Moscow University Mathematics Bulletin Volume 68 Issue 1

Journal Article

Examples of divergent Fourier series for a wide class of rearranged Walsh-Paley system

Polyakov, I.

2013 Moscow University Mathematics Bulletin

A rearranged Walsh system is considered in the paper. An example of a Fourier series from the class $$Lo\left( {\sqrt {\ln ^ + } } \right)L$$ divergent almost everywhere is constructed.

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Journal Article

Construction of generator polynomials for residue codes of degrees 5–8

Artamonov, A.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010026

A generalization of quadratic residue codes to the case of higher degree is considered. Properties of h-power residue codes are studied. In some cases, it is possible to indicate the form and method of construction of a generator polynomial. Using the results obtained here, generator polynomials...

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Journal Article

Bounded strict solar property of strict suns in the space C(Q)

Alimov, A.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010038

The intersection of an arbitrary strict sun M in C(Q) with a closed span Π ⊂ C(Q) (in particular, with a closed ball) is shown to be a strict protosun, provided that the natural condition M ∩ int Π ≠ Ø is satisfied. This property is shown to characterize closed spans in C(Q).

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Journal Article

Efficient portfolio dependent on Cox-Ingersoll-Ross interest rate

Kambarbaeva, G.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S002713221301004X

We solve a certain problem of portfolio optimization in the case of asset price trends dependent on the bank interest rate governed by the Cox-Ingersoll-Ross dynamics. This work continues a series of papers where the interest rate was modeled by a linear stochastic differential equation with a...

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Journal Article

Piecewise periodicity structure estimates in Shirshov’s height theorem

Kharitonov, M.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010051

The Gelfand-Kirillov dimension of l-generated general matrices is equal to (l − 1)n 2 + 1. Due to the Amitzur-Levitsky theorem, the minimal degree of the identity of this algebra is 2n. That is why the essential height of A being an l-generated PI-algebra of degree n over every set of words is...

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Journal Article

Asymptotics of stationary measure under scaling in stochastic exchange processes

Odnobokov, N.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010063

Asymptotic properties of an invariant distribution of exchange processes are studied on a two-dimensional lattice with fixed boundary conditions.

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Journal Article

Convergence of orthogonal greedy algorithm with errors in projectors

Fedotov, N.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010075

A model of orthogonal greedy algorithm is proposed. This model allows one to consider computational errors and to study the stability of this algorithm with respect to errors in projections onto subspaces. A criterion for the convergence of orthogonal greedy expansion to the expanded element is...

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Journal Article

Abelian subgroups generated by Dehn twists in homeomorphism group

Permyakov, D.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010087

The subgroup of homeoniorphisni group generated by Dehn twists along the set of simple closed pairwise non-homotopic curves with some conditions is studied. It is proved that this group is isomorphic to a free Abelian group of rank k, where k is the number of curves in the set. In the case of an...

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Journal Article

Inverse coding theorem for infinite-dimensional quantum channels

Kuznetsova, A.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010099

In this paper we make a conjecture about the quantum capacity of an infinite-dimensional quantum channel. The proof of the inverse theorem is given based on definitions and properties of the coherent information in the infinite-dimensional case.

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Journal Article

Laws of rolling simplexes (feild equations according to Tycho Brahe)

Razmyslov, Yu.

2013 Moscow University Mathematics Bulletin

doi:10.3103/S0027132213010105

Models of central power fields with quadratic dynamics suggested by René Descartes are studied. These examples gradually lead the reader to the understanding of base notions of differen-tial algebraic-geometric theory of Brahe-Descartes-Wotton including central fields whose dynamics is formed by...

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Moscow University Mathematics Bulletin Volume 68 Issue 1

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