Czechoslovak Mathematical Journal最新文献

The Turán number of a given graph H, denoted by ex(n, H), is the maximum number of edges in an H-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(n, K_p ∪ K_q) of a vertex-disjoint union of cliques K_p and K_q for all values of n.

It is known that if f is holomorphic in the open unit disc (mathbb{D}) of the complex plane and if, for some c > 0, ∣f(z)∣ ⩽ 1/(1−∣z∣²)^c, (z in mathbb{D}), then ∣f′(z)∣ ⩽ 2(c+1)/(1−∣z∣²)^c+1. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.

Given a graph G = (V, E), if we can partition the vertex set V into two nonempty subsets V₁ and V₂ which satisfy Δ(G[V₁]) ⩽ d₁ and Δ(G[V₂]) ⩽ d₂, then we say G has a (({{rm{Delta }}_{{d_1}}},,{{rm{Delta }}_{{d_2}}}))-partition. And we say G admits an (({F_{d_{1}}}, {F_{d_{2}}}))-partition if G[V₁] and G[V₂] are both forests whose maximum degree is at most d₁ and d₂, respectively. We show that every planar graph with girth at least 5 has an (F₄, F₄)-partition.

Let G be a finite group and construct a graph Δ(G) by taking G {1} as the vertex set of Δ(G) and by drawing an edge between two vertices x and y if 〈x, y〉 is cyclic. Let K(G) be the set consisting of the universal vertices of Δ(G) along the identity element. For a solvable group G, we present a necessary and sufficient condition for K(G) to be nontrivial. We also develop a connection between Δ(G) and K(G) when ∣G∣ is divisible by two distinct primes and the diameter of Δ(G) is 2.

Let j ⩾ 2 be a given integer. Let H_k* be the set of all normalized primitive holomorphic cusp forms of even integral weight k ⩾ 2 for the full modulo group SL(2, ℤ). For f ∈ H_k*, denote by ({{rm{lambda }}_{{rm{sy}}{{rm{m}}^j}{kern 1pt} f}}(n)) the nth normalized Fourier coefficient of jth symmetric power L-function (L(s, sym^jf)) attached to f. We are interested in the average behaviour of the sum

where x is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).

A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof of Feynman’s assertion.

Abstract

We introduce a type of n-dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.

Abstract

Let D be a nonempty open set in a metric space (X, d) with ∂D ≠ Ø. Define $$h_{D,c}(x,y)=logleft(1+c{{{d(x,y)}}over{{sqrt{d_{D}(x)d_{D}(y)}}}}right).$$ where d_D(x) = d(x, ∂D) is the distance from x to the boundary of D. For every c ⩾ 2, h_D,c is a metric. We study the sharp Lipschitz constants for the metric h_D,c under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball.

We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.

We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded ϕ-Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.