On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.     

On Extended Polar Decomposition

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.     

Electromagnetic radiation from a conducting tether moving in the ionosphere

Summary We set up a model to compute electromagnetic radiation associated with the motion of a conductor through a magnetized plasma. Calculations are carried out, in the framework of cold-plasma theory, for radiation near the ion cyclotron frequency. Results are applied to the TSS (Tethered Satellite System) project presently under development.

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Riassunto S’imposta il formalismo generale per il calcolo della radiazione elettromagnetica associata con il moto di un conduttore in moto attraverso un plasma magnetizzato. I calcoli sono poi fatti specificamente per la radiazione nelle vicinanze della frequenza di ciclotrone degli ioni. I risultati sono applicati ai parametri del progetto spaziale TSS (Tethered Satellite System) che è attualmente in fase di sviluppo.

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Резюме Мы предлагаем модель для вычисления электромагнитного излучения, связанного с движением проводника через намагниченныю плазму. Вычисления проводятся в рамках теории холодной плазмы для изучения вблизи ионной циклотронной частоты. Полученные результаты применяются к ТСС (связанная система спутников), проект которой разрабатывается в настояцее время.

     

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.