假设检验的偏好性

根据假设检验的基本原理 ,给出 3种单侧假设检验在相同的显著性水平下具有相同的拒绝域 ,并指出在实际应用中如何选择原假设和备择假设及其相互关系 .     

一类半线性椭圆型方程Dirichlet问题解的存在性与非存在性

讨论边界数据与解存在性的关系，并利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ度论估计解的个数     

The stability of a cubic type functional equation with the fixed point alternative

In this note we investigate the generalized Hyers-Ulam-Rassias stability for the new cubic type functional equation f(x+y+2z)+f(x+y−2z)+f(2x)+f(2y)=2[f(x+y)+2f(x+z)+2f(x−z)+2f(y+z)+2f(y−z)] by using the fixed point alternative. The first systematic study of fixed point theorems in nonlinear analysis is due to G. Isac and Th.M. Rassias [Internat. J. Math. Math. Sci. 19 (1996) 219-228].     

Fixed-point theorems for S-KKM maps

A number of new fixed-point results are presented for S-KKM self maps. Also the notion of essentiality for S-KKM maps is introduced.     

Theorems of the Alternative over Indefinite Inner Product Spaces

In this paper, we study the Farkas alternative over indefinite inner product spaces using the recently proposed indefinite matrix product.     

Analyse asymptotique des équations de Transport dans le cas d’évolution

Nous démontrons la convergence de la solution d’une équation de Transport vers la solution d’une équation de Diffusion quand Je libre parcours moyen tend vers zéro, pour des équations d’évolution et un domaine borné dans deux cas: flux incident nul et réflexion spéculaire.     

Alternative splicing and expression of the insulin-like growth factor （IGF-1） gene in osteoblasts under mechanical stretch

Insulin-like growth factor 1 (IGF-1) promotes osteoblasts differentiation and bone formation, and its expression is induced by mechanical stretch, thus IGF-1 has been considered an effector molecule that links mechanical stimulation and local tissue responses. In this study, a mechanical stretching device was designed to apply physiological level static or cyclic stretching stimulation to osteoblasts. Different isoforms of IGF-1 mRNA were amplified by RT-PCR from the cells using respective primers and these amplified products were sequenced. An iso-form of IGF-1 splicing product was found to be selectively produced by osteoblasts under stretching stimulation. This IGF-1 isoform had identical sequence with the mechano growth factor (MGF) which was originally identified in muscle cells. Regulations of the expression of the liver-type IGF (L.IGF-1) and MGF in osteoblasts under stretch stimulation were further studied using semi-quantitative RT-PCR. Stretch stimulation was found to promot the expression of IGF-1 (L.IGF-1 and MGF), and for both isoforms expression was more effectively stimulated by cyclic stretch than static stretch. MGF was detected only in osteoblasts subjected to mechanical stretch, suggesting MGF was a stretch sensitive growth factor. Expression of MGF peaked earlier than that of L.IGF-1, which was similar to their regulation in muscle and suggested similar roles of MGF and L.IGF-1 in bone as in muscle cells. The functions of MGF and LIGF-1 in osteoblasts shall be established by further experimental studies.     

Billiards in rational polygons: Periodic trajectories, symmetries, and d-stability

Periodic trajectories of billiards in rational polygons satisfying the Veech alternative, in particular, in right triangles with an acute angle of the form π/n with integern are considered. The properties under investigation include: symmetry of periodic trajectories, asymptotics of the number of trajectories whose length does not exceed a certain value, stability of periodic billiard trajectories under small deformations of the polygon. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 66–75, July, 1997. Translated by V. N. Dubrovsky     

The range of the p-Laplacian

We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L²(0,1) such that the problem

− (|u′|^p−2 u′)′ − λ|u|^p−2u = f, in (0,1)

, subject to certain separated boundary conditions on (0,1), has a solution for f B.