In this article, we focus our attention on (q,h)-Gauss?s binomial formula from which discover the additive property of (q; h)-exponential functions. We state (q,h)-analogue Gauss?s in terms proper polynomials T(q,h) own essential properties similar to ordinary polynomials. present (q,h)-Taylor series and analyze conditions for its convergence. introduce a new (q,h)-analytic exponential function...

Let q (G) denote the spectral radius of the signless Laplacian matrix of a graph G, also known as the Q-index of G. The aim of this note is to study a general extremal problem: How large can q (G) be when G belongs to an abstract graph property? Even knowing very little about the graph property, this paper shows that useful conclusions about the asymptotics of q (G) can be made, which turn out ...

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P ,Q)-total coloring ∗Research supported in part by Slovak VEGA Grant 2/0194/10. 210 M. Borowiecki, A. Kemnitz, M. Marangio and P. Mihók of a simple graphG is a coloring of the vertices V (G) and edgesE(G) of G...

We prove that for almost all 2 G(Q) e the eld ~ Q() has the following property: For each absolutely irreducible aane variety V of dimension r and each dominating separable rational map ': V ! A r there exists a point a 2 V (~ Q()) such that '(a) 2 Z r. We then say that ~ Q() is PAC over Z. This is a stronger property then being PAC. Indeed we show that beside the elds ~ Q() other elds which are...

We present new numerical characterization of DNA sequences that is based on the modified graphical representation proposed by Hamori. While Hamori embeds the sequence into Euclidean space, we use analogous embedding into the strong product of graphs, K4 ×Pn, with weighted edges. Based on this representation, a novel numerical characterization was proposed in [Pesek and Žerovnik, MATCH Commun. M...

In the article we settle down the problem of permanence of property RD under group extensions. We show that if 1 → N → G → Q → 1 is a short exact sequence of compactly generated groups such that Q has property RD, and N has property RD with respect to the restriction of a word-length on G, then G has property RD. We also generalize the result of Ji and Schweitzer stating that locally compact gr...

Let A be a finitely generated domain of GK dimension less than 3 over a field K and let Q(A) denote the quotient division algebra of A. Using the ideas of Smoktunowicz, we show that if D is a finitely generated division subalgebras of Q(A) of GK dimension at least 2, then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dime...

We investigate two types of semicontinuity for set-valued maps, Painlevé–Kuratowski semicontinuity and Cesari’s property (Q). It is shown that, in the context of convexvalued maps, the concepts related to Cesari’s property (Q) have better properties than the concepts in the sense of Painlevé–Kuratowski. In particular, we give a characterization of Cesari’s property (Q) by means of upper semicon...

A family of sets has the (p; q) property if among any p members of the family some q have a nonempty intersection. The authors have proved that for every p q d + 1 there is a c = c(p; q; d) < 1 such that for every family F of compact, convex sets in R d which has the (p; q) property there is a set of at most c points in R d that intersects each member of F, thus settling an old problem of Hadwi...

A family of sets has the (p, q) property if among any p members of the family some q have a nonempty intersection. It is shown that for every p ≥ q ≥ d + 1 there is a c = c(p, q, d) < ∞ such that for every family F of compact, convex sets in R which has the (p, q) property there is a set of at most c points in R that intersects each member of F . This settles an old problem of Hadwiger and Debr...