Following the work of Cline and Samorodnitsky (Stoch. Process. Their Appl. 49(1):75–98, 1994), we reexamine the subexponentiality of the product of two random variables, X and Y, which are independent and have distributions F and G, respectively. The main result is the following: If F belongs to the class A [that is to say, F is subexponential and lim supx→∞ F(vx)/F(x) < 1 holds for some v > 1]...

We find a full system of invariants with respect to gauge transformations L → g−1Lg for third-order hyperbolic linear partial differential operators on the plane. The operators are considered in a normalized form, in which they have the symbol SymL = (pX + qY )XY for some non-zero bivariate functions p and q. For this normalized form, explicit formulae are given. The paper generalizes a previou...

Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class L(γ ) or S(γ ) for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class L(0) or S(0) accordingly. Hence, the multiplier Y builds a bridge between ...

We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual " string hypothesis " incorrectly predicts the number of real solutions and the 1

It is conjectured that given positive integers l, m, n with l−1 + m−1 + n−1 < 1 and an integer g > 0, the triangle group ∆ = ∆(l,m, n) = 〈X,Y,Z|X l = Y m = Z = XY Z = 1〉 contains infinitely many subgroups of finite index and of genus g. A slightly stronger version of this conjecture is as follows: given positive integers l, m, n with l−1 + m−1 + n−1 < 1 and an integer g > 0, there are infinitel...

A domain in a Langmuir monolayer can be expected to have a shape that reflects the textural anisotropy of the material it contains. This paper explores the consequences of XY-like ordering. It is found that an extension of the Wulff construction allows for the calculation of two-dimensional domain shapes when each segment of the perimeter has an energy that depends both on its orientation and i...

This paper gives an overview of the NTCIR-5 Cross-Lingual Question Answering Task (CLQA1), an evaluation campaign for Cross-Lingual Question Answering technology. This evaluation was carried out in June 2005. In CLQA1, we aimed to promote research on cross-lingual Question Answering technology mainly for East Asian languages. As the first attempt, we conducted evaluations of five subtasks: JE, ...

We report the design, fabrication and electromechanical performance of a newly developed micro electromechanical XYscanner for micro-optical spatial light modulation using the silicon micromachining technology. A two-dimensional stage is integrated with a silicon micro lens to scan a transmitting infrared light of 1.55-micronwavelength by the mechanism of the f -θ lens scanner. Mechanical displ...

Although the classical dividend discount model (DDM) is a wellknown and widely used model in evaluating the intrinsic price of common stock, the practical pattern of dividends, required rate of return or growth rate of dividend do not generally coincide with any of the model’s assumptions. It is just the opportunity to develop a fuzzy logic system that takes these vague parameters into account....

We discuss the dynamics of the Ising model as a computational mesoscopic system. The simplicity of the Ising model allows a Hamiltonian dynamics to be developed from renormalization group theory considerations for the model which is not overly complicated and preserves a close connection with thermodynamics. At the same time, the additional structure gives the potential for application to neura...