Given a monotone graphical property Q, how large should d(n) be to ensure that if (Hn) is any sequence of graphs satisfying |Hn| = n and (Hn)¿d(n), then almost every induced subgraph of Hn has property Q? We prove essentially best possible results for the following monotone properties: (i) k-connected for :xed k, (ii) Hamiltonian. c © 2002 Elsevier Science B.V. All rights reserved.

A dualMarkov branching process (DMBP) is by definition a Siegmund’s predual of some Markov branching process (MBP). Such a process does exist and is uniquely determined by the so-called dual-branching property. Its q-matrix Q is derived and proved to be regular and monotone. Several equivalent definitions for a DMBP are given. The criteria for transience, positive recurrence, strong ergodicity,...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

Stirling numbers of second kind S(n,k) denotes the number ways partitioning a set n elements into k nonempty sets. There are many types stirling which studied up to now. In this study, we use extended defined for arbitrary reals. First, define relation between and q-B-splines by using property that divided differences have representation with q-B-splines. addition, derive identities on q-integr...

A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott’s Theorem, which has many Diophantine applications, states that sets of bounded degree have the Northcott property. Bombieri, Dvornicich and Zannier raised the problem of finding fields of infinite degree with this property. Bombieri and Zannier have shown that Q ab , the max...

An ovoid of PG(3, q) can be defined as a set of q + 1 points with the property that every three points span a plane and at every point there is a unique tangent plane. In 2000 M. R. Brown ([5]) proved that if an ovoid of PG(3, q), q even, contains a pointed conic, then either q = 4 and the ovoid is an elliptic quadric, or q = 8 and the ovoid is a Tits ovoid. Generalising the definition of an ov...

in which the front square is a pull-back. Then P is often called the fibre-product o f f and p, and it is also said that ~: P ~ X is induced by f from p. The map ~: Q~ P is determined by ~01 and q)2. Our object is to give conditions on the front and back squares which ensure that if q~l, q~2 and ~o are homotopy equivalences, then so also is ~. First of all we shall assume throughout that the ba...

We introduce several q-differential equations of higher order which are related to q-Bernoulli polynomials and obtain a symmetric property in this paper. By giving q-varying variations, we identify the shape approximate roots polynomials, solution order, find conjectures associated with them. Furthermore, based on create Mandelbrot set Julia variety figures.

A word w over a finite alphabet Σ is n-collapsing if for an arbitrary deterministic finite automaton A = 〈Q,Σ, δ〉, the inequality |δ(Q,w)| ≤ |Q| − n holds provided that |δ(Q, u)| ≤ |Q| − n for some word u ∈ Σ (depending on A ). We prove that the the property of being n-collapsing is algorithmically recognizable for any given positive integer n. We also prove that the language of all n-collapsin...

Introduction. Diophantus noted that the rational numbers 1/16, 33/16, 17/4 and 105/16 have the following property: the product of any two of them increased by 1 is a square of a rational number (see [2, 3]). Let n be an integer. A set of positive integers {a1, a2, . . . , am} is said to have the property D(n) if aiaj + n is a perfect square for all 1 ≤ i < j ≤ m. Such a set is called a Diophant...