DSpace Collection: Volume 26 Number 2
http://hdl.handle.net/10525/399
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Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral
http://hdl.handle.net/10525/414
Title: Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral<br/><br/>Authors: Petrogradsky, V.<br/><br/>Abstract: Let Uc be the variety of associative algebras generated by thealgebra of all upper triangular matrices, the field being arbitrary. We provethat the upper exponent of any subvariety V ⊂ Uc coincides with the lowerexponent and is an integer.<br/><br/>Description: Partially supported by grant RFFI 98-01-01020.On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem
http://hdl.handle.net/10525/413
Title: On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem<br/><br/>Authors: Iliev, Valentin<br/><br/>Abstract: Pólya’s fundamental enumeration theorem and some resultsfrom Williamson’s generalized setup of it are proved in terms of Schur-Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutationgroup W ≤ Sd and a one-dimensional character χ of W , the polynomialfunctor Fχ corresponding via S-MT to the induced monomial representationUχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ )is the weighted inventory of some set J(χ) of W -orbits in the integer-valuedhypercube [0, ∞)d . The elements of J(χ) can be distinguished among allW -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of bothcharacteristics is a consequence of S-MT, and is equivalent to a result ofWilliamson. Pólya’s theorem can be obtained from the above identity bythe specialization χ = 1W , where 1W is the unit character of W.Asymptotic Behaviour of Colength of Varieties of Lie Algebras
http://hdl.handle.net/10525/412
Title: Asymptotic Behaviour of Colength of Varieties of Lie Algebras<br/><br/>Authors: Mishchenko, S.; Zaicev, M.<br/><br/>Abstract: We study the asymptotic behaviour of numerical characteristicsof polynomial identities of Lie algebras over a field of characteristic 0. Inparticular we investigate the colength for the cocharacters of polynilpotentvarieties of Lie algebras. We prove that there exist polynilpotent Lie varietieswith exponential and overexponential colength growth. We give the exactasymptotics for the colength of a product of two nilpotent varieties.<br/><br/>Description: This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and00-15-96128.Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation
http://hdl.handle.net/10525/411
Title: Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation<br/><br/>Authors: Di Pomponio, Stefania<br/><br/>Abstract: We treat the oscillatory problem for semilinear wave equation.The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x).By using suitable variants of Strichartz estimate we extend the results from[6] on a priori estimates of the approximations of geometric optics.The mainimprovement is the fact that we can obtain a priori estimates for the caseσ = 1, while in [6] we could treat only the case σ > n/2 − 1.<br/><br/>Description: The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodinella Teoria delle Equazioni Iperboliche”.On Minimizing ||S−(AX−XB)||Pp
http://hdl.handle.net/10525/410
Title: On Minimizing ||S−(AX−XB)||Pp<br/><br/>Authors: Mecheri, Salah<br/><br/>Abstract: In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp ,where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such thatAX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.Primitive Ideals and Symplectic Leaves of Quantum Matrices
http://hdl.handle.net/10525/409
Title: Primitive Ideals and Symplectic Leaves of Quantum Matrices<br/><br/>Authors: Mosin, V. G.<br/><br/>Abstract: It is proved that there exists a bijection between the primitive ideals of the algebra of regular functions on quantum m × n-matrices and the symplectic leaves of associated Poisson structure.On Averaging Null Sequences of Real-Valued Functions
http://hdl.handle.net/10525/408
Title: On Averaging Null Sequences of Real-Valued Functions<br/><br/>Authors: Kiriakouli, P. Ch.<br/><br/>Abstract: If ξ is a countable ordinal and (fk) a sequence of real-valuedfunctions we define the repeated averages of order ξ of (fk). By using apartition theorem of Nash-Williams for families of finite subsets of positiveintegers it is proved that if ξ is a countable ordinal then every sequence(fk) of real-valued functions has a subsequence (f'k) such that either everysequence of repeated averages of order ξ of (f'k) converges uniformly to zeroor no sequence of repeated averages of order ξ of (f'k) converges uniformly tozero. By the aid of this result we obtain some results stronger than Mazur’stheorem.