Volume 57, Nº 4 (2016)
- Ano: 2016
- Artigos: 16
- URL: https://journals.rcsi.science/0037-4466/issue/view/10380
Article
On spectra of almost simple groups with symplectic or orthogonal socle
Resumo
Finite groups are said to be isospectral if they have the same sets of the orders of elements. We investigate almost simple groups H with socle S, where S is a finite simple symplectic or orthogonal group over a field of odd characteristic. We prove that if H is isospectral to S, then H/S presents a 2-group. Also we give a criterion for isospectrality of H and S in the case when S is either symplectic or orthogonal of odd dimension.
The partial clone of linear terms
Resumo
Generalizing a linear expression over a vector space, we call a term of an arbitrary type τ linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type τ, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.
On subordination of some analytic functions
Resumo
We define V (α, β) (α < 1 and β > 1), the new subclass of analytic functions with bounded positive real part, \(V\left( {\alpha ,\beta } \right): = \left\{ {f \in A:\alpha < \operatorname{Re} \left\{ {{{\left( {\frac{z}{{f\left( z \right)}}} \right)}^2}f'\left( z \right)} \right\} < \beta } \right\}\), and study some properties of V (α, β). We also study the class U (γ) (γ > 0): \(u\left( \gamma \right): = \left\{ {f \in A:\left| {{{\left( {\frac{z}{{f\left( z \right)}}} \right)}^2}f'\left( z \right)} \right| - 1 < \gamma } \right\}\), where A is the class of normalized functions.
Holomorphic extension of functions along finite families of complex straight lines in an n-circular domain
Resumo
We consider the continuous functions on the boundary of a bounded n-circular domain D in ℂn, n > 1, which admit one-dimensional holomorphic extension along a family of complex straight lines passing through finitely many points of D. The question is addressed of the existence of a holomorphic extension of these functions to D.
Large-time behavior of solutions to degenerate damped hyperbolic equations
Resumo
We investigate the asymptotic behavior of solutions to damped hyperbolic equations involving strongly degenerate differential operators. First we establish the existence of a global attractor for the damped hyperbolic equation under consideration. Then we prove the finite dimensionality of the global attractor.
On bounded solutions to weakly nonlinear vector-matrix differential equations of order n
Resumo
To prove existence and uniqueness (or just existence) of a bounded solution to nonlinear differential equations of higher order, we employ the contraction mapping principle and the Tikhonov Fixed Point Theorem. A quantitative estimate of a nonlinear perturbation preserving basic features of behavior of the corresponding linear equation (asymptotic stability or exponential dichotomy) is important when we pass to a nonlinear equation.
Isotopes of the alternative monster and the Skosyrsky algebra
Resumo
We prove that the isotopes of the alternative monster and the Skosyrsky algebra satisfy the identity Пi=14 [xi, yi] = 0. Hence, the algebras themselves satisfy the identity Пi=14 (c, xi, yi) = 0. We also show that none of the identities Пi=1n(c, xi, yi) = 0 holds in all commutative alternative nil-algebras of index 3. Thus, we refute the Grishkov–Shestakov hypothesis about the structure of the free finitely generated commutative alternative nil-algebras of index 3.
The commutator width of some relatively free lie algebras and nilpotent groups
Resumo
We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank.
On weakly SΦ-supplemented subgroups of finite groups
Resumo
Let G be a finite group. We say that a subgroup H of G is weakly SΦ-supplemented in G if G has a subgroup T such that G = HT and H∩T ≤ Φ(H)HsG, where HsG is the subgroup of H generated by all those subgroups of H that are s-permutable in G. In this paper, we investigate the influence of weakly SΦ-supplemented subgroups on the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained.
Study of degenerate evolution equations with memory by operator semigroup methods
Resumo
We reduce the problem with some history prescribed for an integrodifferential equation in a Banach space including memory effect to the Cauchy problem for some evolution system with a constant operator in a larger space that possesses a resolvent (C0)-semigroup. This enables us to state conditions for the existence of a unique classical solution to the original problem. We use the results to study the unique solvability of problems with history prescribed for degenerate linear evolution equations with memory in Banach spaces. We show that the initial-boundary value problem for the linearized integrodifferential Oskolkov system describing the dynamics of Kelvin–Voigt fluids in linear approximation belongs to this class of problems.
The invariance principle for nonautonomous differential equations with discontinuous right-hand side
Resumo
We study limit differential inclusions for nonautonomous differential equations with discontinuous right-hand side and Filippov solutions. Using Lyapunov functions with derivatives of constant sign, we establish an analog of LaSalle’s invariance principle. We study differential equations with either measurable or piecewise continuous right-hand side.
A p-adic hard-core model with three states on a Cayley tree
Resumo
We examine the p-adic hard-core model with three states on a Cayley tree. Translationinvariant and periodic p-adic Gibbs measures are studied for the hard-core model for k = 2. We prove that every p-adic Gibbs measure is bounded for p ≠ 2. We show in particular that there is no strong phased transition for a hard-core model on a Cayley tree of order k.
On {2, 3}-groups without elements of order 6
Resumo
We describe {2, 3}-groups in which the order of a product of every two elements of orders at most 4 does not exceed 9 and the centralizer of every involution is a locally cyclic 2-subgroup. In particular, we will prove that these groups are locally finite.