Properties of Some Families of Meromorphic Multivalent Functions Associated with Generalized Hypergeometric Functions

We introduce and study two subclasses ?_([α_1])(A, B, λ) and ?_([α_1])~+ (A, B, λ) of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ?_([α_1])~+(α, β, γ, λ).     

Some subclasses of multivalent functions involving a certain linear operator

The authors investigate various inclusion and other properties of several subclasses of the class Ap of normalized p-valent analytic functions in the open unit disk, which are defined here by means of a certain linear operator. Problems involving generalized neighborhoods of analytic functions in the class Ap are investigated. Finally, some applications of fractional calculus operators are considered.     

Best Local Approximation in Orlicz Spaces

We get results in Orlicz spaces L ^φ about best local approximation on non-balanced neighborhoods when φ satisfies a certain asymptotic condition. This fact generalizes known previous results in L ^p spaces.     

New relationships for multi-neighborhood search for the minimum linear arrangement problem

We develop a series of theorems about the graph structure of the classical Minimum Linear Arrangement (MinLA) problem which disclose properties that can be exploited by Multi-Neighborhood Search (MNS) algorithms. As a foundation, we differentiate between swaps of labels attached to adjacent and non-adjacent nodes to create two new neighborhood classes, and show how our theorems yield efficient algorithms for updating key arrays used by local search procedures. In addition, we introduce a class of neighborhoods called set-based neighborhoods supported by a theorem that identifies solutions (labelings) for the MinLA problem in polynomial time that dominate exponential numbers of alternative solutions. The component neighborhoods within this new neighborhood class can be applied in various sequences in conjunction with the first two new neighborhoods introduced. Our results also apply to problems with objectives different than those of MinLA. Finally, our results make it possible to exploit the new neighborhoods according to the user's choice of MNS protocols and alternative local search algorithms.     

Quadruple systems with independent neighborhoods

A 4-graph is odd if its vertex set can be partitioned into two sets so that every edge intersects both parts in an odd number of points. Let

     

Local Gaussian Process Approximation for Large Computer Experiments

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, providing a nonstationary modeling feature as a bonus. We demonstrate our method on two examples using designs with thousands of data points, and compare to the method of compactly supported covariances. Supplementary materials for this article are available online.     

LF拓扑空间的Es-紧性

利用α-E_s远域族在LF拓扑空间中引进了E_s-紧性的概念,得到了E_s-紧空间.此外,给出了E_s-紧空间的3种等价刻画,证明了E_s-紧性是L-好的推广,讨论了E_s-紧性的一些基本性质,如:E_s闭遗传性和弱E_s同胚不变性.