DSpace Collection: Volume 34, Number 4
http://hdl.handle.net/10525/2578
Serdica Mathematical Journal Volume 34, Number 4, 2008The Collection's search engineSearch the Channelsearch
http://sci-gems.math.bas.bg/jspui/simple-search
New Upper Bound for the Edge Folkman Number Fe(3,5;13)
http://hdl.handle.net/10525/2627
Title: New Upper Bound for the Edge Folkman Number Fe(3,5;13)<br/><br/>Authors: Kolev, Nikolay<br/><br/>Abstract: For a given graph G let V(G) and E(G) denote the vertex and the edge set of G respevtively.The symbol G e → (a1, …, ar)means that in every r-coloring of E(G) there exists a monochromatic ai-clique of color i for some i ∈ {1,…,r}. The edge Folkman numbers are defined by the equalityFe(a1, …, ar; q) = min{|V(G)| : G e → (a1, …, ar; q) and cl(G) < q}.In this paper we prove a new upper bound on the edge Folkman number Fe(3,5;13), namelyFe(3,5;13) ≤ 21. This improves the bound Fe(3,5;13) ≤ 24, proved by Kolev and Nenov.<br/><br/>Description: 2000 Mathematics Subject Classification: 05C55.Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II
http://hdl.handle.net/10525/2626
Title: Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II<br/><br/>Authors: Komeda, Jiryo; Ohbuchi, Akira<br/><br/>Abstract: A 4-semigroup means a numerical semigroup whose minimum positive integer is 4. In [7] we showed that a 4-semigroup with some conditions is the Weierstrass semigroup of a ramification point on a double covering of a hyperelliptic curve. In this paper we prove that the above statement holds for every 4-semigroup.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials
http://hdl.handle.net/10525/2625
Title: Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials<br/><br/>Authors: Ezzaldine, Hayssam; Kostov, Vladimir Petrov<br/><br/>Abstract: In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs.<br/><br/>Description: 2000 Mathematics Subject Classification: 12D10.Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation
http://hdl.handle.net/10525/2624
Title: Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation<br/><br/>Authors: Dhagat, Vanita Ben; Sharma, Akshay<br/><br/>Abstract: The concept of semi compatibility is given in probabilistic metric space and it has been applied to prove the existence of unique common fixed point of four self-maps with weak compatibility satisfying an implicit relation. At the end we provide examples in support of the result.<br/><br/>Description: 2000 Mathematics Subject Classification: 54H25, 47H10.Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term
http://hdl.handle.net/10525/2623
Title: Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term<br/><br/>Authors: Hassan, Taher S.<br/><br/>Abstract: It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term(a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0,where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example.<br/><br/>Description: 2000 Mathematics Subject Classification: 34C10, 34C15.Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces
http://hdl.handle.net/10525/2622
Title: Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces<br/><br/>Authors: De Beule, J.; Metsch, K.; Klein, A.; Storme, L.<br/><br/>Abstract: We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces.<br/><br/>Description: 2000 Mathematics Subject Classification: 05B25, 51E20.