ON L^p-MATRICIALLY NORMED SPACES

It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Space of Operators and Property (MB)

In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.

Prototype of a large neutron detector based on MWPC

A prototype of large-area position sensitive neutron detector was designed and constructed according to the requirements of the Small-Angle Scattering spectrometer of China Spallation Neutron Source(CSNS).The detector was based on the 3He neutron convertor and MWPC with an effective area of 650 mm×650 mm.A prototype was completed and tested with 55Fe X-ray.The high-pressure vessel was designed and constructed with high-strength aluminum alloy.A position resolution of about 4.6mm×2.3 mm(FWHM)and efficiency>65%for neutrons with wavelength of 1.8?was determined after the operational gas filled.

EXISTENCE OF NON-TRIVIAL SOLUTION FOR SUPERLINEAR SYSTEM OF INTEGRAL EQUATIONS AND ITS APPLICATIONS

In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.

BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE

In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.