Showing papers in "Annales Umcs, Mathematica in 2014"
TL;DR: In this article, the Radic's determinant of a rectangular matrix is represented as a sum of determinants of square matrices and the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column.
Abstract: In this paper we present new identities for the Radic’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column.
8 citations
TL;DR: In this article, the maximum number of edges in a graph on n vertices which does not contain a subgraph as a sub-graph has been investigated and the number of disjoint copies of a path has been shown to be 3P_4.
Abstract: Let \(ex(n, G)\) denote the maximum number of edges in a graph on \(n\) vertices which does not contain \(G\) as a subgraph. Let \(P_i\) denote a path consisting of \(i\) vertices and let \(mP_i\) denote \(m\) disjoint copies of \(P_i\). In this paper we count \(ex(n, 3P_4)\).
7 citations
TL;DR: In this paper, the authors considered Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces and extended some results from these papers.
Abstract: We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces \(A^2_{\alpha}\), \(−1 < \alpha < \infty\). These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.
6 citations
TL;DR: In this paper, q-analogues of three Appell polynomials, H-polynomials, the Apostol-Bernoulli and Apostol Euler, are studied, whereby two new q-difference operators and the NOVA q-addition play key roles.
Abstract: We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to some related polynomials. In order to find a certain formula, we introduce a q-logarithm. We conclude with a brief discussion of multiple q-Appell polynomials.
5 citations
TL;DR: In this paper, the authors show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree, and minimum degree, respectively, and extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289-1294].
Abstract: In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph \(G\) is defined as \[\xi ^{sv} (G)= \sum_{v\in V(G)}{\frac{\varepsilon (v) D(v)}{deg(v)}},\] where \(\varepsilon(v)\) is the eccentricity of the vertex \(v\), \(deg(v)\) is the degree of the vertex \(v\) and \[D(v)=\sum_{u\in V(G)}{d(u,v)}\] is the sum of all distances from the vertex \(v\).
3 citations
TL;DR: In this article, the Fekete-Szego problem for the generalized linear differential operator (GLD) was solved for strongly starlike and strongly convex functions, respectively.
Abstract: In the present investigation we solve Fekete-Szego problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions. In the present investigation we solve Fekete-Szego problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.
3 citations
TL;DR: In this article, the authors generalize this isomorphism to the base-preserving vector bundle map (C_M(g):T^{(r)M\mathrel{\tilde=}T^*M\to T^{r*}M\) depending on a Riemannian metric in terms of natural tensor fields on the manifold.
Abstract: If \((M,g)\) is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism \(TM\mathrel{\tilde=}T^*M\) given by \(v\to g(v,-)\) between the tangent \(TM\) and the cotangent \(T^*M\) bundles of \(M\). In the present note, we generalize this isomorphism to the one \(T^{(r)}M\mathrel{\tilde=} T^{r*}M\) between the \(r\)-th order vector tangent \(T^{(r)}M=(J^r(M,R)_0)^*\) and the \(r\)-th order cotangent \(T^{r*}M=J^r(M,R)_0\) bundles of \(M\). Next, we describe all base preserving vector bundle maps \(C_M(g):T^{(r)}M\to T^{r*}M\) depending on a Riemannian metric \(g\) in terms of natural (in \(g\)) tensor fields on \(M\).
2 citations
TL;DR: In this article, it was shown that if Poncelet's closure theorem holds for k-gons circumscribed to C R C r, then there exist circles inside this annulus which satisfy Poncelets closure theorem together with C r, with n- gons for any n > k.
Abstract: Let C R C r denote an annulus formed by two non-concentric circles C R , C r in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to C R C r , then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with C r , with n- gons for any n > k.
2 citations
TL;DR: In this paper, the sharp upper bound to the second Hankel determinant for a certain class of analytic functions in the unit disk has been determined, and several majorization properties for functions belonging to a subclass of the analytic functions are investigated.
Abstract: The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class \(R^{\lambda}(a,c,A,B)\) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass \(\widetilde {R}^{\lambda}(a,c, A,B)\) of \(R^{\lambda}(a,c,A,B)\) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.
1 citations
TL;DR: In this paper, the existence of an integer (g_r) such that for every integer g r, there is a smooth curve of genus g with g r + 1 > s_r(C)/r, i.e. in the sequence of all birational gonalities of G r, at least one slope inequality fails.
Abstract: Let \(C\) be a smooth curve of genus \(g\). For each positive integer \(r\) the birational \(r\)-gonality \(s_r(C)\) of \(C\) is the minimal integer \(t\) such that there is \(L\in \mbox{Pic}^t(C)\) with \(h^0(C,L) =r+1\). Fix an integer \(r\ge 3\). In this paper we prove the existence of an integer \(g_r\) such that for every integer \(g\ge g_r\) there is a smooth curve \(C\) of genus \(g\) with \(s_{r+1}(C)/(r+1) > s_r(C)/r\), i.e. in the sequence of all birational gonalities of \(C\) at least one of the slope inequalities fails.
1 citations
TL;DR: In this paper, the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space is proved.
Abstract: A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.
TL;DR: In this article, the deviation from the weak Banach-saks property of an operator of a certain class between direct sums is defined as the supremum of such deviations attained on the coordinates X v.
Abstract: We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (X v ) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(X v ) is equal to the supremum of such deviations attained on the coordinates X v . This is a quantitative version for operators of the result for the Kothe–Bochner sequence spaces E(X) that if E has the Banach–Saks property, then E(X) has the weak Banach–Saks property if and only if so has X.
TL;DR: In this article, the authors determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J 2 Y →M of Y→M.
Abstract: We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J 2 Y → M of Y → M.
TL;DR: In this paper, it was shown that for every Banach space containing asymptotically isometric copy of the space c_0, there is a bounded, closed and convex set with the Chebyshev radius r(C) = 1.
Abstract: The aim of this paper is to show that for every Banach space \((X, \|\cdot\|)\) containing asymptotically isometric copy of the space \(c_0\) there is a bounded, closed and convex set \(C \subset X\) with the Chebyshev radius \(r(C) = 1\) such that for every \(k \geq 1 \) there exists a \(k\)-contractive mapping \(T : C \to C\) with \(\| x - Tx \| > 1 − 1/k\) for any \(x \in C\).
TL;DR: In this paper, the exact values of the Ramsey number R(P_n, K_1,m, F_m) were derived for the case that F has at least one odd component.
Abstract: Let \(G_1\) and \(G_2\) be two given graphs. The Ramsey number \(R(G_1,G_2)\) is the least integer \(r\) such that for every graph \(G\) on \(r\) vertices, either \(G\) contains a \(G_1\) or \(\overline{G}\) contains a \(G_2\). Parsons gave a recursive formula to determine the values of \(R(P_n,K_{1,m})\), where \(P_n\) is a path on \(n\) vertices and \(K_{1,m}\) is a star on \(m+1\) vertices. In this note, we study the Ramsey numbers \(R(P_n,K_1\vee F_m)\), where \(F_m\) is a linear forest on \(m\) vertices. We determine the exact values of \(R(P_n,K_1\vee F_m)\) for the cases \(m\leq n\) and \(m\geq 2n\), and for the case that \(F_m\) has no odd component. Moreover, we give a lower bound and an upper bound for the case \(n+1\leq m\leq 2n-1\) and \(F_m\) has at least one odd component.
TL;DR: In this paper, the authors discuss some subordination results for a subclass of functions analytic in the unit disk U and show that the subordination result holds for all functions analytic functions in the U.
Abstract: In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U.