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In this paper, we introduce a notion of weak $% \mathcal{MT}$-cyclic Kannan contractions with respect to a $\mathcal{MT}$% -function $\varphi$ and then we shall prove some new convergent and existence theorems of best proximity point theorems for these contractions in uniformly Banach spaces.

In the recent developments of fixed point theorems is proving the existence of fixed points on partially ordered metric spaces [20, 23], a generalization of the Banach contraction principle for an integral-type inequality [2, 10, 21], and even some applications to matrix equations and ordinary differential equations. In this paper, we want to illustrate some new fixed point theorems for generalized distances with τ -function in the partially ordered metric space rather than w-distance [23]. In short, we would like to utilize τ -function to provide the existence of fixed points on partially ordered metric spaces which is our goal.

This article describes an object-oriented implementation of the finite element method and the finite volume method in a unified adaptive system using the programming language C++. The system applies to various types of mathematical model problems. Traditionally, different numerical methods for different types of problems are implemented independently by procedural languages such as C and Fortran. Moreover, adaptive analysis programs are more complicated than nonadaptive programs. Nevertheless, these methods share many common properties such as linear system solvers, data structures, a posteriori error analyses, and refinement processes. Some advantageous features of object-oriented programming are demonstrated through the integration of these properties in the adaptive system. New data types of objects specific to adaptive methods are also introduced. The system is well-structured, extendable, and maintainable due mainly to the nature of encapsulation and inheritance of object-oriented programming.

A factorization theorem is proved in the Hardy spaces H p H^p of the bi-upper half plane, 0 > p ≤ 1 0>p\le 1 . The proof is based on some fundamental work of Chang-Fefferman on atomic decompositions of H p H^p .

In this paper, we first establish some new existence theorems of coincidence points and common fixed points for MT Open image in new window-functions. By applying our results, we obtain some generalizations of Mizoguchi-Takahashi’s fixed point theorem, Nadler’s fixed point theorem and the Banach contraction principle. Some examples illustrating our results are also given. Our results generalize and improve some main results in the literature and references therein.

For a tvs-G-cone metric space $(X,G)$ and for the family $\mathrm{\scr A}$ of subsets of X, we introduce a new notion of the tvs-ℋ -cone metric ℋ with respect to G, and we get a fixed result for the $\mathrm{\scr C}\scr B\mathrm{\scr W}$ -tvs-G-cone-type function in a complete tvs-G-cone metric space $(\mathrm{\scr A},\scr H)$ . Our results generalize some recent results in the literature.

A BSE-MHA (Back-Side Exposure Multi-domain. We developed a new design to improve optical performance. The optical transmittance was improved by newly introduced Superimposed Spacing Wall-Bump (SSWB) structure to freeze the disclination lines. The transmittance improvement effect is measured to be 20%, more than 70% of TN-LCD, in typical. The SSWB type BSE-MHA also makes the spacers spraying process unnecessary by the Superimposed Spacing Method (SSM). Homeotropically Aligned) TFT-LCD panel has been demonstrated in 1999. It has excellent high performance and been manufacturing without rubbing and polymer stabilized process. However, the light efficiency of BSE-MHA LCD is only 60% of TN (Twisted Nematic)-LCD

We have studied the influences of monomers on polymer stabilized homeotropically aligned (PSHA) liquid crystal displays (LCD). PSHA-LCD is formed by mixing a small amount of monomers into nematic liquid crystal with negative dielectric anisotropy, then photo-polymerizing the mixtures. The voltage holding ratio (VHR) and the DC offset voltage of PSHA-LCD have been measured for studying the effect of photo-polymerized monomers on PSHA-LCD. We demonstrate the measurement method as well as the results.

An adaptive least finite element method is presented for Navier-Stokes equations which are cast into a first order velocity-vorticity-pressure form. The least square formulation results in positive definite systems of algebraic equations, accurate approximation of the vorticity, flexible elements for all state variables, and very effective error estimation in adaptive computation. The adaptive method is also highly parallel in the sense that the assembly of global matrix is not required and that the error estimation is completely localized without any communication traffics across neighboring elements.

A novel method to realize the good performance of transflective LCD is indicated. In one pixel, two LTPS (Low-temperature poly-Si) TFT devices control the optical intensity of the transmissive and reflective regions respectively. We call this way as double gamma method (DGM). Uni-gap transflective LCD attached the DGM will have both merits of simplifying processes and good legibility. Meanwhile, we show the experimental results of optical characteristics with uni-gap homeotropic panel design. It obviously shows that high contrast ratio and wide viewing angle have been achieved.

The split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present a descent-conjugate gradient algorithm for the split variational inclusion problems in Hilbert spaces. Next, a strong convergence theorem of the proposed algorithm is proved under suitable conditions. As an application, we give a new strong convergence theorem for the split feasibility problem in Hilbert spaces. Finally, we give numerical results for split variational inclusion problems to demonstrate the efficiency of the proposed algorithm.

In this paper, we introduce the notions of soft Meir-Keeler contractive mappings and weaker ϕ-Meir-Keeler contractive mappings, and the purpose of this paper is to prove two theorems which assures the existence of fixed points for these two soft Meir-Keeler type contractive mappings on a soft metric space. Our results generalize and improve many recent fixed point results in the literature.

In this paper, we first establish some new fixed point theorems for M T -functions. By using these results, we can obtain some generalizations of Kannan's fixed point theorem and Chatterjea's fixed point theorem for nonlinear multivalued contractive maps in complete metric spaces. Our results generalize and improve some main results in the literature and references therein. Mathematics Subject Classifications 47H10; 54H25