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A matrix M is nilpotent of index 2 if M2=0. Let V be a space of nilpotent n×n matrices of index 2 over a field k where and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that . We show that the inequality is sharp and const...
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A (non-associative) algebra A, over a field k, is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of A. Suppose A is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that x(2) = 0 for all x in A, and so xy = yx...
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BACKGROUND: Inactivity is a leading contributor to chronic health problems. Here, we examined the effects of a pedometer-based physical activity intervention (Prince Edward Island-First Step Program, PEI-FSP) on activity and specific health indices in 106 sedentary workers. METHODS: Participants wer...
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An empirical tight-binding (ETB) approach combined with a Green's-function (GF) method has been employed to investigate the electronic structure of the Si(111) and arsenic-passivated Si(111) surfaces. An accurate silicon band structure has first been developed keeping up to second-nearest-neigh...
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The Michelin Tire Company requires its tires to be very uniform in order to provide a smooth, quiet ride. The design of the appropriate manufacturing technique leads to a problem in harmonic analysis, and to the problem of the design of a statistical experiment to accurately measure the harmonic...
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An information theoretic measure is introduced to compare the disorder in non-periodic sequences. It is shown that the measure correctly distinguishes quasiperiodic and aperiodic sequences which have been deduced from earlier studies using diffraction patterns, although it is often necessary to use ...
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We study the existence of common invariant subspaces for semigroups of idempotent operators. It is known that in finite dimensions every such semigroup is simultaneously triangularizable. The question; of the existence of even one non-trivial invariant subspace is still open in infinite dimensions. ...
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Profiles of selected phenolic constituents of 2 apple cultivars, Northern Spy and Ida Red, commonly used for processed products Were compared. Although chlorogenic acid was the principal phenolic in both cultivars, there were significant quantitative differences. A new solid-phase extraction (SPE) a...
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This paper deals with semigroups of linear transformations which act transitively on a finite-dimensional vector space. An explicit canonical form is obtained for the semigroups which lack proper transitive left ideals. The class of such semigroups can be considered to be an extention of the class o...
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It is known that the smallest complete bipartite graph which is not 3-choosable has 14 vertices. We show that the extremal configuration is unique.
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The usual tight-binding (TB) approximation, employed in electronic structure calculations, is extended to include the more-distant neighbor sites than the first. In doing so, a simple power law is adopted to describe the bond and overlap contributions, which enables the energy dispersion relation to...
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The following questions are studied: Under what conditions does the existence of a (nonzero) fixed point for every member of a semigroup of matrices imply a common fixed point for the entire semigroup? What is the smallest number k such that the existence of a common fixed point for every k members ...
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An approximate solution of the Klein-Gordon equation for the general Hulthen-type potentials in D -dimensions within the framework of an approximation to the centrifugal term is obtained. The bound state energy eigenvalues and the normalized eigenfunctions are obtained in terms of hypergeometric pol...
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