Ukrainian Mathematical Journal最新文献

We study RG-modules that do not contain nonzero G-perfect factors. In particular, it is shown that if a group G is finite and R is a Dedekind domain with some additional restrictions, then these RG-modules are G-nilpotent.

We continue the development of the theory of moduli of the families of surfaces, in particular, of strings of various dimensions m = 1, 2, . . . ,n − 1 in Euclidean spaces ({mathbb{R}}^{n}) , n ≥ 2. On the basis of the proof of the lemma on the relationships between the moduli and Lebesgue measures, we prove the corresponding analog of the Fubini theorem in terms of moduli that extends the well-known Väisälä theorem for the families of curves to the families of surfaces of arbitrary dimensions. It should be emphasized that the crucial role in the proof of the mentioned lemma is played by a proposition on measurable (Borel) hulls of sets in Euclidean spaces. In addition, we also prove a similar lemma and a proposition for the families of concentric balls.

We consider graphs whose Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an L-borderenergetic graph. First, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non-L-borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities, we give new bounds for the number of edges of a non-L-borderenergetic graph. Third, we use recent bounds established by Milovanovic, et al. for the Laplacian energy to get similar conditions for non-L-borderenergetic graphs. Our bounds depend only on the degree sequence of a graph, which is much easier than computing the spectrum of the graph. In other words, we develop a faster approach to exclude non-L-borderenergetic graphs.

Suppose that R is a prime ring with char(R) ≠ 2 and f(ξ₁, . . . , ξ_n) is a noncentral multilinear polynomial over C(= Z(U)), where U is the Utumi quotient ring of R. An additive mapping h : R ⟶ R is called homoderivation if h(ab) = h(a)h(b)+h(a)b+ah(b) for all a, b ∈ R. We investigate the behavior of three generalized derivations F, G, and H of R satisfying the condition

(Fleft({xi }^{2}right)=Gleft({xi }^{2}right)+Hleft(xi right)xi +xi Hleft(xi right))

for all ξ ∈ f(R) = {f(ξ₁, . . . , ξ_n) | ξ₁, . . . , ξ_n ∈ R}.

Let p = (p_j) and q = (q_k) be real sequences of nonnegative numbers with the property that

(begin{array}{ccccccc}{P}_{m}=sum_{j=0}^{m}{p}_{j}ne 0& {text{and}}& {Q}_{m}=sum_{k=0}^{n}{q}_{k}ne 0& mathrm{for all}& m& {text{and}}& n.end{array})

Also let (P_m) and (Q_n) be regularly varying positive indices. Assume that (u_mn) is a double sequence of complex (real) numbers, which is ( (overline{N }) , p, q; α, β)-summable and has a finite limit, where (α, β) = (1, 1), (1, 0), or (0, 1). We present some conditions imposed on the weights under which (u_mn) converges in Pringsheim’s sense. These results generalize and extend the results obtained by the authors in [Comput. Math. Appl., 62, No. 6, 2609–2615 (2011)].

We apply the technique of matching functions in the setting of contact Anosov flows satisfying a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman and Ornstein [Ergodic Theory Dynam. Syst., 7, No. 1, 49–72 (1987)]. Namely, we show that if two Anosov flow of this kind are C⁰ conjugate, then they are C^r conjugate for some r ∈ [1, 2) or even C^∞ conjugate under certain additional assumptions. This, e.g., applies to geodesic flows on compact Riemannian manifolds of 1/4-pinched negative sectional curvature. We can also use our result to recover Hamendstädt’s marked length spectrum rigidity result for real hyperbolic manifolds.

We provide a cohomology of n-Hom–Lie color algebras, in particular, a cohomology governing oneparameter formal deformations. Then we also study formal deformations of the n-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on an n-Hom–Lie color algebra, which may give rise to infinitesimally trivial (n − 1)th-order deformations. Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure on n-Hom–Lie color algebras.

We develop new Hermite–Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined T_q-integrals. Then the obtained Hermite–Hadamard inequality for p-convex functions is used to get a new Hermite–Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.

We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear mth order autoregressive sequences of random variables.

We revisit Schmidt’s theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also establish a sharper result for this kind for homogeneous polynomials, assuming that the characteristic does not divide the degree. Further, we use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection of homogeneous polynomials of the same degree) with the codimension of the singular locus of the corresponding hypersurface (resp., intersection of hypersurfaces). This gives an effective version of Ananyan–Hochster’s theorem [J. Amer. Math. Soc., 33, No. 1, 291–309 (2020), Theorem A].