Subjects -> MATHEMATICS (Total: 1013 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (714 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (714 journals)                  1 2 3 4 | Last

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 Czechoslovak Mathematical JournalJournal Prestige (SJR): 0.307 Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1572-9141 - ISSN (Online) 0011-4642 Published by Springer-Verlag  [2469 journals]
• On an additive problem of unlike powers in short intervals

Abstract: Abstract We prove that almost all positive even integers n can be represented as p 2 2 + p 3 3 + p 4 4 + p 5 5 with $$\left {p_k^k - {1 \over 4}N} \right \leqslant {N^{1 - 1/54 + \varepsilon }}$$ for 2 ⩽ k ⩽ 5. As a consequence, we show that each sufficiently large odd integer N can be written as p1 + p 2 2 + p 3 3 + p 4 4 + p 5 5 with $$\left {p_k^k - {1 \over 5}N} \right \leqslant {N^{1 - 1/54 + \varepsilon }}$$ for 1 ⩽ k ⩽ 5.
PubDate: 2022-06-06

• Truncations of Gauss’ square exponent theorem

Abstract: Abstract We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer n $$\sum\limits_{k = 0}^n {{{\left( { - 1} \right)}^k}\left[ {\matrix{{2n - k} \cr k \cr } } \right]\,\,{{\left( {q;{q^2}} \right)}_{n - k}}{q^{\left( {\matrix{{k + 1} \cr 2 \cr } } \right)}} = \sum\limits_{k = - n}^n {{{\left( { - 1} \right)}^k}{q^{{k^2}}},} }$$ where $$\left[ {\matrix{n \cr m \cr } } \right] = \prod\limits_{k = 1}^m {{{1 - {q^{n - k + 1}}} \over {1 - {q^k}}}\,\,\,\,{\rm{and}}\,\,\,\,{{\left( {a;q} \right)}_n} = \prod\limits_{k = 0}^{n - 1} {\left( {1 - a{q^k}} \right).} }$$
PubDate: 2022-06-06

• On a family of elliptic curves of rank at least 2

Abstract: Abstract Let Cm:y2 = x3 − m2x + p2q2 be a family of elliptic curves over ℚ, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of Cm(ℚ). More specifically, we prove that the torsion subgroup of Cm(ℚ) is trivial and the ℚ-rank of this family is at least 2, whenever m ≢ 0 (mod 3), m ≢ 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.
PubDate: 2022-06-06

• Maximum bipartite subgraphs in H-free graphs

Abstract: Abstract Given a graph G, let f(G) denote the maximum number of edges in a bipartite subgraph of G. Given a fixed graph H and a positive integer m, let f(m, H) denote the minimum possible cardinality of f(G), as G ranges over all graphs on m edges that contain no copy of H. In this paper we prove that $$f\left( {m,{\theta _{k,s}}} \right) \geqslant {1 \over 2}m + \Omega \left( {{m^{\left( {2k + 1} \right)/\left( {2k + 2} \right)}}} \right)$$ , which extends the results of N. Alon, M. Krivelevich, B. Sudakov. Write K k ′ and K t,s ′ for the subdivisions of Kk and Kt,s. We show that $$f\left( {m,K_k^\prime } \right) \geqslant {1 \over 2}m + \Omega \left( {{m^{\left( {5k - 8} \right)/\left( {6k - 10} \right)}}} \right)$$ and $$f\left( {m,K_{t,s}^\prime } \right) \geqslant {1 \over 2}m + \Omega \left( {{m^{\left( {5t - 1} \right)/\left( {6t - 2} \right)}}} \right)$$ , improving a result of Q. Zeng, J. Hou. We also give lower bounds on wheel-free graphs. All of these contribute to a conjecture of N. Alon, B. Bollobás, M. Krivelevich, B. Sudakov (2003).
PubDate: 2022-06-03

• The relation between the number of leaves of a tree and its diameter

Abstract: Abstract Let L(n, d) denote the minimum possible number of leaves in a tree of order n and diameter d. Lesniak (1975) gave the lower bound B(n,d) = ⌈2(n − 1)/d⌉ for L(n,d). When d is even, B(n,d) = L(n,d). But when d is odd, B(n,d) is smaller than L(n,d) in general. For example, B(21, 3) = 14 while L(21, 3) = 19. In this note, we determine L(n, d) using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.
PubDate: 2022-06-01

• On Bernstein inequalities for multivariate trigonometric polynomials in
Lp, 0 ⩽ p ⩽ ∞

Abstract: Abstract Let $${{\mathbb{T}}_n}$$ be the space of all trigonometric polynomials of degree not greater than n with complex coefficients. Arestov extended the result of Bernstein and others and proved that $${\left\ {(1/n)T_n^\prime } \right\ _p} \leqslant {\left\ {{T_n}} \right\ _p}$$ for 0 ⩽ p ⩽ ∞ and $${T_n} \in {{\mathbb{T}}_n}$$ . We derive the multivariate version of the result of Golitschek and Lorentz $${\left\ {{{\left {{T_n}\cos \alpha + {1 \over n}\nabla {T_n}\sin \alpha } \right }_{l_\infty ^{(m)}}}} \right\ _p} \leqslant{\left\ {{T_n}} \right\ _p},\,\,\,\,\,\,\,0 \leqslant p \leqslant\infty$$ for all trigonometric polynomials (with complex coefficients) in m variables of degree at most n.
PubDate: 2022-06-01

• New Einstein metrics on Sp(n) which are non-naturally reductive

Abstract: Abstract We prove that there are at least two new non-naturally reductive Ad(Sp(l) × Sp(k) × Sp(k) × Sp(k)) invariant Einstein metrics on Sp(l + 3k) (k < l). It implies that every compact simple Lie group Sp(n) for n = l + 3k > 4 admits at least $$2[{1 \over 4}(n - 1)]$$ non-naturally reductive Ad(Sp(l) × Sp(k) × Sp(k) × Sp(k)) invariant Einstein metrics.
PubDate: 2022-06-01

• The Massera-Schäffer problem for a first order linear differential
equation

Abstract: Abstract We consider the Massera-Schäffer problem for the equation $$- y\prime (x) + q(x)y(x) = f(x),\,\,\,\,\,x \in \mathbb{R},$$ where $$f \in L_p^{{\rm{loc}}}(\mathbb{R})$$ , p ∈ [1, ∞) and $$0 \leqslant q \in L_p^{{\rm{loc}}}(\mathbb{R})$$ . By a solution of the problem we mean any function y, absolutely continuous and satisfying the above equation almost everywhere in $$\mathbb{R}$$ . Let positive and continuous functions μ(x) and θ(x) for $$x \in \mathbb{R}$$ be given. Let us introduce the spaces $$\matrix{{{L_p}(\mathbb{R},\mu ) = \left\{ {f \in L_p^{{\rm{loc}}}(\mathbb{R}):\left\ f \right\ _{{L_p}(\mathbb{R},\mu )}^p = \int_{ - \infty }^\infty {{{\left {\mu (x)f(x)} \right }^p}{\rm{d}}x < \infty } } \right\},} \hfill \cr {{L_p}(\mathbb{R},\theta ) = \left\{ {f \in L_p^{{\rm{loc}}}(\mathbb{R}):\left\ f \right\ _{{L_p}(\mathbb{R},\theta )}^p = \int_{ - \infty }^\infty {{{\left {\theta (x)f(x)} \right }^p}{\rm{d}}x < \infty } } \right\}.} \hfill \cr }$$ We obtain requirements to the functions μ θ and q under which (1) for every function $$f \in {L_p}(\mathbb{R},\theta )$$ there exists a unique solution $$y \in {L_p}(\mathbb{R},\mu )$$ of the above equation; (2) there is an absolute constant c(p) ∈ (0, ∞) such that regardless of the choice of a function $$f \in {L_p}(\mathbb{R},\theta )$$ the solution of the above equation satisfies the inequality $${\left\ y \right\ _{{L_p}(\mathbb{R},\mu )}} \leqslant c(p){\left\ f \right\ _{{L_p}(\mathbb{R},\theta ).}}$$ .
PubDate: 2022-06-01

• Extension of semiclean rings

Abstract: Abstract This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
PubDate: 2022-06-01

• Wiener index of graphs with fixed number of pendant or cut-vertices

Abstract: Abstract The Wiener index of a connected graph is defined as the sum of the distances between all unordered pairs of its vertices. We characterize the graphs which extremize the Wiener index among all graphs on n vertices with k pendant vertices. We also characterize the graph which minimizes the Wiener index over the graphs on n vertices with s cut-vertices.
PubDate: 2022-06-01

• On the symmetric algebra of certain first syzygy modules

Abstract: Abstract Let (R, $$\mathfrak{m}$$ ) be a standard graded K-algebra over a field K. Then R can be written as S/I, where I ⊆ (x1,…, xn)2 is a graded ideal of a polynomial ring S = K[x1,…, xn]. Assume that n ⩽ 3 and I is a strongly stable monomial ideal. We study the symmetric algebra SymR(Syz1( $$\mathfrak{m}$$ )) of the first syzygy module Syz1( $$\mathfrak{m}$$ ) of $$\mathfrak{m}$$ . When the minimal generators of I are all of degree 2, the dimension of SymR (Syz1( $$\mathfrak{m}$$ )) is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.
PubDate: 2022-06-01

• Degree sums of adjacent vertices for traceability of claw-free graphs

Abstract: Abstract The line graph of a graph G, denoted by L(G), has E(G) as its vertex set, where two vertices in L(G) are adjacent if and only if the corresponding edges in G have a vertex in common. For a graph H, define $${\overline \sigma _2}(H) = \min \left\{{d(u) + d(v):\;\;uv\; \in \;E(H)} \right\}$$ . Let H be a 2-connected claw-free simple graph of order n with δ(H) ⩾ 3. We show that, if $${\overline \sigma _2}(H)\geqslant {1 \over 7}(2n - 5)$$ and n is sufficiently large, then either H is traceable or the Ryjáček’s closure cl(H) = L(G), where G is an essentially 2-edge-connected triangle-free graph that can be contracted to one of the two graphs of order 10 which have no spanning trail. Furthermore, if $${\overline \sigma _2}(H)\; > \;{1 \over 3}(n - 6)$$ and n is sufficiently large, then H is traceable. The bound $${1 \over 3}(n - 6)$$ is sharp. As a byproduct, we prove that there are exactly eight graphs in the family $${\cal G}$$ of 2-edge-connected simple graphs of order at most 11 that have no spanning trail, an improvement of the result in Z. Niu et al. (2012).
PubDate: 2022-06-01

• Solutions of the generalized Dirichlet problem for the iterated slice
Dirac equation

Abstract: Abstract Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.
PubDate: 2022-06-01

• On the Choquet integrals associated to Bessel capacities

Abstract: Abstract We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.
PubDate: 2022-06-01

• A convex treatment of numerical radius inequalities

Abstract: Abstract We prove an inner product inequality for Hilbert space operators. This inequality will be utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to obtain such versions.
PubDate: 2022-06-01

• On the multiplicity of Laplacian eigenvalues for unicyclic graphs

Abstract: Abstract Let G be a connected graph of order n and U a unicyclic graph with the same order. We firstly give a sharp bound for mG(μ), the multiplicity of a Laplacian eigenvalue μ of G. As a straightforward result, mU(1) ⩽ n − 2. We then provide two graph operations (i.e., grafting and shifting) on graph G for which the value of mG(1) is nondecreasing. As applications, we get the distribution of mU (1) for unicyclic graphs on n vertices. Moreover, for the two largest possible values of mU(1) ∈ {n − 5, n − 3}, the corresponding graphs U are completely determined.
PubDate: 2022-06-01

• Local cohomology, cofiniteness and homological functors of modules

Abstract: Abstract Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules H I j (M) are I-cofinite for all finitely generated R-modules M and all j ∈ ℕ0 if and only if the R-modules Ext R i (N,H I j (M)) and Tor R i (N, H I j (M)) are I-cofinite for all finitely generated R-modules M, N and all integers i, j ∈ ℕ0.
PubDate: 2022-06-01

• Isolated Subgroups of Finite Abelian Groups

Abstract: Abstract We say that a subgroup H is isolated in a group G if for every x ∈ G we have either x ∈ H or 〈x〉 ∩ H = 1. We describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.
PubDate: 2022-03-04
DOI: 10.21136/CMJ.2022.0085-21

• Regularity and Intersections of Bracket Powers

Abstract: Abstract Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence. Connections are made with Ohm-Rush content theory, intersection-flatness of the Frobenius map, and various flatness criteria.
PubDate: 2022-03-01
DOI: 10.21136/CMJ.2022.0066-21

• The Potential-Ramsey Number of Kn and K t −k

Abstract: Abstract A nonincreasing sequence π = (d1,…, dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. In this case, G is referred to as a realization of π. Given two graphs G1 and G2, A. Busch et al. (2014) introduced the potential-Ramsey number of G1 and G2, denoted by rpot(G1, G2), as the smallest nonnegative integer m such that for every m-term graphic sequence π, there is a realization G of π with G1 ⊆ G or with $${G_2} \subseteq \overline G$$ , where $$\overline G$$ is the complement of G. For t ≽ 2 and $$0\leqslant k\leqslant \left\lfloor {{t \over 2}} \right\rfloor$$ , let K t −k be the graph obtained from Kt by deleting k independent edges. We determine rpot (Kn, K t −k ) for $$t\geqslant 3,1\leqslant k\leqslant \left\lfloor {{t \over 2}} \right\rfloor$$ and $$n\geqslant \left\lceil {\sqrt {2k}} \right\rceil$$ , which gives the complete solution to a result in J. Z. Du, J. H. Yin (2021).
PubDate: 2022-03-01
DOI: 10.21136/CMJ.2022.0017-21

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