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Wyświetlanie 1-15 z 68
Tytuł:
Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory
Autorzy:
Agarwal, R.
O'Regan, D.
Sahu, D.
Powiązania:
https://bibliotekanauki.pl/articles/729475.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
multivalued maps
Fréchet space
degree and index theory
projective limit
Opis:
New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 399-409
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination
Autorzy:
Amos, David
Asplund, John
Brimkov, Boris
Davila, Randy
Powiązania:
https://bibliotekanauki.pl/articles/32083827.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Slater number
domination number
sub- k -domination number
k -domination number
degree sequence index strategy
Opis:
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide structural results on sub-k-domination, and explore properties of graphs which are subk(G)-critical with respect to addition and deletion of vertices and edges.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 209-225
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Describing Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree 6 or 7
Autorzy:
Batueva, Ts.Ch-D.
Borodin, O.V.
Ivanova, A.O.
Nikiforov, D.V.
Powiązania:
https://bibliotekanauki.pl/articles/32361718.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
structural properties
3-polytope
5-star
neighborhood
Opis:
In 1940, in attempts to solve the Four Color Problem, Henry Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. This description depends on 32 main parameters. (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13) Not many precise upper bounds on these parameters have been obtained as yet, even for restricted subclasses in P5. In 2018, Borodin, Ivanova, Kazak proved that every forbidding vertices of degree from 7 to 11 results in a tight description (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6). Recently, Borodin, Ivanova, and Kazak proved every 3-polytope in P5 with no vertices of degrees 6, 7, and 8 has a 5-vertex whose neighborhood is majorized by one of the sequences (5, 5, 5, 5, ∞) and (5, 5, 10, 5, 12), which is tight and improves a corresponding description (5, 5, 5, 5, ∞), (5, 5, 9, 5, 17), (5, 5, 10, 5, 14), (5, 5, 11, 5, 13) that follows from the Lebesgue Theorem. The purpose of this paper is to prove that every 3-polytope with minimum degree 5 and no vertices of degree 6 or 7 has a 5-vertex whose neighborhood is majorized by one of the ordered sequences (5, 5, 5, 5, ∞), (5, 5, 8, 5, 14), or (5, 5, 10, 5, 12).
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 535-548
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Degree sequences of monocore graphs
Autorzy:
Bickle, Allan
Powiązania:
https://bibliotekanauki.pl/articles/30148681.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
monocore graph
degeneracy
degree sequence
Opis:
A $k$-monocore graph is a graph which has its minimum degree and degeneracy both equal to $k$. Integer sequences that can be the degree sequence of some $k$-monocore graph are characterized as follows. A nonincreasing sequence of integers $d_1, . . ., d_n$ is the degree sequence of some $k$-monocore graph $G, 0 ≤ k ≤ n − 1$, if and only if $k ≤ di ≤ min {n − 1, k + n − i}$ and $⨊d_i = 2m$, where $m$ satisfies $$\lceil\frac{k·n}{2}\rceil ≤ m ≤ k ・ n − \binom{k+1}{2}$$
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 585-592
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Key moments of the mutual influence of the Polish and Soviet schools of nonlinear functional analysis in the 1920s--1950s
Autorzy:
Bogatov, Egor Mikhailovich
Powiązania:
https://bibliotekanauki.pl/articles/749784.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Polish school of functional analysis, Soviet school of functional analysis, fixed point theorem, Orlicz space, nonlinear integral equations, mapping degree, convex sets, retracts theory
Polska szkoła analizy funkcjonalnej, radziecka szkoła analizy funkcjonalnej, twierdzenie o punkcie stałym, przestrzeń Orlicza, nieliniowe równanie całkowe, stopień odwzorowania, zbiory wypukłe, teoria retraktów
Opis:
Artykuł zawiera kluczowe aspekty historii rozwoju metod jakościowych nieliniowej analizy funkcjonalnej (twierdzenia o punkcie stałym, teoria stopnia odwzorowania, teoria przestrzeni Orlicza), w~ramach których najbardziej uwidoczniły się wzajemne oddziaływania polsko-radzieckie. Do połowy XX wieku w dziedzinach tych  dokonał się  postęp za sprawą  przedstawicieli lwowskiej szkoły matematycznej, warszawskiej szkoły matematycznej, moskiewskiej szkoły matematycznej  i odeskiej szkoły matematycznej. Analiza ich rezultatów stanowi główną część niniejszej pracy. Szczególną uwagę zwracamy na badania matematyka radzieckiego M. A. Krasnosel'skiego, który korzystał z wyników J. Schaudera i K. Borsuka oraz z przestrzeni Orlicza przy rozwiązywaniu szerokiej klasy problemów z jakościowej teorii nieliniowych równań całkowych.
The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within the framework of which Polish-Soviet interaction was most clearly manifested. In the period up to the mid-twentieth century these areas were advanced by the representatives of Lvov Mathematical School, Warsaw Mathematical School, Moscow Mathematical School and Odessa Mathematical School. Examination of their results is a significant part of this work. Much attention is paid to the investigations of the Soviet mathematician M.A. Krasnosel'skii, who used the achievements of J. Schauder and K. Borsuk as well as Orlicz spaces for solving a wide class of problems in qualitative theory of nonlinear integral equations. 
Źródło:
Antiquitates Mathematicae; 2017, 11
1898-5203
2353-8813
Pojawia się w:
Antiquitates Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
5-stars of low weight in normal plane maps with minimum degree 5
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Jensen, Tommy R.
Powiązania:
https://bibliotekanauki.pl/articles/30148303.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
plane map
vertex degree
weight
light subgraph
Opis:
It is known that there are normal plane maps $M_5$ with minimum degree 5 such that the minimum degree-sum $w(S_5)$ of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an $M_5$ has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then $w(S_5) ≤ 68$. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free $M_5$ with $w(S_5) = 48$.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 539-546
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Describing Neighborhoods of 5-Vertices in 3-Polytopes with Minimum Degree 5 and Without Vertices of Degrees from 7 to 11
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Kazak, Olesya N.
Powiązania:
https://bibliotekanauki.pl/articles/31342287.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
structure properties
3-polytope
neighborhood
Opis:
In 1940, Lebesgue proved that every 3-polytope contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13). In this paper we prove that every 3-polytope without vertices of degree from 7 to 11 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6), where all parameters are tight.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 615-625
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Light Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No 6-Vertices
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Vasil’eva, Ekaterina I.
Powiązania:
https://bibliotekanauki.pl/articles/31348169.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar map
planar graph
3-polytope
structural properties
5-star
weight
height
Opis:
In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. Given a 3-polytope P, by w(P) denote the minimum of the degree-sum (weight) of the neighborhoods of 5-vertices (minor 5-stars) in P. In 1996, Jendrol’ and Madaras showed that if a polytope P in P5 is allowed to have a 5-vertex adjacent to four 5-vertices, then w(P) can be arbitrarily large. For each P in P5 without vertices of degree 6 and 5-vertices adjacent to four 5-vertices, it follows from Lebesgue’s Theorem that w(P) ≤ 68. Recently, this bound was lowered to w(P) ≤ 55 by Borodin, Ivanova, and Jensen and then to w(P) ≤ 51 by Borodin and Ivanova. In this note, we prove that every such polytope P satisfies w(P) ≤ 44, which bound is sharp.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 985-994
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Low 5-Stars at 5-Vertices in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree from 7 to 9
Autorzy:
Borodin, Oleg V.
Bykov, Mikhail A.
Ivanova, Anna O.
Powiązania:
https://bibliotekanauki.pl/articles/31348144.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar map
planar graph
3-polytope
structural properties
5-star
weight
height
Opis:
In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class $P_5$ of 3-polytopes with minimum degree 5. Given a 3-polytope $P$, by $h_5(P)$ we denote the minimum of the maximum degrees (height) of the neighborhoods of 5-vertices (minor 5-stars) in $P$. Recently, Borodin, Ivanova and Jensen showed that if a polytope $P$ in $P_5$ is allowed to have a 5-vertex adjacent to two 5-vertices and two more vertices of degree at most 6, called a (5, 5, 6, 6, ∞)-vertex, then $h_5(P)$ can be arbitrarily large. Therefore, we consider the subclass \(P_5^\ast\) of 3-polytopes in $P_5$ that avoid (5, 5, 6, 6, ∞)-vertices. For each $P^\ast$ in $P_5^\ast$ without vertices of degree from 7 to 9, it follows from Lebesgue’s Theorem that $h_5(P^\ast) ≤ 17$. Recently, this bound was lowered by Borodin, Ivanova, and Kazak to the sharp bound $h_5(P^\ast) ≤ 15$ assuming the absence of vertices of degree from 7 to 11 in $P^\ast$. In this note, we extend the bound $h_5(P^\ast) ≤ 15$ to all $P^\ast$s without vertices of degree from 7 to 9.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1025-1033
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decomposition of the Product of Cycles Based on Degree Partition
Autorzy:
Borse, Y. M.
Shaikh, S. R.
Powiązania:
https://bibliotekanauki.pl/articles/31343576.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypercube
Cartesian product
n-connected
regular
bipan- cyclic
spanning subgraph
Opis:
The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n1+ n2+ ・ ・ ・ + nk with k ≥ 2 and ni ≥ 2 for each i. We prove that if k = 2, then G can be decomposed into two spanning subgraphs G1 and G2 such that each Gi is ni-regular, ni-connected, and bipancyclic or nearly bipancyclic. For k > 2, we establish that if all ni in the partition of 2n are even, then G can be decomposed into k spanning subgraphs G1, G2, . . ., Gk such that each Gi is ni-regular and ni-connected. These results are analogous to the corresponding results for hypercubes.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 241-256
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Universality in Graph Properties with Degree Restrictions
Autorzy:
Broere, Izak
Heidema, Johannes
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/30146518.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
countable graph
universal graph
induced-hereditary
k-degenerate graph
graph with colouring number at most k + 1
graph property with assignment
Opis:
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set ℐc of all countable graphs (since every graph in ℐc is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of ℐc is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 477-492
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Po co psychologia?
What is psychology for?
Autorzy:
Brzeziński, Jerzy Marian
Powiązania:
https://bibliotekanauki.pl/articles/1178119.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Kazimierza Wielkiego w Bydgoszczy
Tematy:
5-year master’s degree
Empirically Based Assessment
antireductionism
empirical research
empirical theory
ethical awareness
falsification
full-time
methodological awareness
plagiarism
program in psychology
psychology
science
scientific misconduct: fabrication
social practice
Opis:
Three main problems are considered. The first is that psychology should avoid any inclination towards neuroscience or a type of brain science. Making use of the achievements of natural sciences, psychology should take into regard the cultural conditions [determinants] and methods worked out in social sciences. Thus, it should adopt the antireductionistic methodological programme. The second problem is that psychology must reject the papers that entice with apparent scientific approach being actually of no real worth. Also the threat posed to psychological practice by pseudo-scientific monographs and pseudo-test should be recognised. They offer scientifically false basis of practical work of psychologists in the sphere of social practice. The third problem is that each psychological practice should be preceded by a psychological theory that is empirical and needs to be verified by a methodologically correct method. Thee underlying empirical psychological theory makes a given psychological practice sensible and ethical. The status of psychology as a science and the status of psychological practice are related to the quality of education of future psychologists. The author definitely opts for the model of full-time 5-year master’s degree studies (so against the Bologna model of 3-year licentiate (BA) followed by a 2-year master’s degree study (MA)), supplemented with a one-year training under supervision of an experienced specialist. The effective and ethical work of professional psychologists in Poland suffers from the lack of legal regulations that would protect this profession against the infiltration of all kinds of charlatans offering pseudo-scientific diagnostic tools like e.g. the Tree test of Charles Koch and therapies like e.g. the Systemic Constellation of Bert Hellinger. Of utmost importance is development of not only methodological awareness but also ethical awareness in psychologists and students of psychology. Moreover, the education should bring the realisation of the effects and danger of scientific misconduct of FFP type, that is fabrication, falsification, plagiarism.
Źródło:
Polskie Forum Psychologiczne; 2014, XIX, 3; 285-304
1642-1043
Pojawia się w:
Polskie Forum Psychologiczne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination Number of Graphs with Minimum Degree Five
Autorzy:
Bujtás, Csilla
Powiązania:
https://bibliotekanauki.pl/articles/32222697.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
domination number
discharging method
Opis:
We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 763-777
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An implicit weighted degree condition for heavy cycles
Autorzy:
Cai, Junqing
Li, Hao
Ning, Wantao
Powiązania:
https://bibliotekanauki.pl/articles/30148719.pdf
Data publikacji:
2014-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weighted graph
hamiltonian cycles
heavy cycles
implicit degree
implicit weighted degree
Opis:
For a vertex v in a weighted graph G, idw(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a hamiltonian cycle or a cycle of weight at least 2t/3. This generalizes the result of Zhang et al. [9].
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 4; 801-810
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Saturation Number for the Length of Degree Monotone Paths
Autorzy:
Caro, Yair
Lauri, Josef
Zarb, Christina
Powiązania:
https://bibliotekanauki.pl/articles/31339330.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
paths
degrees
saturation
Opis:
A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known Erdős- Szekeres theorem, has been studied by the authors in two earlier papers. Here we consider a saturation problem for the parameter mp(G). We call G saturated if, for every edge e added to G, mp(G + e) > mp(G), and we define h(n, k) to be the least possible number of edges in a saturated graph G on n vertices with mp(G) < k, while mp(G+e) ≥ k for every new edge e. We obtain linear lower and upper bounds for h(n, k), we determine exactly the values of h(n, k) for k = 3 and 4, and we present constructions of saturated graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 557-569
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 68

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