`=1 ∫ |x|>ε |x| μn`(dx) = 0 for all ε > 0, where x 7→ |x| denotes a fixed homogeneous norm on the Heisenberg group. Professor E. Siebert suggested a way to prove similar results for a Lie group G. The main step is the generalization of Lemma 1 in Pap [4] for an arbitrary Lie group G, which gives an estimation for the Fourier transform of a probability measure on G in terms of integrals of local...

where the equations a0x+ b0y + c0 = 0 and a1x+ b1y + c1 = 0 define any two distinct lines. It is known that any conic section can be “generated by the intersection of corresponding lines of two related pencils in a plane” [Som51], p.388. In other words, given two distinct pencils, (a00x+b00y+c00)(1−t)+(a10x+b10y+c10)t = 0 and (a01x+b01y+c01)(1−t)+(a11x+b11y+c11)t = 0, to each value of t corresp...

f (0) = 0, f (0) = 1 and zf (z) f ′(z) ≺ τ z + 2τ 2z2 1 − τ z − τ 2z2 (z ∈ ∆), where, the number τ = (1− √ 5)/2 is such that |τ | fulfils the golden section of the segment [0, 1]. Some relevant remarks and useful connections of the main results are also pointed out. © 2011 Elsevier Ltd. All rights reserved.

where the equations a0x+ b0y + c0 = 0 and a1x+ b1y + c1 = 0 define any two distinct lines. It is known that any conic section can be “generated by the intersection of corresponding lines of two related pencils in a plane” [Som51], p.388. In other words, given two distinct pencils, (a00x+b00y+c00)(1−t)+(a10x+b10y+c10)t = 0 and (a01x+b01y+c01)(1−t)+(a11x+b11y+c11)t = 0, to each value of t corresp...

1. I N T R O D U C T I O N This paper discusses the existence of one (or indeed more) solutions to singular integral equations of the form y(t) = O(t) + k(t, s)[g(y(s)) + h(y(s))] ds, for t ~ [0, 1]; (1.1) here our nonlinearity g + h may be singular at y = 0. In [1], we established the existence of one nonnegative solution to (1.1) using the Leray-Schauder alternative. However, in [1], we had t...

and Applied Analysis 3 For the case λ 0, we consider general bounded Radon measure μ which is independent of time. We provide the uniqueness of approximated solutions for the parabolic problem and its corresponding elliptic problem. Then we prove that the approximated solution of the parabolic equations converges to the unique approximated solution of the corresponding elliptic equations in the...

Let (Xij: i > 0, i > 0} be a double sequence of independently, identically distributed random variables (i.i.d.) which takes values in the d-dimensional integer lattice Ed . The double sequence {Sm,,: m > 0, n > 0} defined by Sllan= xy=, zyW, Xgj is called the random walk in two-dimensional time generated by 41, or a two-parameter random walk, or simply a random walk when there is no danger of ...

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

LetG be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny τ : b G → G is bijective. In particular, f...

and Applied Analysis 3 when ω 1 and δ 0, 1.4 reduces to the probability of ruin ψi u P T < ∞ | J 0 i,U 0 u , u ≥ 0. 1.6 The purpose of this paper is to present some numerical results on the GerberShiu function for the Markov-modulated diffusion risk model with arbitrary upward and downward jumps. In Section 2 we derive a system of integrodifferential equations and approximate solutions for φi u...