Some recent results on the distribution of zeros of real entire functions are surveyed.

We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.

In this paper we first introduce a space of homogeneous type X, and we consider a kind of generalized upper half-space X (0, ). We are mainly concerned with some inequalities in terms of Carleson measures or in terms of certain maximal operators with respect to general approach regions in X (0, ). The main tool of the proof is the Whitney decomposition.

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowzC, t[0, 1) defined by the equation z = tT(z)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

Suppose { } sequence of finite dimensional Banach spaces and suppose that X is either a closed subspace of (equation omitted) or a closed subspace of (equation omitted) with p>2. We show that every bounded linear operator from X to a Banach space Y of cotype q(2q〈p) is compact.t.t.

We study a unifying method to obtain nondegenerate isometric immersions of manifolds of constant sectional curvatures c with flat normal bundles into the space forms of curvature c for c= -1,0,1.

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R . The approach is global in the sense that the objects are Radon measures on R and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

We consider the Hausdorff measure for Brownian motion(BM) in ι. Several path properties of BM in ι are used to show the upper bound of Hausdorff measure. We also show the lower bound of it applying a law of iterated logarithm for the occupation time of BM in ι.

A central limit theorem is obtained for a stationary multivariate linear process of the form (equation omitted), where { } is a sequence of strictly stationary m-dimensional associated random vectors with E = O and E∥ ∥ < and { } is a sequence of coefficient matrices with (equation omitted) and (equation omitted).ted)..ted).).

A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

Null designs form a vector space and there are only finite number of minimal null designs(up to scalar multiple), hence it is natural to look at the convex polytopes of minimal null designs. For example, when t = 0, k = 1, the convex polytope of minimal null designs is the polytope of roofs of type An. In this article, we look at the convex polytopes of minimal null designs and find many general properties on the vertices, edges, dimension, and some structural properties that might help to understand the structure of polytopes for big n, t through the structure of smaller n, t.

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.

The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.