activity paths, with whom he collaborated and co-wrote. Professor Andrzej Malawski was an unusual man and the image of this exceptional man and excellent researcher will remain forever in the memory of a great many people./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6444Selected applications of differential equations in Vanilla Options valuation.
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In financial models one of the basic assumptions about investors is that they want to gain as much as it is possible but they have aversion to take the risk. Each investing strategy can be considered as a compromise between willing of profit and fear of losses - usually possible profit increase with probability of loss. Option can be considered as some kind of insurance - a more prudent speculator might want to reduce the maximal loss by a quantity $K>0$. He thus will buy an option which would correspond to the strike price $K$. For him (option holder) it is the way to protect himself against the risk, for option issuer it is possibility to profit by selling this financial product. The fundamental question is what is the value of this security? The answer has essential meaning in financial world and global economy.The first record of an option contract can be found in the "Politics" of Aristotle. According to the story Greek philosopher Thales profited by option-type agreement around the 6th century B.C. The problem of fair valuing this kind of financial instrument was not formalized until 1900.At this year L.Bachelier by his pioneering thesis began the theory of option pricing. In the same work he initiated the study of diffusion processes five years before recognized as the groundbreaking works of A.Einstein, M.Smoluchowski and decades before famous works of K.It\^{o}, P.L\'{e}vy and N.Wiener. Bachelier as the first developed the theory of Brownian motion and found practical application of this concept in financial engineering.The culminating event in developing theory of option pricing was 1973 when Black, Scholes and Merton found consistent formulas for the fair prices of European options. The discovery was of such great importance that the autors were awarded the Nobel Prize for Economics in 1997. Very interesting is fact that for short time to maturity formulas of Bachelier are very close to results of Black, Merton and Scholes.Until today, there is no knowledge of any analytical formula of American option fair price, which could have any practical application. In order to determine this value, as a rule it is given main importance to Monte Carlo methods. Usually they are easier to implement, but require more time or are related to higher numerical errors than deterministic methods./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6352Conferences in Applied Mathematics
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1. XLVII National Conference on Applications of Mathematics, September 4-11, 2018, Zakopane-Kościelisko (Ł. Stettner) The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville, USA and Łódź University of Technology) and Heinz Schättler (Washington University, St. Louis, USA) with optimal control in biomedical problems. 2. GAMENET Conference Kraków 2018, 17 -- 21 września 2018, Kraków(F.Falniowski) On September 17-21, 2018 an international conference GAMENET Conference Kraków 2018 summarizing the first year of activity of the European network for game theoretic research GAMENET was held at the Cracow University of Economics. The main event of the first two days was a training school on the recent applications of Game Theory. The training school was build around three courses delivered by Olivier Baude (Électricité de France), Luiz DaSilva (Trinity College Dublin) and Vianney Perchet (CMLA, ENS Paris-Saclay & Criteo AI Lab). 3. Conference "Social sciences - mathematical or mathematizable?", 27 -- 28 września 2018, Kraków(Agnieszka Lipieta) The conference was held at Cracow University of Economics on September 27-28, 2018. It was devoted to the memory of outstanding mathematician, philosopher, and economist Professor Andrzej Malawski, who passed away in 2016. 4. VII Hurwicz Workshop on Mechanism Design Theory, 7--8 grudnia 2018 (Łukasz Woźny) IM PAN WarszawaThe 2018 Hurwicz Workshop on Mechanism Design Theory is a continuation of the initiative started in 2009 of holding an annual confernce to honour the 2007 Nobel Prize Laureate in Economics, professor Leonid Hurwicz. Leonid Hurwicz lived in Warsaw until 1938 and studied at the University of Warsaw. He frequently visited Poland in 1990's. In 1994 he obtained the Doctor Honoris Causa of Warsaw School of Economics. A special plaque commemorates his contacts with Warsaw School of Economics. Hurwicz is often credited with introducing rigorous mathematical approach to economic analysis. He received the Nobel Prize in Economic Sciences in 2007 for his fundamental contributions to the theory of the design of economic mechanisms. Theory of mechanism design relies heavily on mathematical methods of functional analysis, differential equations, differential topology, dynamical systems, etc. Hurwicz has made important contributions to mathematics as well as economics, in particular, to non-linear programming. 5. Conference “Mathematical Statistics”. Będlewo, December 2--7, 2018 (Przemysław Grzegorzewski). On December 2--7, 2018, in Będlewo, the XLIV Conference "Mathematical Statistics" was held, organized by the Banach Center of Institute of Mathematics Polish Accademy of Science, the Committee on Statistics of the Committee of Mathematics of the Polish Academy of Sciences, and the Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Toruń. During the 19 sessions, a total of 46 lectures and a series of lectures on "Bayesian Inference in Intractable Likelihood Models", i.e. on Bayesian modeling with a difficult likelihood function, were given. The lecture was delivered by Krzysztof Łatuszyński from the University of Warwick in Great Britain. 6. XLVIII Seminar on Applied Mathematics-XLVIII Seminarium Zastosowań Matematyki, 9-11.09.2018 Boguszów-Gorce (Mieczysław Chalfen)/resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6438Applied Mathematics on joint Meeting of UMI-SIMAI-PTM, September 17-20, 2018
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The 2018 Forum of Mathematician was organized with cooperation of Italian Mathematical Union (Union e Matematica Italiana) and the Italian Society of Industrial and Applied Mathematics (Società Italiana di Matematica Applicata e Industriale). The meeting aims at continuation of the tradition of bilateral meetings held in the last years by the Polish Mathematical Society together with other national societies. This forum does not exclude the participation of mathematicians from other countries. The Forum in Wroclaw also hosted a large group of participants from outside Poland and Italy. The meeting was hosted by the Faculty Mathematics and Computer Science of the University of Wrocław and the Faculty of of Pure and Applied Mathematics of Wrocław University of Science and Technology. It was the fourth bilateral symposium of PTM after the Second World War (cf. Duda(2018)): AMS-PTM Joint Meeting (Warsaw) in 2007, IMU-PTM Joint meeting (Łódź) in 2011 and DMV-PTM Joint Metting (Poznań) in 2014./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6454Strongly Time-Consistent Core in Differential Games with Discrete Distribution of Random Time Horizon
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In this paper we investigate the problem of strong time-consistency of the core for a particular class of differential games with random time horizon, namely, it is assumed that there exists a set of probabilities of the end of the game at discrete time instants. A condition guaranteeing the strong time consistency of the core is presented./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_5135The interplay between stochastic gene switching and certain metronomics therapies.
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In this work I present some preliminary results of the exploration of the interplay between stochastic gene switching and certain metronomics therapies. During the research a simple model of gene-mRNA-protein network subjected to the metronomic therapy was investigated. The results show that the stochastic gene switching process, especially the time expected between successive switching plays a significant role in determining the size of the responding cells fraction./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6392Ananysis of a predator-prey model with disease in the predator species
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In the paper we analyse a diffusive predator-prey model with disease in predator species proposed by Qiao et al. (2014). In the original article there appears a mistake in the procedure of the model undimensionalisation. We make a correction in this procedure and show that some changes in the model analysis are necessary to obtain results similar to those presented by Qiao et al.We propose corrected conditions for global stability of one of existing equilibria -- disease free steady state and endemic state in the case without diffiusion as well as in the model with diffusion. On the basis of the corrected analysis we present new stability results./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6385The use of certain staffing requirements as a means of benchmarking academic staff structure
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Considering the statutory staffing requirements by the National Universities Commission in Nigeria, this study develops a model to benchmark the academic staff structure that will meet the staffing requirements. The model utilises the absorbing Markov chain framework as its theoretical underpinning. An upper bound on the structure that will mature to meet the statutory staffing requirement is developed. Empirical data are used to demonstrate the utility of the model./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_5175On a method of obtaining exact fair divisions
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Let the unit interval I represent a cake to be divided among n players estimating the measurable subsets of I by nonatomic probability n measures. We show a method of obtaining an exact fair division of the cake such that i-th each part has i-th measure equals 1/n for all players./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_5134A Large Population Partnership Formation Game with Associative Preferences and Continuous Time
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A model of partnership formation is considered in which there are two classes of player (called male and female). There is a continuum of players and two types of both sexes. These two types can be interpreted, e.g. as two subspecies, and each searcher prefers to pair with an individual of the same type. Players begin searching at time zero and search until they find a mutually acceptable prospective partner or the mating season ends. When a pair is formed, both individuals leave the pool of searchers. Hence, the proportion of players still searching and the distribution of types changes over time. Prospective partners are found at a rate which is non- decreasing the proportion of players still searching. Nash equilibria are derived which satisfy the following optimality criterion: each searcher accepts a prospective partner if and only if the reward from such a partnership is greater or equal to the expected reward obtained from future search. So called ”completely symmetric” versions of this game are considered, where the two types of player are equally frequent. A unique Nash equilibrium exists regardless of the precise rule determining the rate at which prospective partners are found. Two examples are given. /resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i2_5128On the nonlocal discretization of the simplified Anderson-May model of viral infection
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We present five nonstandard finite difference methods designed for numerical simulation of the simplified Anderson-May model of viral infection. The proposed methods, based solely on the principle of nonlocal discretization, are able to preserve all of the essential qualitative features of the original model: the non-negativity of the solution and local stability of the equilibrium points, along with their stability conditions. One of the proposed methods preserves the types of the equilibrium points (i.e. the presence and absence of oscillations) as well. All of these results are independent of the chosen step-size of simulation./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6395A mathematical model of some viral-induced autoimmune diseases
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We consider a mathematical model of autoimmune disease. The model is described by a bilinear system of four integro-differential equations of Boltzmann type. We present numerical results illustrating several typical outcomes of autoimmune disease. In particular, special attention is devoted to the role of viral infections for development of autoimmune diseases./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6391Dynamics of simplified HPT model in relation to 24h TSH profiles
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We propose a simplified mathematical model of the hypothalamus-pituitary-thyroid (HPT) axis in an endocrine system. The considered model is a modification of the model proposed by Mukhopadhyay in [9]. Our system of delay differential equations reconstructs the HPT-axis in relation to 24h profiles of human in physiological conditions. Homeostatic control of the thyroid-pituitary axis is considered by using feedback and delay in our model. The influence of delayed feedback on the stability behaviour of the system is discussed./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6389National Conference Applications of Mathematics to Biology and Medicine
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It is unbelievable that this year we will meet at the National Conference Applications of Mathematics to Biology and Medicine for the 24th time. The initiator, chairman of the Scientific Committee and tireless participant of all previous conferences is Prof. Mariusz Ziółko who in the 1970s participated in the Schools of Mathematical Modeling in Biology organized by Prof. Adam Łomnicki, an outstanding biologist and ecologist from the Jagiellonian University. In 1994, M. Ziółko suggested to Prof. Łomnicki reactivation of these schools, thanks to which many young people got a chance to become a recognizable researcher. Unfortunately, he met with refusal. However, Prof. Łomnicki suggested that Prof. Ziółko continue the work, but according to his own concept. In 1995, the first conference took place - we met in an elegant centre in Zakopane, and I owe my presence to this conference to my late professor, Wiesław Szlenk, who also participated schools organized by Prof. Łomnicki. Therefore he appeared on the list of people to whom M. Ziółko sent out invitations. While the supervisor sent me to the conference... That's how it was - I participated in all (except one) conferences, actively co-organizing many of them.This year we have another experiment - instead of the conference materials, we give up the readers a special issue of Mathematica Applicanda. I hope that thanks to this the articles will reach a wider group of potential readers, and the conference will gain new participants in the future./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6401Composition of wavelet and Fourier transforms
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The paper presents the basic properties of the serial composition of two transformations: wavelet and Fourier. Two types of transformations were obtained because wavelet and Fourier transformations do not commute. The consequences of a phenomenon known as a "wavelet crime" are presented. Using wavelets with compact support in the frequency domain (e.g. Meyer wavelets) leads to the representation of signals as sparse matrices. Speech signals were used to test the presented transforms./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6376Method for mass spectrometry spectrum deisotoping based on fuzzy inference systems
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Nowadays, mass spectrometry is widely used in proteomics for confident and precise identification of the protein. One of the most important steps in the signal analysis is deisotoping because some peaks in the spectrum are not the unique compound, but there are members of an isotopic envelope. Although the mass spectrometry is present in proteomics for a long time already, the problem of isotope peaks identification is not solved yet. The existing algorithms, usually designed for the particular type of spectrometer, are semi-supervised and do not give satisfactory results. We propose a new algorithm based on fuzzy inference systems that can accurately identify the isotopic envelopes in the spectrum of the complex structure./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6384Single stranded-DNA detection: the role of Wip1 in ATR-dependent pathway
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Single-stranded DNA (ssDNA) areas arise in cells as a result of exposure to stress agents - like UVC - or during repair of DNA double-strand breaks. ATR(ataxia telangiectasia mutated and Rad3-related) is responsible for detecting ssDNA. Recently, it has been shown that one of the most important components of cellular response to the damage is Wip1 phosphatase, which inactivates main elements of DNA damage response (DDR) pathways. We developed a mathematical model of ATR detector system, connected to p53 tumor suppressor responsible for activation of genes involved in cellular response to the damage (DNA repair/apoptosis). Moreover, we added Wip1 phosphatase, as a main agent responsible for turning o DDR. Our results show that the apoptotic threshold, where more than half of cells die, is equal to 20 J/m2. The threshold shifts when activity of the specied proteins involved in the pathway is blocked or reduced. Moreover with accurate dose of UVC and silenced or blocked Wip1, it may be possible to drive cancer cells to apoptotic pathway./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6375A model for random fire induced tree-grass coexistence in savannas
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Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce minimalistic model of tree-grass coexistence where fires occur according to stochastic process. We use the tools of linear semigroup theory to provide more careful mathematical analysis of the model. Essentially we show that there exists a unique stationary distribution of tree and grass biomasses./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6382Mathematical model of bats' subpopulations development
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The paper deals with the description of the mathematical model of bats' subpopulations and fission-fusion societies development. Model is based on the system of ordinary differential equations. Bats' behaviour and their searching strategy is presented on the basis of cavity roosting bats living in Bia\l{}owie\.{z}a Forest located in Poland. Theoretical results are illustrated by computer simulation and its comparison with biological remarks./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6371Mathematical model of endothelial cell proliferation and maturation
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Blood vessel sprouting (angiogenesis) is one of the hallmarks of cancer. Better quantitative understanding of this process would allow more effective antiangiogenic therapies to be developed. It has been hypothesised that not only the number of endothelial cells, but also the quality of the vasculature play an important role in how chemo- and radiotherapies are delivered to tumour site. Hence in this study a minimally-parametrised mathematical model of endothelial cell proliferation and maturation is developed. Endothelial cells are subdivided into two compartments -- mature and immature (or proliferating). The cells are assumed to undergo a self-mediated maturation, while loss of blood vessel quality is mediated by an external growth factor (here VEGF). The model is fitted to experimental data. The model shows how inhibition of VEGF results in better quality vasculature and slower proliferation./resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6383Nonparametric estimation of quantile versions of the Lorenz curve
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Estimators of quantile versions of the Lorenz curve are proposed. The pointwise consistency and asymptotic normality of the estimators is proved. The efficiency of the estimators is also studied in simulations/resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6372Jan Ptaszycki (1854-1912)
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Jan Ptaszycki was a Polish mathematician working in St. Petersburg in the period 1876--1912. In Poland, he is forgotten, and in Russia considered generally for Russian mathematician, known there as Ivan Lvovich Ptaszycki. There is no article about it on Polish {\it Wikipedia}, while there are three articles in Russian. In historical-mathematical Russian literature, depending on the author, it is reported that Ptaszycki was a Russian mathematician or, more rarely, a Polish mathematician as, for example, in [Lo15a] and [Lo15b]. In Polish, we can find information about it in the dictionaries [DW63], [SW03] and the obituary written by S. Dickstein [Di12], while in Russian in the papers [Pt96]-[Pt16], [Ju68], [Lo15a], [Lo15b], [Od14], and obituary written by Posse [Po12] (reprinted in [Pt3], without providing the author of the article). We underline that important information about Ptaszycki comes from the obituaries of K. A. Posse [Po12] and S. Dickstein [Di12] and from the memoirs of I. Ja. Depman [De60], this is from people who knew him personally. Ptaszycki in 1876 graduated from the University of Petersburg and until the end of his life he worked in this University. He, obtained a doctor's degree (Polish PhD) in 1881 and a Russian doctorate (Polish habilitation degree) in 1888. He was appointed an associate professor in 1897 and ordinary in 1901. From 1880, he taught in the Tsar Alexander II men gymnasium in Peterhof, from 1883 lectured at the university and from 1891 also at the Mikhailov Academy of Artillery. His main works were devoted to the problem of the so-called integration in finite terms of various types of differentials: algebraic, irrational, elliptical and other.We wanted to make known to the contemporary reader this forgotten Polish mathematician working in St. Petersburg. We tried to reach his work and achievement in mathematics as well as information about his activity. After discussing his biography, we briefly discuss his mathematical work. At the end of this work, we present a full list of published works and books by Ptaszycki, a list of works where one can find information about him and we quote articles and books related to his scientific achievements./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6406Anna Zofia Krygowska 30th anniversary of death
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Anna Zofia Krygowska/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6457[unknown2]
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/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6434On students’ difficulties in changing their original procedure on the example of a task concerning differential comparison
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Recognising and understanding the difficulties, which students show at different levels of teaching mathematics, can result in increased effectiveness of teaching. In this article, difficulties of students from the second to the fifth grade of primary school are analysed, revealed while they were solving tasks regarding differential comparison. Those difficulties, seemingly related to a relatively easy subject, make one realise how complex the process of learning mathematics is. The problem of differential comparison is only an example aimed at illustrating what impact previous experiences of a student have on the formation of pieces of their new knowledge./resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6455[unknown2]
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/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6458[unknown2]
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/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6437[unknown2]
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/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6435[unknown2]
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/resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6432Relate before calculate: Students’ ways of experiencing relationships between quantities
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The aim of this article is to contribute with findings concerning students’ ways of experiencing general mathematical structures and, in particular, relationships in additive structures.When students discern relationships in additive structures, it may lead to positive consequences for students’ future ability to perform calculations in addition and subtraction tasks. In the study, semi-structured interviews were conducted with students in grades 3, 8, and 9. An illustration showing a set of different quantities was the starting point during the interviews, together with an opening question regarding how the diverse quantities could be equalised. After the students’ discussions, they were asked if this could be described mathematically using written symbols. The students’ expressions concerning the phenomenon “relationships between quantities” were analyzed using phenomenography as an analytical tool. According to phenomenography, there are a limited number of ways in which a phenomenon can be experienced. Further, it is not about exploring how many individuals hold a specific experience that is of interest. In the case of this article, it is about capturing qualitatively different ways of experiencing the phenomenon relationships between quantities. Despite no specific numbers being presented, many students attributed specific numbers and values when expressing relationships between quantities. The students expressed general mathematical structures only to a limited extent and, in those cases, mostly only after encouragement from the interviewer. Following the phenomenographical analysis, the students’ ways of experiencing “relationships between quantities” are: as something that has to be calculated, or as something that has to be related. The first of these was most common in all grades. In this study, one critical aspect was identified, namely, that quantities are related to each other, additively. Instead of introducing mathematics with a focus on answer-oriented tasks, it is essential to introduce mathematics based on general structures such as additive structures. Even if the students are not familiar with such a mathematical “culture”, it is worth it. This was confirmed in our study./resource/bwmeta1.element.ojs-doi-10_14708_dm_v40i0_6431Results of Polish mathematicians concerning the Baire classification.
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The paper describes results of Polish mathematicians of XX century concerning the Baire classification of functions and Borel classification of sets. As usual, numerous theorems came from Wacław Sierpiński, remaining are due to Kazimierz Kuratowski, Stefan Banach, Stefan Kempisty, Edward Szpilrajn (Marczewski), Andrzej Alexiewicz, Władysław Orlicz, Adolf Lindenbaum, Roman Sikorski, Ryszard Engelking, Włodzimierz Holsztyński, Tadeusz Traczyk, Janina Staniszewska, Zygmunt Zahorski and Samuel Eilenberg./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_5125Monitoring of mean for asymmetric distributions.
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Nowadays control charts are used not only to control glass thickness, the diameter of rods etc. Have been invented many types of modern charts to control meteorological, medical, financial or telecommunications data. They often have heavy tails, skewness, and asymmetry. Approximation such data by Gaussian distribution is not the most beneficial. We need to model. Hence the need to model data with a different distribution. Controlling a process that exhibits asymmetry is a more difficult task than monitoring symmetric features (v. Figueiredo \& Gomes (2013)). It was assumed to construct a chart to control the work of the heart. This is definitely an asymmetrical process. Three control charts were constructed: to monitor average and grand mean of Rayleigh distribution and grand mean for approximated distribution to Gaussian distribution. /resource/bwmeta1.element.ojs-doi-10_14708_ma_v46i1_6373One hundred years of the Polish Mathematical Society
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The paper deals with the history of Polish mathematical societies since 1917, when the Mathematical Society in Lvov was founded. In the second half of the 19th century there appeared first national mathematical societies in Russia, France, United Kindom, Italy, United States, Germany. In Poland, partitioned then by neighbour powers (Russia, Prussia, Austria) whose policy was to deny Polish national development - it was not possible. An attempt has been made abroad in the form of the Society of Exact Sciences in Paris (Polish society, with a dozen or so mathematicians as members), which acted 1870-1882. The situation has changed by the outbreak of World War I and the subsequent fall of all three partitioning powers. The Polish Mathematical Society was founded by its constituent assembly on April 2, 1919./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6422A tribute to Juliusz Schauder
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An analysis of the mathematical contributions of Juliusz Schauder through the writings of contemporary mathematicians, and in particular Leray, Hadamard, Banach, Randolph, Federer, Lorentz, Ladyzhenskaya, Ural'tseva, Orlicz, G\aa rding and Pietsch./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6400Briefly about the conference on the history of mathematics: ”Poděbrady 2018”
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In this note, results of the Conference ”Poděbrady 2018” are discussed./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6459Mathematical logic in Poland 1918–1939
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Poland in the years 1918–1939 became one of the main centres of mathematical logic in the entire Word. This paper describes the rise of this field in Poland, Polish logical circles, organizations, journals and the main achievements of Polish logicians./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6411The case of the Steinhaus seminar on applied mathematics. Outline of the concept
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This article is devoted to the Seminar on Applied Mathematics, conducted in 1948-1960 by Professor Hugo Steinhaus in Wroclaw. It is based on the protocols of this Seminar so far not discussed anywhere. Many facts related to Professor Hugo Steinhaus can be found easily in the literature, also in the diary of the professor \emph{Mathematician for all seasons--recollections and notes.} (2016). Steinhaus was an outstanding mathematician. He wrote his doctoral thesis under the direction of David Hilbert at the University of Göttingen. Already at that time, he was interested in applications of mathematics. He also used mathematics as the goal of life in various aspects of economic and social life. During the Wrocław period, when he was running the Applied Mathematics Seminar for people with different professions and interests, he gave the beginning of the Wrocław School of Applied Mathematics. All the problems considered in this Seminar are briefly signaled in the protocols that are presented in the article along with the supplement based on the publication./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6421From the Editor
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We present a subsequent volume, 12 (2018), of the Series VI of Roczniki Polskiego Towarzystwa Matematycznego – “Antiquitates Mathematicae”, a journal devoted to history of mathematics. In it, we offer 10 articles (6 in English, 4 in Polish), a profile of Professor Lech Maligranda-the recipient of the Samuel Dickstein Main Prize of the Polish Mathematical Society for the year 2016, as well as a report on an international conference in history of mathematics organized by the Czech community of historian of mathematics./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6463Helena Rasiowa (1917–1994)
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In the paper, we present Helena Rasiowa's scientific personality emphasizing the period WWII and beginning of her professional activity after 1945./resource/bwmeta1.element.ojs-doi-10_14708_am_v12i1_6445