Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

Nitroxyl free radical binding to Si(1 0 0): a combined scanning tunneling microscopy and computational modeling study

The ultra-high vacuum scanning tunneling microscope (UHV-STM) was used to investigate the addition of the 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) radical to the Si(1 0 0) surface. Room temperature studies performed on clean Si(1 0 0)-2 × 1 confirm the proposed binding of the unpaired valence electron associated with the singly occupied molecular orbital (SOMO) of the molecule with a Si dangling bond. A strong bias dependence in the topography of isolated molecules was observed in the range of −2.0 to +2.5 V. Semiempirical and density functional calculations of TEMPO bound to a three-dimer silicon cluster model yield occupied state density isosurfaces below the highest occupied (HOMO) and unoccupied state densities isosurfaces above the lowest unoccupied molecular orbital (LUMO) which trend in qualitative agreement with the bias dependent STM topography. Furthermore, the placement of TEMPO molecules on dangling bonds was controlled with atomic precision on the monohydride Si(1 0 0) surface via electron stimulated desorption of H, demonstrating the compatibility of nitroxyl free radical binding chemistries with nanopatterning techniques such as feedback controlled lithography.     

关于(QU)型模糊拓扑群的直积

研究(QU)型模糊拓扑群族直积,证明了任意(QU)型模糊拓扑群族的直积仍是(QU)型模糊拓扑群;研究了(QU)型模糊拓扑群族直积的模糊单位元之重域基的结构,得到了(QU)型模糊拓扑群族直积的一些重要性质.     

Hermitian阵的 Hadamard积的Schur补的一些不等式（英文）

本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式，进而，给出了他们的一些应用，这些改进了近期的一些结束．     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997     

A New Derivation of the Inner Product Formula for the Macdonald Symmetric Polynomials

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type A_n-1. As a special case, the corresponding constant term conjecture is also proved.     

A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices

In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.

     

反超图的笛卡儿积的上色数

讨论反超图的笛卡儿积的着色理论 ,求出了满足一定条件的反超图的笛卡儿积的上色数 .     

Colossal magnetoresistance manganites: A new approach

Manganites of the LA_1−x Ca _x MnO₃ family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degeneratee _g states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund’s couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. Dedicated to Professor C N R Rao on his 70th birthday     

Symplectic Generating Functions and Moyal Products

We introduce an affine-invariant version of generating functions of symplectic transformations of affine symplectic spaces, together with a generalization for other symmetric symplectic spaces. The composition of these functions has a nice connection with the Moyal product.