Toward the Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve

This is a first step toward the determination of the parameters of two-point codes on a Hermitian curve. We describe the dimension of such codes and determine the minimum distance of some two-point codes.AMS Classification: 94B27, 14H50, 11T71, 11G20Masaaki Homma - Partially supported by Grant-in-Aid for Scientific Research (15500017), JSPS.Seon Jeong Kim - Partially supported by Korea Research Foundation Grant (KRF-2002-041-C00010).     

Bruhat Order for Two Flags and a Line

The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a linear space V under linear transformations of V; or equivalently, it describes the closure of an orbit of GL(V acting diagonally on the product of two flag varieties.We consider the degenerations of a triple consisting of two flags and a line, or equivalently the closure of an orbit of GL(V) acting diagonally on the product of two flag varieties and a projective space. We give a simple rank criterion to decide whether one triple can degenerate to another. We also classify the minimal degenerations, which involve not only reflections (i.e., transpositions) in the Weyl group S_VSn = dim(V, but also cycles of arbitrary length. Our proofs use only elementary linear algebra and combinatorics.     

体模型的一种细分格式

In this paper, a subdivision scheme which generalizes a surface scheme in previous papers to volume meshes is designed. The scheme exhibits significant control over shrink-age/size of volumetric models. It also has the ability to conveniently incorporate boundaries and creases into a smooth limit shape of models. The method presented here is much simpler and easier as compared to MacCracken and Joy‘s. This method makes no restrictions on the local topology of meshes. Particularly, it can be applied without any change to meshes of nonmanifold topology.     

Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails

Recently, Tang established a local asymptotic relation for the ruin probability in the Cramer-Lundberg risk model. In this short note we extend the corresponding result to the equilibrium renewal risk model.     

S-polar sets of super-brownian motions and solutions of nonlinear differential equations

This paper gives probabilistic expressions of the minimal and maximal positive solutions of the partial differential equation -1/2△v(x) γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 < α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.     

Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

Geometric Integration Methods that Preserve Lyapunov Functions

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function. AMS subject classification (2000) 65L05, 65L06, 65L20, 65P40     

Weighted BMO and discrete time hedging within the Black-Scholes model

The paper combines two objects rather different at first glance: spaces of stochastic processes having weighted bounded mean oscillation (weighted BMO) and the approximation of certain stochastic integrals, driven by the geometric Brownian motion, by integrals over piece-wise constant integrands. The consideration of the approximation error with respect to weighted BMO implies L_p and uniform distributional estimates for the approximation error by a John-Nirenberg type theorem. The general results about weighted BMO are given in the first part of the paper and applied to our approximation problem in the second one.     

Commutators of integral operators with variable kernels on Hardy spaces

LetT _Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, T_Ω,α] be the commutator generated by T_Ω,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, T_Ω,α] on the Hardy spaces, under some assumptions such as theL ^r -Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators . The smoothness conditions imposed on are weaker than the corresponding known results.     

<Emphasis Type="Italic">p</Emphasis>-Laplace Operator and Diameter of Manifolds

Let be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian and we prove that the limit of when is 2/d(M), where d(M) is the diameter of M. Moreover, if is an oriented compact hypersurface of the Euclidean space or , we prove an upper bound of in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of then: . Mathematics Subject Classifications (2000): 53A07, 53C21.