罗尔中值定理的一些新证法(英文)

给出了罗尔微分中值定理的三种新的证明方法,其中第二种很简便的方法仅依赖于大家熟知的Heine-Borel有限覆盖定理.由此可见罗尔微分中值定理可以是实数的完备性的直接推论.     

Sequential Completeness of LF-Spaces

Any LF-space is sequentially complete iff it is regular.     

The completeness of the sines and cosines in the space of integrable functions

The paper addresses the completeness of sines and cosines with non-integer indices in the space of Lebesgue-integrable functions. The criteria for the variation from the integer value have been found such that sine and cosine systems are complete.     

软土地区人工冻土无侧限瞬时抗压强度的试验研究

冻结法施工在上海隧道建设中(如隧道旁通道、地下泵房等的设计与施工)得到广泛应用,也曾引发过严重的地质灾害(如上海地铁4号线外滩段的地质灾害)。因此安全、经济、合理地将冻结法用于上海软土地区隧道建设中已经成为上海工程建设中的一个重要的研究课题。本文以上海复兴东路越江隧道旁通道冻结法施工中遇到的第⑥层粉质粘土及第⑦层粉细砂为研究对象,针对设计冻结壁重要强度参数无侧限瞬时抗压强度,进行了室内试验研究,揭示了两种土的冻结强度随温度的变化关系,同时研究了粉细砂的冻结强度随含水率的变化规律。     

Determining Asymptotic Behavior from the Dynamics on Attracting Sets

Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to another. A sufficient condition for asymptotic completeness of invariant exponential attractors is found, obtaining similar results as in the theory of inertial manifolds. Furthermore, such sets are shown to be retracts of the phase space, which implies that they are simply connected.     

On a class of difference sequences related to the ℓ<Superscript>p</Superscript> space defined by Orlicz functions

In this article we introduce the difference sequence space m(M, Δ, φ) using the Orlicz function. We study its different properties like solidity, completeness etc. Also we obtain some inclusion relations involving the space m(M, Δ, φ).      

An extension of Ekeland's variational principle to locally complete spaces

We prove an extension of Ekeland's variational principle to locally complete spaces which uses subadditive, strictly increasing continuous functions as perturbations.     

The Basis Properties of Power Systems in L p

We consider power systems with complex-valued coeficients. We establish a necessary and suficient condition for completeness and minimality and also a necessary condition for the basis property of these systems in Lebesgue spaces.     

Cocompact CAT(0) spaces are almost geodesically complete

We prove that, under mild conditions, a cocompact CAT(0) space is almost geodesically complete.     

A comparative post-Hartree–Fock and density functional theory study of monochalcogenide diatomic molecules

HOMO and LUMO (FMOs) play important role in the optical properties of meridianal isomer of tris(8-hydroxyquinolino)aluminum (mer-Alq3) and its derivatives. The frontier molecular orbitals (FMOs) also play a vital role in the process of charge transport. It is urgent to find the reason of FMO distribution pattern among the ligands. The structures of mer-Alq3 and its “CH”/N substituted derivatives have been optimized at the B3LYP/6-31G^* level. Energy decomposition analysis has been performed at the B3LYP/DZP level. The results of energy-partitioning analysis of ground states are discussed. It has been explained that HOMOs are on A-ligands due to weaker electrostatic interaction energy between L_a-AlL_bL_c fragments while LUMOs are on B-ligands due to weaker orbital interaction energy between L_b-AlL_aL_c fragments.