On Semi-Pseudo-Ovoids

In this paper we introduce semi-pseudo-ovoids, as generalizations of the semi-ovals and semi-ovoids. Examples of these objects are particular classes of SPG-reguli and some classes of m-systems of polar spaces. As an application it is proved that the axioms of pseudo-ovoid O(n,2n,q) in PG(4n−1,q) can be considerably weakened and further a useful and elegant characterization of SPG-reguli with the polar property is given.Research Assistant of the Fund for Scientific Research Flanders (FWO-Vlaanderen)     

Focussing and defocussing of ballistic phonons in diamond and Nb3Sn

The ballistic propagation of phonons in diamond and Nb₃Sn at 40 and at 4.2 K is examined. The nature of variation of the phonon magnification factor has been analysed both in the wave vector as well as group velocity spaces. Using the Polar Schmidt-net with Pole at (π/2,π/2), the mappings of phonon focussing and defocussing are made. It is shown that the mapping for theFTA mode for Nb₃Sn exhibits islands acting as impenetrable barriers for phonon propagation.     

Products of B-patches

Products and tensor products of multivariate polynomials in B-patch form are viewed as linear combinations of higher degree B-patches. Univariate B-spline segments and certain regions of simplex splines are examples of B-patches. A recursive scheme for transforming tensor product B-patch representations into B-patch representations of more variables is presented. The scheme can also be applied for transforming ann-fold product of B-patch expansions into a B-patch expansion of higher degree. Degree raising formulas are obtained as special cases. The scheme calculates the blossom of the (tensor) product surface and generalizes the pyramidal recursive scheme for B-patches.     

ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

1IntroductionSelf-similarMarkoyprocesseson(0,co)wereintroducedbyLamperti[ZI.AnormalMarkovprocessX=(fi,F,R,Xt,ot,p")withstatespace(0,co)iscalledself-similarMarkovprocessoforderorjor>0,ifitstransitionfunctionPt(x,A)satisfiesPt(x,A)=Pa,(a"x,a"A)Vt>9,a>0,x>0,AEB(0,co).Itwasshownin[2]and[11]thateveryself-similarMarkovprocesson(0,co)automaticllyisstronglyMarkovianandhasanicepath",soitisaHuntprocessinthesenseof[1].Thefractalpropertiesoftheprocesseswerestudiedin[6]and[8].TheitoExcursiontheor…     

极分解定理的注记

设H和K是Hilbert空间.首先,对给定的算子T∈B（H,K）,刻画了集合U_T={U∈B（H,K）：U是部分等距算子并且T=U（T^*T）^1/2}. 其次,对部分等距算子U∈B（H,K）,还给出集合T_U={T∈B（H,K）：N（T）=N（U）,R（T）=R（U）,T=U（T^*T）^1/2}的刻画. 最后,作为主要结果的应用得到了相关结论.     

Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets

In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters.     

Possibility of Coexistence of Spin Density Wave and Superconductivity in Organic Conductor (TMTSF)2PF6

A theory for the coexistence problem of the spin density wave (SDW) and superconductivity (SC) in highly anisotropic materials is presented. On the basis of a simplified electronic band model a Hartree-Fock approximation is applied. It is concluded that SDW is precluded when SC developes at a higher temperature. When the SDW onset temperature is higher than that of SC, these long range orders generally coexist unless two orders interchange by a first order phase transition. Discussions on possible phase diagrams for (TMTSF)₂PF₆ under pressure are given.     

Conductivity and Optical Properties of a Polyiodine Canal Complex (Benzophenone)9(KI)2I7, CHCl3

Abstract

(Benzophenone)₉(KI)₂I₇, CHCl₃ single crystals have a golden metallic reflection on the surfaces parallel to the polyiodine chain axis. The compound is a member of a large class of channel-like inclusion compounds in which isolated iodine atom chains are the only possible conducting strands in an otherwise insulating matrix. The (contactless) microwave conductivity is ～ 10 Ω^?1 cm^?1 at room temperature with an activation energy of ～0.03 eV down to 70°K, while the dc conductivity is ～10^?-⁶. Conductivity is strongly frequency dependent and contact problems are severe.