Cyclic weak φ-contraction mapping is introduced in Menger space and fixed point theorem for such mappings are studied in Menger space. Mathematics Subject Classification 47H10, 54H25

Recent studies in mammals have documented the neural expression and mobility of retrotransposons and have suggested that neural genomes are diverse mosaics. We found that transposition occurs among memory-relevant neurons in the Drosophila brain. Cell type-specific gene expression profiling revealed that transposon expression is more abundant in mushroom body (MB) αβ neurons than in neighboring...

The lysosomal storage disorder mucolipidosis III αβ is caused by mutations in the αβ subunits of UDP-GlcNAc:lysosomal enzyme N-acetylglucosamine-1-phosphotransferase (phosphotransferase). This Golgi-localized enzyme mediates the first step in the synthesis of the mannose 6-phosphate recognition marker on lysosomal acid hydrolases, and loss of function results in impaired lysosomal targeting of ...

BLK, which encodes B lymphoid kinase, was recently identified in genome wide association studies as a susceptibility gene for systemic lupus erythematosus (SLE), and risk alleles mapping to the BLK locus result in reduced gene expression. To determine whether BLK is indeed a bona fide susceptibility gene, we developed an experimental mouse model, namely the Blk+/-.lpr/lpr (Blk+/-.lpr) mouse, in...

Dedicated to Louis Nirenberg with admiration and friendship In this talk I describe some recent joint work with Louis. Please see [8] for details. Let D be a bounded domain in R n. For positive constants 0 < λ ≤ Λ < ∞, let A(λ, Λ) denote the class of measurable coefficients {A αβ ij (x)}, 1 ≤ α, β ≤ n, 1 ≤ i, j ≤ N, which satisfy |A αβ ij (x)| ≤ Λ ∀ α, β, i, j, and x ∈ D, (1) and D

The Multi-model search framework generalizes minimax to allow exploitation of recursive opponent models. In this work we consider adding pruning to the multi-model search. We prove a sufficient condition that enables pruning and describe two pruning algorithms, αβ∗ and αβ∗ 1p. We prove correctness and optimality of the algorithms and provide an experimental study of their pruning power. We show...

We establish some second order necessary conditions for optimal control problems of evolution equations involving final point equality and inequality constraints. Compared with the existing works, main difference is due to presence end-point With such constraints, we cannot simply use variational techniques since perturbations a given may be no longer admissible. also Ekeland’s principle, which...

This paper introduces the idea of pre-searching a position—searching it before αβ determines that it needs to be searched. Consider the case where an iteration of αβ search comes across a position p that needs to be searched to depth d1, and the transposition table reveals that p will likely need to be searched later in that iteration to depth d2 greater than d1. Pre-searching involves speculat...

We introduce methods for identifying operator preconditions that need not be expanded further. The methods are proved to be admissible , that is, they will not cause a solution to be missed when one exists. In certain cases, the methods also identify operator reformulations that increase the number of nonexpandable preconditions. This approach provides effective loop control in common situation...

In [4] we introduced a product construction for cyclic Steiner quadruple systems. The purpose of this paper is to modify the construction so that it is applicable to cyclic Steiner 2-designs. A cyclic Steiner 2-design is a Steiner system s(t, k, u), 2 d t < k < u, in which t = 2 and which has an automorphism of order u. We denote such a system by CS(2, k, u). Under suitable conditions we show h...