ON UNIFORM CONVERGENCE OF LINEAR OPERATORS ON THE PROBABILISTIC NORMED SPACE

In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.

Quantum Wormholes with Nonminimal Coupling

A Robertson-Walker geometry with nonnuniinal coupled scalar Held has been quantized by the ca.nonical formulation fdz constrained Ha,iniltonia.n systems.The exact solutions have been found for corresponding Wheeler-DeWitt equation.These so-lutions sa.tisfy the needs of Hawkingboundary condition for the wormhole wave function.Thus they can provide a quantuni-mechanical description of wormholes in a theory with a nonminimal coupled scalar field.The characteristic scale of the ground state of the worinhole is of the order of Planck length.

Tunneling Wave Function with Induced Gravity

A Tunneling wave function of the universe with induced gravity in the WKB approximation is discussed and using Vilenkin’s boundary condition we obtain the probability density for the scale factor a at a given value of the scalar field.It is shown that when the universe spontaneously nucleates,the minimum value of the scale factor of the classical universe is of the order of Planck length.

Multiple Production of Bianchi Type-I Universes

The procedure similar to an ordinary quantum held theory in curved spacetime is applied to study the Bianchi type-I universes with a radiation field source.The Wheeler-De Witt equation satisfied by the cosmological wave function is found.After the wave function was regarded as a universe held in the minisuperspace,not only the difficulty in a probabilistic interpretation in the quantum cosmology can be circumvented,but also the conclusion of the multiple production of universes is obtained,and the average number of various universes created from‘nothing’is estimated.

The Educational Differences between China and America

Nowadays, with the fast development of science and technology in China, there is an increasing number of people going to study abroad (taking America as an example). For one hand, they want to get a better educational background to have a more promising career in the future. For the other, they want to change the way of getting knowledge, because they think the Chinese educational system still has a lot to be improved. With such tendency, more people are looking forward to an article that has a thorough analysis to reveal the educational differences between China and America from couple of aspects. It elaborates the educational differences in many ways with authentic research then comes to an analytic conclusion on what we can do to make a contribution to the Chinese educational system as a graduate student.

MATHEMATICAL ANALYSIS OF THE COLLAPSE IN BOSE-EINSTEIN CONDENSATE

In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrdinger equation iψt + 1/2 △ψ - 1/2 ω2|x|2ψ + |ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T . Furthermore, the L2-concentration property of the radially symmetric collapse solutions is obtained.

Influence of electron screening on electron capture rate under high density of stellar interior

The influence of electron screening on electron capture rate in strong screening is investigated, in which the Gamow-Teller resonance transition is considered and the matrix elements for the resonance transition are calculated on the basis of a shell model. The effect of electron screening on electron capture by 56Co is discussed. It is shown that the screening decreases evidently the capture rates in lower temperature and higher density. The effect of electron screening on other nuclear capture rates is estimated. The conclusion derived may influence the research for late stellar evolution and supernova explosion.

Guo Moruo’s Early Esthetics and Western Romanticism

is an initial study of the influence of Western romanti- cism on Guo Moruo’s early esthetic views.Wang and Luo believe that Guo Moruo atthat time from his philosophical perspective on to his literary and artistic opinionswas under the influence of the romantic ideas of such Western poets as Shelley,Goethe,Whitman,Wordsworth and Coleridge,and these laid the foundation for hisearly esthetic views.The literary and artistic theories of such estheticians of thelate nineteenth and early twentieth century as Croce,Bergson,Nietzsche,Freud,Paterand Oscar Wilde as well as Western symbolists and expressionists also had some im-pact on Guo Moruo’s early views.However,since Guo Moruo assimilated theirtheories from his own romantic esthetic perspective,even though their influence addedsome different factors to his early esthetic views,they did not effect any qualitativechange in them.

HD 93044 IS A NEW δ SCUTI VARIABLE

Using the 60 cm reflector of Beijing Observatory at Xinglong Station and its receiving system working on DC mode, we took differential photometric measurements for five stars of HD 93044 (SAO 043461 ), HD 92370 (SAO 043428), HD 92221 (SAO 043420), HD 93457 (SAO 043475 )and HD 93664 (SAO 043482 )for two nights on April 8 and 9,

THE FIXED POINT AND EIGENVALUES OF NONLINEAR OPERATOR

I. INTRODUCTION Let E be a Banach space, and P be a cone in E, P_R={x∈P|‖x‖<R}, P_R={x∈P|‖x‖=R}, u∈P\{θ}, P(u)= {x∈P|αx≥u, for some positive number α}. After Krasnosel’skii et al. studied the compression of the cone theorem, their result consists of the following.

ON LIMIT CYCLES FOR A CLASS OF E_3

q=r=s=O, etc., System (1) becomes van der Pol’s equation. The singular points of System (1) in bounded region are: (0,0) being focus, stable or unstable according to-2<a<0 or O<a<2;