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For the perturbed Hamiltonian of a multifrequency resonance harmonic oscillator, a new approach to calculating the coefficients in the procedure of quantum averaging is proposed. The procedure of quantum averaging is transferred to the space of the graded algebra of symbols by using twisted product introduced in the paper. As a result, the averaged Hamiltonian is represented as a function of generators of the quantum symmetry algebra of the harmonic part of the Hamiltonian. The proposed method is applied to the spectral problem for the Hamiltonian of the cylindrical Penning trap. [ABSTRACT FROM AUTHOR]

In 1993, I. P. Shestakov posed the question of the existence of a central simple finite-dimensional algebra over a field of characteristic zero whose identities are not given by a finite set of identities. In 2012, I. M. Isaev and the author of the present paper constructed an example of a seven-dimensional central simple algebra over any field that does not have a finite basis of identities. In the present paper, we construct an example of a six-dimensional central simple algebra over a field of characteristic zero which has no finite basis of identities. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing semiclassical asymptotics for the tunnel splitting of the spectrum of an operator defined on an irreducible representation of the Lie algebra . It is assumed that the operator is a quadratic function of the generators of the algebra. We present coherent states and a unitary coherent transform that allow us to reduce the problem to the analysis of a second-order differential operator in the space of holomorphic functions. Semiclassical asymptotic spectral series and the corresponding wave functions are constructed as decompositions in coherent states. For some values of the system parameters, the minimal energy corresponds to a pair of nondegenerate equilibria, and the discrete spectrum of the operator has an exponentially small tunnel splitting of the levels. We apply the complex WKB method to prove asymptotic formulas for the tunnel splitting of the energies. We also show that, in contrast to the one-dimensional Schrödinger operator, the tunnel splitting in this problem not only decays exponentially but also contains an oscillating factor, which can be interpreted as tunneling interference between distinct instantons. We also show that, for some parameter values, the tunneling is completely suppressed and some of the spectral levels are doubly degenerate, which is not typical of one-dimensional systems. [ABSTRACT FROM AUTHOR]

Let be an embedded projective variety. The Lie algebra defined by the tangent directions to at smooth points is an interesting algebraic invariant of . In some cases, this algebra is isomorphic to the symbol algebra of a filtered system of distributions on a Fano manifold, which plays an important role in the theory of these manifolds. In addition, algebras defined by tangent directions are interesting on their own right. In this paper, we study the Lie algebra corresponding to a variety that is the projectivization of the orbit of the lowest weight vector of an irreducible representation of a complex semisimple Lie group. We describe these algebras in terms of generators and relations. In many cases, we can describe their structure completely. [ABSTRACT FROM AUTHOR]

In the paper, we consider the problem of uniform approximation of a continuous function defined on a compact metric space by elements of the sum of two algebras in the space of all continuous functions on . We prove a Chebyshev-type theorem for characterization of best approximation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations. [ABSTRACT FROM AUTHOR]

An algebra is called a binary Leibniz algebra if each of its two-generated subalgebras is a Leibniz algebra. In the present paper, we give a description of binary Leibniz algebras in terms of identities. As a consequence, we show that the variety of binary Leibniz algebras is not Schreier and that the freedom theorem fails to hold for this variety. [ABSTRACT FROM AUTHOR]

In the paper, we continue the study of the relatively free Grassmann algebra without unit over an infinite field of characteristic 2, which was initiated in previous works of the author. The main attention is paid here to the relationship between the -spaces of n-words, i.e., the -spaces generated by all monomials in containing each of their variables with multiplicity n. The results of this note will enable one to form a more complete picture of possible inclusions between the -spaces of r-and n-words for r > n. [ABSTRACT FROM AUTHOR]

The present paper is devoted to estimating the codimensions cn for the variety of associative algebras given by the identity [x1, ..., xl] = 0 for odd l. The characteristic of the ground field is different from 2 and 3. The construction of the so-called extended Grassmann algebra is applied very effectively. [ABSTRACT FROM AUTHOR]

Suppose that A and B are C*-algebras, A is separable, and B is stable. The elements of the group E1(A, B) in Connes—Higson E-theory are represented by *-homomorphisms from the suspension of A to the asymptotic algebra 21B. In the paper, an endofunctor M in the category of C* -algebras is constructed and a set of special homotopy classes of *-homomorphisms from A to MUB is defined so that this set endowed with the natural structure of an Abelian group coincides with E1(A,B). [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of predual spaces of JBW-algebras. It is proved that the predual space of a JBW-algebra is a strongly facially symmetric space if and only if this algebra is the direct sum of an Abelian algebra and an algebra of type I2. [ABSTRACT FROM AUTHOR]

The paper deals with the Rees algebra R of a graded ideal I of a standard graded algebra A generated by a subset of generators of the maximal graded ideal of A. We compute the cohomology modules of R in terms of the cohomology modules of A and depth( R ) in terms of depth (A). [ABSTRACT FROM AUTHOR]

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., 'Remarks on 'Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings',' Math. Comput. Modelling 54, 1467-1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we give necessary and sufficient conditions for the boundedness of commutators of fractional maximal operator on Orlicz spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators. [ABSTRACT FROM AUTHOR]

Numerical characteristics of identities of nonassociative algebras are considered. A series of algebras with subexponential colength growth is constructed. [ABSTRACT FROM AUTHOR]

In this paper, some converses of Jessen's inequality, in terms of the time scale calculus, are proved. The obtained results are used to derive new converse inequalities for generalized means, power means and Hölder's inequality. [ABSTRACT FROM AUTHOR]

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejér (or ( C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Gá t in 1997. The aim of this paper is to investigate the maximal operator of the sup |σ|. Among other things, we prove that this operator is bounded from the Hardy space H to the Lebesgue space L if and only if 1/2 < p < ∞. The two-dimensional maximal operator is also discussed. [ABSTRACT FROM AUTHOR]

Earlier, for odd n, the author described unitary n × n matrices U with the following property: if H is a Hankel matrix, then U* HU is a Hankel matrix as well. In the present paper, it is shown that this description also holds for even n starting from n = 4. [ABSTRACT FROM AUTHOR]

Formulas for the regularized trace of the one-dimensional non-self-adjoint Dirac operator with L-potential are obtained. The cases of periodic and antiperiodic boundary conditions as well as of the Dirichlet boundary conditions are considered. The formulas are obtained by using the method of similar operators on the basis of results from the papers [1] and [2]. [ABSTRACT FROM AUTHOR]

For the irrationalitymeasures of the numbers 2k−1 arctan(2k−1/(k−1)), where k is an even positive integer, upper bounds are presented. [ABSTRACT FROM AUTHOR]

By a result of Gerstenhaber and Schack, the simplicial cohomology ring of a poset is isomorphic to the Hochschild cohomology ring of the category algebra , where the poset is viewed as a category and is a field. Extending results of Mishchenko, under certain assumptions on a category , we construct a category and a graded -linear isomorphism . Interpreting the degree one cohomology, we also show how the -space of derivations on graded by some semigroup corresponds to the -space of characters on . [ABSTRACT FROM AUTHOR]

The C*-simplicity of n-periodic products is proved for a large class of groups. In particular, the n-periodic products of any finite or cyclic groups (including the free Burnside groups) are C*-simple. Continuum-many nonisomorphic 3-generated nonsimple C*-simple groups are constructed in each of which the identity x = 1 holds, where n ≥ 1003 is any odd number. The problem of the existence of C*-simple groups without free subgroups of rank 2 was posed by de la Harpe in 2007. [ABSTRACT FROM AUTHOR]

The article discusses the axiom of Sasakian hypersurfaces and explores the topic on the Hermitian submanifolds of the octonion algebra.

The finite-gap approach to constructing the discrete Schrödinger operator on a quad graph expressed as a two-dimensional integer sublattice in d-dimensional space is used. The Green function for this operator is explicitly expressed as an integral over special contours of the differential constructed from spectral data. The resulting function has a well-known asymptotics. [ABSTRACT FROM AUTHOR]

A ring K is called a unique addition ring (a UA-ring) if there exists a unique binary operation + on the multiplicative semigroup ( K, · ) of K such that ( K, ·, +) is a ring. We say that an abelian group is an End-UA-group if its endomorphism ring is a UA-ring. We find End-UA-groups in the class of completely decomposable quotient divisible abelian groups. [ABSTRACT FROM AUTHOR]

An algebra is said to be Cantor if a theorem similar to the Cantor– Bernstein– Schröder theorem holds for it; namely, if, for any algebra , the existence of injective homomorphisms and implies the isomorphism . Necessary and sufficient conditions for an act over a finite commutative semigroup of idempotents to be Cantor are obtained under the assumption that all connected components of this act are finite. [ABSTRACT FROM AUTHOR]

Codes in the dihedral group algebra F q D 2 n , i.e., left ideals in this algebra, are studied. A generating idempotent is constructed for every code in F q D 2 n given by its image under the Wedderburn decomposition of this algebra. By using a selected set of idempotents, the inverse Wedderburn transform for the algebra F q D 2 n is constructed. The image of some codes under the Wedderburn decomposition is described directly in terms of their generating idempotents. Examples of the application of the obtained results to induced codes are considered. [ABSTRACT FROM AUTHOR]

The algebra of symmetries of a quantum three-frequency hyperbolic resonance oscillator is studied. It is shown that this algebra is determined by a finite set of generators with polynomial commutation relations. The irreducible representations of this algebra and the corresponding coherent states are constructed. [ABSTRACT FROM AUTHOR]

The notion of a Hadamard decomposition of a semisimple associative finite-dimensional complex algebra generalizes the notion of classical Hadamard matrices, which correspond to the case of commutative algebras. Algebras admitting a Hadamard decomposition are said to be Hadamard. Images of orthogonal bases of involution in Hadamard algebras under the canonical projections of these algebras onto their simple components are studied. Using a technique related to the study of central primitive idempotents of Hadamard algebras, we obtain a necessary condition for a family of involutory matrices of fixed order to be such an image. It is also shown that this necessary condition is not sufficient. We also present new proofs of results proved earlier. [ABSTRACT FROM AUTHOR]

We describe homogeneous locally nilpotent derivations of the algebra of regular functions for a class of affine trinomial hypersurfaces. This class comprises all nonfactorial trinomial hypersurfaces. [ABSTRACT FROM AUTHOR]

An essentially nonlinear equation containing the product of the p-Laplacian and a nonsymmetric difference operator is considered. Sufficient conditions guaranteeing the coercivity and pseudomonotonicity of the corresponding nonlinear difference-differential operator are obtained. The existence of a generalized solution of the Dirichlet problem for the nonlinear equation under consideration is proved. [ABSTRACT FROM AUTHOR]

The problem concerning the form of the maximal ideal space of an almost-periodic algebra formed by functions on ℝ is considered. It is shown that this space is homeomorphic to the topological group dual to the group of frequencies of the algebra under consideration. In the case of a quasiperiodic algebra, the mappings of ℝ generating automorphisms of the algebra are described. Several specific examples are given and a relation to the theory of quasicrystals is indicated. [ABSTRACT FROM AUTHOR]

Generalized hypergeometric differential equations of arbitrary order are considered. Necessary and sufficient conditions for the algebraic independence of solutions of collections of such equations, as well as of their values at algebraic points, are obtained. [ABSTRACT FROM AUTHOR]

The article explores the superactivation of the capacity of quantum channels generated by a noncommutative operator graph. The close relation of the value of the quantum capacity to the so-called operator graph of the quantum channel is tackled. The algebra generated by the noncommutative operator graph is also outlined to construct low-dimensional examples of superactivation for quantum capacity.

The homotopy theory of ∞-simplicial coalgebras is developed; in terms of this theory, an additional structure on the tensor bigraded coalgebra of a graded module is described such that endowing the coalgebra with this structure is equivalent to endowing the given graded module with the structure of a homotopy unital A-algebra. [ABSTRACT FROM AUTHOR]

The article explores the complexity functions of varieties of leibniz algebras with nilpotent commutator subalgebra. Topics discussed include relation of these algebras to differential geometry, classical algebraic topology, and noncommutative geometry, example of an exponential generating function, and assertions for the variety of Leibniz algebras over an arbitrary field.

The theory of Henstock-Kurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas. [ABSTRACT FROM AUTHOR]

For multiplicative Fourier transforms, analogs of results obtained by R. P. Boas, F. Moricz, M. I. D'yachenko, I. P. Liflyand, and S. Yu. Tikhonov and dealing with conditions for the uniform convergence and weighted integrability with power weight of classical Fourier transforms as well as conditions for these transforms to belong to Lipschitz classes are proved. Certain results of C. W. Onneweer concerning conditions for multiplicative Fourier transforms to belong to Lipschitz-Besov and Herz spaces are also generalized. [ABSTRACT FROM AUTHOR]

The classical Goursat lemma is extended to classes of differentiable mappings of domains of real Banach spaces to algebras of linear operators acting on these spaces. We clarify the modification of the form and content of this lemma in dependence on the choice of the original object. The case in which the original space is a Banach algebra and Fréchet derivatives are operators of multiplication by elements of this algebra is considered separately. [ABSTRACT FROM AUTHOR]

The logistic equation supplemented with a summand characterizing delay is considered. The local and nonlocal dynamics of this equation are studied. For equations with delay, we use the standard Andronov-Hopf bifurcation methods and the asymptotic method developed by the author and based on the construction of special evolution equations defining the local dynamics of the equations containing delay. In addition, we study the existence and methods of constructing the asymptotics of nonlocal relaxation cycles. A comparison of the results obtained with those for the Hutchinson equation and some of its generalizations is given. [ABSTRACT FROM AUTHOR]

On the basis of the colored version of Koszul duality, the notion of a differential module with ∞-simplicial faces is introduced. By using the homotopy technique of differential Lie modules over colored coalgebras, the homotopy invariance of the structure of a differential module with ∞-simplicial faces is proved. A relationship between differential modules with ∞-simplicial faces and A-algebras is described. The notions of the chain realization of a differential module with ∞-simplicial faces and the tensor product of differential modules with ∞-simplicial faces are introduced. It is shown that the chain realization of a tensor differential module with ∞-simplicial faces constructed from an A-algebra and the B-construction over this A-algebra are isomorphic differential coalgebras. [ABSTRACT FROM AUTHOR]