Results 1 - 10 of 1975
Results 1 - 10 of 1975. Search took: 0.02 seconds
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[en] Positive-definite Hankel matrices have an important property: the ratio of the largest and the smallest eigenvalues (the spectral condition number) has as a lower bound an increasing exponential of the order of the matrix that is independent of the particular matrix entries. The proof of this fact is related to the so-called Vandermonde factorizations of positive-definite Hankel matrices. In this paper the structure of these factorizations is studied for real sign-indefinite strongly regular Hankel matrices. Some generalizations of the estimates of the spectral condition number are suggested
[en] The impact of possible sources of lepton-flavor mixing on K → πν(bar ν) decays is analyzed. At the one-loop level lepton-flavor mixing originated from non-diagonal lepton mass matrices cannot generate a CP-conserving KL → π0ν(bar ν) amplitude. The rates of these modes are sensitive to leptonic flavor violation when there are at least two different leptonic mixing matrices. New interactions that violate both quark and lepton universalities could enhance the CP-conserving component of Λ(KL → π0ν(bar ν)) and have a substantial impact. Explicit examples of these effects in the context of supersymmetric models, with and without R-parity conservation, are discussed
[en] There is a broad generalization of a uniformly distributed sequence according to Weyl where the frequency of elements of this sequence falling into an interval is defined by using a matrix summation method of a general form. In the present paper conditions for uniform distribution are found in the case where a regular Voronoi method is chosen as the summation method. The proofs are based on estimates of trigonometric sums of a certain special type. It is shown that the sequence of the fractional parts of the logarithms of positive integers is not uniformly distributed for any choice of a regular Voronoi method.
[en] We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
[en] Necessary and sufficient conditions for the transfer function of a passive linear stationary scattering (or resistance) system are found ensuring that minimal systems in this class are determined by their transfer functions up to similarity. The criteria are stated in terms of a Hankel operator the symbol of which is a contractive operator-valued function defined by the transfer function and having the meaning of the inner scattering suboperator of a simple conservative scattering (respectively, resistance) system with the transfer function in question. A connection between the similarity criterion and the corona theorem and its matrix generalizations is revealed
[en] Let f be a function on the set Mnxn of all n by n real matrices. If f is rotationally invariant with respect to the proper orthogonal group, it has a representation f-tilde through the signed singular values of the matrix argument A element of M-circumflexnxn. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of f-tilde
[en] Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra Mn(C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type An-1 into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in 'Russian Math. Surveys' in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type An-1 in the case where n is a prime-power.
[en] We consider specializations of quadratic matrix equations preserving the invariant type of the equation and the weight formula for representations of the quadratic form by a genus of positive definite forms. We apply our results to the forms of cubic and Gosset lattices