Singular Measures and (1,p)-Capacity on Weighted Sobolev Classes

Conditions are studied under which the contribution of the singular part of a measure to the (1,p)-capacity of an arbitrary condenser is zero.     

A class of B-(p,r)-invex functions and mathematical programming

Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems.     

Ck（X）的扇密度和强Frechet性质

本文证明了如下两个定理：（１）Ｃ＿ｋ（Ｘ）为强Ｆｒｅｃｈｅｔ空间（或者Ｆｒｅｃｈｅｔ空间）的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝，存在Ｕ＿ｎ∈ｕ＿ｎ，使｛Ｕ＿ｎ：ｎ∈Ｎ｝为Ｘ的Ｋ－序列，（２）Ｃ＿ｋ（Ｘ）有可数扇密度的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝存在ｕ＿ｎ的有限于族ｕ＇＿ｎ，使｛ｕ＇＿ｎ：ｎ∈Ｎ｝是Ｘ的开Ｋ－覆盖．     

Eigenvalues of p(x)-Laplacian Dirichlet problem

This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem

     

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L^?-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.     

Lower bounds on mt(r, s)

Useful lower bounds are obtained for m_t(r, s), s a prime power, r ? t ? 3, by relating (t ? 1)-flats of PG(r ? 1, s) to (t ? 1) and lower dimensional flats of its subgeometries. Explicit expressions in general are obtained for these bounds when t = 3. A general method is developed for deriving these bounds when t > 3.     

Enumeration of (p,q)-parking functions

Parking functions are central in many aspects of combinatorics. We define in this communication a generalization of parking functions which we call (p₁,…,p_k)-parking functions. We give a characterization of them in terms of parking functions and we show that they can be interpreted as recurrent configurations in the sandpile model for some graphs. We also establish a correspondence with a Lukasiewicz language, which enables to enumerate (p₁,…,p_k)-parking functions as well as increasing ones.     

Lyapunov, Opial and Beesack inequalities for one-dimensional p(t)-Laplacian equations

We generalize the classical Lyapunov, Opial and Beesack inequalities for one-dimensional differential equations to nonstandard growth p(t)-Laplacian.     

Weak solution of (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0))u′(0) = ku(0), r(L, u(L))u′ (L) = hu(L) and k, h are suitable elements of [0, ∞]

We consider weak solutions to the nonlinear boundary value problem (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0)) u′(0) = ku(0), r(L, u(L)) u′(L) = hu(L) and k, h are suitable elements of [0, ∞]. In addition to studying some new boundary conditions, we also relax the constraints on r(x, u) and (Fu)(x). r(x, u) > 0 may have a countable set of jump discontinuities in u and r(x, u)^?1?L_q((0, L) × (0, p)). F is an operator from a suitable set of functions to a subset of L_p(0, L) which have nonnegative values. F includes, among others, examples of the form (Fu)(x) = (1 ? H(x ? x₀)) u(x₀), (Fu)(x) = ∫_x^Lf(y, u(y)) dy where f(y, u) may have a countable set of jump discontinuities in u or F may be chosen so that (Fu)′(x) = ? g(x, u(x)) u′(x) ? q(x) u(x) ? f(x, u(x)) where q is a distributional derivative of an L₂(0, L) function.     

Approximation of Surface Measures in a Locally Convex Space

The main result of the paper is an analog of the surface layer theorem for measures given on a locally convex space with a continuously and densely embedded Hilbert subspace (for a surface of finite codimension). Earlier, the surface layer theorem was proved only for Banach spaces: for surfaces of codimension 1 by Uglanov (1979) and for surfaces of an arbitrary finite codimension by Yakhlakov (1990). In these works, the definition of the surface layer and the proof of the theorem essentially use the fact that the original space is equipped with a norm.     

拟桶式空间的强对偶空间值的向量测度

证明了在某种紧性条件下拟桶式空间的强对偶空间值的向量测度的唯一存在性。     

Controlling setup cost in (Q, r, L) inventory model with defective items

This study discusses a mixture inventory model with back orders and lost sales in which the order quantity, reorder point, lead time and setup cost are decision variables. It is assumed that an arrival order lot may contain some defective items and the number of defective items is a random variable. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. Finally we develop two computational algorithms to obtain the optimal ordering policy. A computer code using the software Matlab is developed to derive the optimal solution and present numerical examples to illustrate the models. Additionally, sensitivity analysis is conducted with respect to the various system parameters.     

One-Dimensional Representations of U (p,q) and the Howe Correspondence

We explicitly determine the theta lifts of all one-dimensional representations of U (p,q) in terms of Langlands parameters, and determine exactly which lifts are unitary. Moreover, we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form A_q(λ). Finally, we show that the correspondence of unitary representations behaves well with respect to associated cycles.     

Generalized composition operators from F(p, q, s) spaces to Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the unit ball B of Cⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator

     

Continuity of Sobolev Functions and Dirichletg Finite Harmonic Measures

We investigate the existence of finely continuous Sobolev functions u which have traces equal to the characteristic function of a bounded set E . As an application we examine the existence of Dirichlet finite p-harmonic measures on the unit ball of R ⁿ.     

Composition operators from F(p, q, s) spaces to the nth weighted-type spaces on the unit disc

In this note we characterize the boundedness and compactness of the composition operator from the general function space F(p, q, s) to the nth weighted-type space on the unit disk, where the nth weighted-type space has been recently introduced by Stevo Stevi?.