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The g-Drazin Invertibility of a Block Operator Matrix Math. Notes (IF 0.6) Pub Date : 2024-03-12 Huanyin Chen, Marjan Sheibani
Abstract We present new additive properties of the g-Drazin inverse of a linear operator on a Banach space. The g-Drazin invertibility of certain \(2\times 2\) block operator matrices on a Banach space is thereby established. These results extend many known results, e.g., by Yang and Liu [J. Comput. Applied Math. 235, 1412–1417 (2011)] and Dopazo and Martinez-Serrano [Linear Algebra Appl. 432, 1896–1904
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On Prime Primitive Roots of $$2^{k}p+1$$ Math. Notes (IF 0.6) Pub Date : 2024-03-12 S. Filipovski
Abstract A prime \(p\) is a Sophie Germain prime if \(2p+1\) is prime as well. An integer \(a\) that is coprime to a positive integer \(n>1\) is a primitive root of \(n\) if the order of \(a\) modulo \(n\) is \(\phi(n).\) Ramesh and Makeshwari proved that, if \(p\) is a prime primitive root of \(2p+1\), then \(p\) is a Sophie Germain prime. Since there exist primes \(p\) that are primitive roots of
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To the Problem of a Point Source in an Inhomogeneous Medium Math. Notes (IF 0.6) Pub Date : 2024-03-12 S. T. Gataullin, T. M. Gataullin
Abstract This paper studies the asymptotic behavior with respect to the complex parameter of the fundamental solution for a second-order elliptic operator with smooth compact coefficients obtained by the V. P. Maslov canonical operator method using the results of V. V. Kucherenko. It is shown that the singular part of the asymptotics can be represented as a series in Hankel functions of the first kind
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Ergodicity Coefficient. New Proofs of Known Properties Math. Notes (IF 0.6) Pub Date : 2024-03-12 Yu. A. Alpin, N. N. Korneeva
Abstract The paper suggests new simple proofs of two known theorems on the ergodicity coefficient of a stochastic matrix.
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An Efficient Algorithm for Decomposing a Vector into Two Vectors with a Small Uniform Norm Math. Notes (IF 0.6) Pub Date : 2024-03-12 B. S. Kashin, D. G. Romskii
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Complete Shrinking General Ricci Flow Soliton Systems Math. Notes (IF 0.6) Pub Date : 2024-03-12 Shahroud Azami
Abstract In this paper, we show that a complete shrinking general Ricci flow soliton system \((M,g,H,X,u,\lambda)\) with condition \(h\geq0\) is compact if and only if \(||X|| \) is bounded on \(M\), where \(h\) is the 2-form with components \(h_{ij}=\frac{1}{2}H_{ikl}H_{j}^{kl}\). We also prove that a complete shrinking general Ricci flow system soliton has finite fundamental group.
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Boundedness of Hadamard–Bergman and Variable Hadamard–Bergman Convolution Operators Math. Notes (IF 0.6) Pub Date : 2024-03-12 A. Karapetyants, E. Morales
Abstract This article continues the study of the Hadamard–Bergman operators in the unit disk of the complex plane. These operators arose as a natural generalization of orthogonal projections and represent an integral realization of multiplier operators. However, the study of operators in integral form offers a number of advantages in the context of the application of the theory of integral operators
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On the Existence of an Element with Given Deviations from an Expanding System of Subspaces Math. Notes (IF 0.6) Pub Date : 2024-03-12 Yu. A. Skvortsov
Abstract We expand the class of deviation sequences for which the problem on the existence of an element of a Banach space with these deviations from a system of nested subspaces is solved positively regardless of the space and the system of subspaces. This result is used to narrow the gap between the weak asymptotics constants in S. V. Konyagin’s theorem on the existence of an element whose deviations
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First Asymptotics of Solutions of Degenerate Second-Order Differential Equations Math. Notes (IF 0.6) Pub Date : 2024-03-12 V. P. Arkhipov, A. V. Glushak
Abstract We propose a method for constructing asymptotic representations of solutions of linear degenerate second-order ordinary differential equations, which permits one to construct exact asymptotics of solutions in a neighborhood of the degeneracy point. An example where one finds a power-law asymptotics is given.
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Isothermic Surfaces Associated with the Cylinder Obtained by Ribaucour Transformations Math. Notes (IF 0.6) Pub Date : 2024-03-12 A. M. V. Corro, M. L. Ferro
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On the Existence of Solutions of the Dirichlet Problem for the $$p$$ -Laplacian on Riemannian Manifolds Math. Notes (IF 0.6) Pub Date : 2024-03-12 S. M. Bakiev, A. A. Kon’kov
Abstract We obtain a criterion for the existence of solutions of the problem $$\Delta_p u=0 \quad\text{in}\quad M \setminus \partial M,\qquad u|_{\partial M}=h$$ with a bounded Dirichlet integral, where \(M\) is an oriented complete Riemannian manifold with boundary and \(h \in W_{p,\mathrm{loc}}^1 (M)\), \(p > 1\).
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On the $$p(x)$$ -Curl-System Problem with Indefinite Weight and Nonstandard Growth Conditions Math. Notes (IF 0.6) Pub Date : 2024-03-12 K. Kefi, B. Ge
Abstract We prove the existence of at least one weak solution for the \(p(x)\)-Curl systems with nonstandard growth conditions. The proof of our main result uses Ekeland’s variational method.
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Equivalence Theorem for Absolute Matrix Summability Methods Math. Notes (IF 0.6) Pub Date : 2023-12-01
Abstract In this paper, we obtain necessary and sufficient conditions for the equivalence of two matrix summability methods. Some known results are also presented.
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A Note on Some New Sharp Results on the Zeros of New Area Nevanlinna Type Spaces in the Unit Disk Math. Notes (IF 0.6) Pub Date : 2023-12-01
Abstract We provide a complete description of zero sets of some new analytic area Nevanlinna type spaces in the unit disk. Our theorems extend recent sharp results of E. Rodikova to larger analytic function spaces of area Nevanlinna type.
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A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincaré Boundary Conditions Math. Notes (IF 0.6) Pub Date : 2023-12-01
Abstract For a certain class of second-order hyperbolic systems, a mixed problem with Dirichlet and Poincaré boundary conditions is studied. In the linear case, an explicit representation of a soultion of this problem is given and questions related to its uniqueness and existence are studied depending on the character of nonlinearities in the system.
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On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems Math. Notes (IF 0.6) Pub Date : 2023-10-24 S. E. Pastukhova
Abstract In the space \(\mathbb R^d\), we consider matrix elliptic operators \(L_\varepsilon\) of arbitrary even order \(2m\ge 4\) with measurable \(\varepsilon\)-periodic coefficients, where \(\varepsilon\) is a small parameter. We construct an approximation to the resolvent of this operator with an error of the order of \(\varepsilon^2\) in the operator \((L^2\to L^2)\)-norm.
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On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators Math. Notes (IF 0.6) Pub Date : 2023-10-24 Yu. Yu. Linke
Abstract The consistency of classical local linear kernel estimators in nonparametric regression is proved under constraints on design elements (regressors) weaker than those known earlier. The obtained conditions are universal with respect to the stochastic nature of design, which may be both fixed regular and random and is not required to consist of independent or weakly dependent random variables
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Approximation of Mathieu Functions by Parabolic Cylinder Functions Math. Notes (IF 0.6) Pub Date : 2023-10-24 E. A. Zlobina
Abstract The Mathieu equation with complex coefficients of a special form is considered. Simple nonuniform asymptotics of its solutions in terms of parabolic cylinder functions are constructed.
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Uniform Convergence of Sine Series with Fractional-Monotone Coefficients Math. Notes (IF 0.6) Pub Date : 2023-10-24 M. I. Dyachenko
Abstract We study how the well-known criterion for the uniform convergence of a sine series with monotone coefficients changes if, instead of monotonicity, one imposes the condition of \(\alpha\)-monotonicity with \(0<\alpha <1\). Moreover, we obtain an addition to the well-known Kolmogorov theorem on the integrability of the sum of a cosine series with convex coefficients tending to zero.
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Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected Math. Notes (IF 0.6) Pub Date : 2023-10-24 B. B. Bednov
Abstract In a three-dimensional normed space \(X\), any bounded Chebyshev set is monotone path connected if and only if one of the following two conditions holds: (1) the set of extreme points of the sphere in the dual space is dense in this sphere; (2) \(X=Y\oplus_\infty \mathbb R\) (i.e., the unit sphere of \(X\) is a cylinder).
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Domain of Existence of the Sum of a Series of Exponential Monomials Math. Notes (IF 0.6) Pub Date : 2023-10-24 A. S. Krivosheev, O. A. Krivosheeva
Abstract In the paper, series of exponential monomials are considered. We study the problem of the distribution of singular points of the sum of a series on the boundary of its domain of convergence. We study the conditions under which, for any sequence of coefficients of the series with a chosen domain of convergence, the domain of existence of the sum of this series coincides with the given domain
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Feedback Strategies in a Game-Theoretical Control Problem for a Nonlocal Continuity Equation Math. Notes (IF 0.6) Pub Date : 2023-10-24 E. A. Kolpakova
Abstract The paper deals with game-theoretical control problem for the continuity equation. It is assumed that all agents of a multiagent system are influenced by the same controls of both players depending only on current time and current distribution of the agents. We extend the notion of \(u\)- and \(v\)-stability and the Krasovskii–Subbotin extremal shift rule to a given case and construct suboptimal
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Dugundji Compacta and the Space of Idempotent Probability Measures Math. Notes (IF 0.6) Pub Date : 2023-10-24 A. A. Zaitov, D. T. Eshkobilova
Abstract For a given group \((G,X,\alpha)\) of topological transformations on a Tikhonov space \(X\), a group \((I(G, X), I(X), I(\alpha))\) of topological transformations on the space \(I(X)\) of idempotent probability measures is constructed. It is shown that, if the action \(\alpha\) of the group \(G\) is open, then the action \(I(\alpha)\) of the group \(I(G,X)\) is also open; while an example
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Traces of Sobolev Spaces on Piecewise Ahlfors–David Regular Sets Math. Notes (IF 0.6) Pub Date : 2023-10-24 A. I. Tyulenev
Abstract Let \((\operatorname{X},\operatorname{d},\mu)\) be a metric measure space with uniformly locally doubling measure \(\mu\). Given \(p \in (1,\infty)\), assume that \((\operatorname{X},\operatorname{d},\mu)\) supports a weak local \((1,p)\)-Poincaré inequality. We characterize trace spaces of the first-order Sobolev \(W^{1}_{p}(\operatorname{X})\)-spaces to subsets \(S\) of \(\operatorname{X}\)
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On the Norms and Eigenvalues of $$r$$ -Circulant Matrices with $$k$$ -Mersenne and $$k$$ -Mersenne–Lucas Numbers Math. Notes (IF 0.6) Pub Date : 2023-10-24 Munesh Kumari, Kalika Prasad, Engin Özkan, Jagmohan Tanti
Abstract In this work, we study the \(r\)-circulant matrix \( C_r = Circ_r(c_0, c_1,c_2,...,c_{n-1})\) such that the entries of \(C_r \) are \(c_i=M_{k,a+ib}\) or \(c_i=R_{k,a+ib}\), where \(M_{k,a+ib}\) and \(R_{k,a+ib}\) are \(k\)-Mersenne and \(k\)-Mersenne–Lucas numbers, respectively. We obtain the eigenvalues and determinants for the matrices and some important identities for the \(k\)-Mersenne
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Asymptotics in the Spectral Parameter for Solutions of $$2 \times 2$$ Systems of Ordinary Differential Equations Math. Notes (IF 0.6) Pub Date : 2023-10-24 A. P. Kosarev, A. A. Shkalikov
Abstract We consider a \(2 \times 2\) system of ordinary differential equations $$y'-By=\lambda Ay, \qquad y=y(x), \quad x \in [0, 1],$$ where \(A=\operatorname{diag}\{a_1(x), a_2(x)\}\), \(B=\{b_{kj}(x)\}_{k, j=1}\), and all functions occurring in the matrices are complex-valued and integrable. In the case $$a_1,a_2, b_{21},b_{12} \in W^n_1[0,1], \qquad b_{11}, b_{22} \in W^{n-1}_1[0,1],$$ we obtain
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On Finite Groups with $$\mathbb{P}_{\pi}$$ -Subnormal Subgroups Math. Notes (IF 0.6) Pub Date : 2023-10-24 T. I. Vasil’eva, A. G. Koranchuk
Abstract Let \(\pi\) be a set of primes. A subgroup \(H\) of a group \(G\) is said to be \(\mathbb{P}_{\pi}\)-subnormal in \(G\) if either \(H=G\) or there exists a chain of subgroups beginning with \(H\) and ending with \(G\) such that the index of each subgroup in the chain is either a prime in \(\pi\) or a \(\pi'\)-number. Properties of \(\mathbb{P}_{\pi}\)-subnormal subgroups are studied. In particular
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Inequalities for Rational Functions with Prescribed Poles Math. Notes (IF 0.6) Pub Date : 2023-10-24 N. A. Rather, A. Iqbal, Ishfaq Dar
Abstract For rational functions \(R(z)=P(z)/W(z)\), where \(P\) is a polynomial of degree at the most \(n\) and \(W(z)=\prod_{j=1}^{n}(z-a_j)\), with \(|a_j|>1,\) \(j\in \{1,2,\dots,n\},\) we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdős-Lax and Turán to rational functions \(R\). In return these reinforced
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Boas and Titchmarsh Type Theorems for Generalized Lipschitz Classes and $$q$$ -Bessel Fourier Transform Math. Notes (IF 0.6) Pub Date : 2023-08-24 S. S. Volosivets, Yu. I. Krotova
Abstract Necessary and sufficient conditions for a function \(f\) to belong to the generalized Lipschitz classes \(H^{m,\omega}_{q,\nu}\) and \(h^{m,\omega}_{q,\nu}\) for fractional \(m\) are given in terms of its \(q\)-Bessel–Fourier transform \(\mathcal F_{q,\nu}(f)\). Dual results are considered as well. An analog of the Titchmarsh theorem for fractional-order differences is proved.
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Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. D. Vishnevskaya, M. V. Demina
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A $$T(P)$$ -Theorem for Zygmund Spaces on Domains Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. V. Vasin, E. S. Dubtsov
Abstract Given a bounded Lipschitz domain \(D\subset \mathbb{R}^d\), a higher-order modulus of continuity \(\omega\), and a convolution Calderón–Zygmund operator \(T\), the restricted operators \(T_D\) that are bounded on the Zygmund space \(\mathcal{C}_{\omega}(D)\) are described. The description is based on properties of the functions \(T_D P\) for appropriate polynomials \(P\) restricted to \(D\)
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Partial Integral Operators on Banach–Kantorovich Spaces Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. D. Arziev, K. K. Kudaybergenov, P. R. Orinbaev, A. K. Tangirbergen
Abstract In this paper, we study partial integral operators on Banach–Kantorovich spaces over a ring of measurable functions. We obtain a decomposition of the cyclic modular spectrum of a bounded modular linear operator on a Banach–Kantorovich space in the form of a measurable bundle of spectra of bounded operators on Banach spaces. The classical Banach spaces with mixed norm are endowed with the structure
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On the Continuous Dependence of a Solution of a Differential Equation on the Right-Hand Side and Boundary Conditions Math. Notes (IF 0.6) Pub Date : 2023-08-24 E. R. Avakov, G. G. Magaril-Il’yaev
Abstract A theorem on the continuous dependence of the solution of a differential equation on the right-hand side and the boundary conditions of general form is proved.
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On Some Properties of the Permanent of Matrices of Small Orders Math. Notes (IF 0.6) Pub Date : 2023-08-24 D. B. Efimov
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Symmetrization and Integral Inequalities Math. Notes (IF 0.6) Pub Date : 2023-08-24 V. S. Klimov
Abstract Steiner symmetrizations of anisotropic integral functionals of multivariate calculus of variations defined on the set of compactly supported functions in the Sobolev class are studied. Applications of the results to embedding theorems for anisotropic Orlicz–Sobolev spaces are outlined, and lower bounds for the values of multidimensional variational problems are found.
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Perturbations of Nonhyperbolic Algebraic Automorphisms of the 2-Torus Math. Notes (IF 0.6) Pub Date : 2023-08-24 V. Z. Grines, D. I. Mints, E. E. Chilina
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Krause Mean Processes Generated by Cubic Stochastic Diagonally Primitive Matrices Math. Notes (IF 0.6) Pub Date : 2023-08-24 Khikmat Saburov
Abstract A multi-agent system is a system of multiple interacting entities, known as intelligent agents, who possibly have different information and/or diverging interests. The agents could be robots, humans, or human teams. Opinion dynamics is a process of individual opinions in which a group of interacting agents continuously fuse their opinions on the same issue based on established rules to reach
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On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. I. Rakhimova
Abstract A differentiation-invariant weighted Fréchet space \({\mathcal E}(\varphi)\) of infinitely differentiable functions in \({\mathbb R}^n\) generated by a countable family \(\varphi\) of continuous real-valued functions in \({\mathbb R}^n\) is considered. It is shown that, under minimal restrictions on \(\varphi\), any continuous linear operator on \({\mathcal E}(\varphi)\) that is not a scalar
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Naimark Problem for a Fractional Ordinary Differential Equation Math. Notes (IF 0.6) Pub Date : 2023-08-24 L. Kh. Gadzova
Abstract For a fractional ordinary differential equation, we consider a problem where the boundary conditions are given in the form of linear functionals. This permits covering a fairly broad class of linear local and nonlocal conditions. The fractional derivative is understood in the sense of Gerasimov–Caputo. A necessary and sufficient condition for the unique solvability of the problem is obtained
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On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces Math. Notes (IF 0.6) Pub Date : 2023-08-24 S. E. Usmanov
Abstract The paper deals with maximal operators associated with a family of singular hypersurfaces in the space \(\mathbb{R}^{n+1}\). The boundedness of these operators in the space of integrable functions is proved for the case in which the singular hypersurfaces are given by parametric equations. The boundedness exponent of maximal operators for spaces of integrable functions is found.
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On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes Math. Notes (IF 0.6) Pub Date : 2023-08-24 M. I. Kamenskii, V. V. Obukhovskii, G. G. Petrosyan
Abstract In the present paper, we consider a control system with feedback in the form of sweeping processes in Hilbert spaces. Using the notion of generalized metric space and A. I. Perov’s contraction mapping principle, we present a theorem on the existence and uniqueness of an almost periodic solution of this system and justify the application of the averaging principle to systems of this kind.
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On the Monopolist Problem and Its Dual Math. Notes (IF 0.6) Pub Date : 2023-08-24 T. V. Bogachev, A. V. Kolesnikov
Abstract In this paper, we study the functional \(\Phi\) that arises in numerous economic applications, in particular, in the monopolist problem. A special feature of these problems is that the domains of such functionals are nonclassical (in our case, increasing convex functions). We use an appropriate minimax theorem to prove the duality relation for \(\Phi\). In particular, an important corollary
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Analog of Schoenberg’s Theorem for $$a$$ -Conditionally Negative Definite Matrix-Valued Kernels Math. Notes (IF 0.6) Pub Date : 2023-08-24 V. P. Zastavnyi
Abstract Schoenberg’s classical 1938 theorem asserts that, given a function \(\rho\colon G\times G\to\mathbb{C}\), the function \(\exp(-t\rho)\) is a positive definite kernel on \(G\times G\) for any \(t>0\) if and only if the kernel \(\rho\) is Hermitian and negative definite on \(G\times G\). An analog of this theorem for matrices was essentially proved by C. Löwner in 1966. Recently (in 2021), C
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On Some Classes of Bases in Finite-Dimensional Lie Algebras Math. Notes (IF 0.6) Pub Date : 2023-08-24 V. V. Gorbatsevich
Abstract In the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in a chosen nilpotent Lie algebra, their number (up to equivalence) is finite. For some Lie algebras of low dimension, it is shown that, when passing from a complex Lie algebra to its realification, the property to have a beautiful basis is lost.
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On Some Quotients of Hyperbolic Groups Math. Notes (IF 0.6) Pub Date : 2023-08-24 O. V. Kulikova
Abstract This paper presents generalizations of results given in the book Geometry of Defining Relations in Groups by A. Yu. Ol’shanskii to the case of noncyclic torsion-free hyperbolic groups. In particular, it is proved that every noncyclic torsion-free hyperbolic group has a non-Abelian torsion-free quotient in which all proper subgroups are cyclic and the intersection of any two of them is nontrivial
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On Some Properties of Solutions of Switched Differential Equations Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. O. Ignatyev
Abstract We consider an important class of hybrid systems, called switching systems, in which a continuous process is controlled by a discrete control between different subsystems. In the case where the switching system has a periodic solution, a lower bound for its period is obtained. For a second-order linear switched differential equation, an inequality is proved that allows one to estimate the
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On the Computational Complexity of Compressed Power Series Math. Notes (IF 0.6) Pub Date : 2023-08-24 E. A. Karatsuba
Abstract We present computational algorithms and complexity estimates for power series in which all exponents are positive integers raised to one and the same integer power \(\ge2\).
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Differential Calculi in Group Algebras and Group Ends Math. Notes (IF 0.6) Pub Date : 2023-08-24 A. A. Arutyunov
Abstract Graphs generalizing Cayley graphs and arising from various actions of groups on themselves are studied. A relationship between such graphs and subalgebras of operators in a group ring is established, which permits one to obtain a formula for the number of ends of such graphs in terms of the dimensions of appropriate character spaces. Examples of group actions and the corresponding graphs are
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Many-Dimensional Duhamel Product in the Space of Holomorphic Functions and Backward Shift Operators Math. Notes (IF 0.6) Pub Date : 2023-06-20 P. A. Ivanov, S. N. Melikhov
Abstract The system \(\mathcal D_0\) of partial backward shift operators in a countable inductive limit \(E\) of weighted Banach spaces of entire functions of several complex variables is studied. Its commutant \(\mathcal K(\mathcal D_0)\) in the algebra of all continuous linear operators on \(E\) operators is described. In the topological dual of \(E\), a multiplication \(\circledast\) is introduced
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Contact Vectors of Point Lattices Math. Notes (IF 0.6) Pub Date : 2023-06-20 V. P. Grishukhin
Abstract The contact vectors of a lattice \(L\) are vectors \(l\) which are minimal in the \(l^2\)-norm in their parity class. It is shown that, in the space of all symmetric matrices, the set of all contact vectors of the lattice \(L\) defines the subspace \(M(L)\) containing the Gram matrix \(A\) of the lattice \(L\). The notion of extremal set of contact vectors is introduced as a set for which
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Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set Math. Notes (IF 0.6) Pub Date : 2023-06-20 M. V. Balashov
Abstract Many problems, for example, problems on the properties of the reachability set of a linear control system, are reduced to finding the projection of zero onto some convex compact subset in a finite-dimensional Euclidean space. This set is given by its support function. In this paper, we discuss some minimum sufficient conditions that must be imposed on a convex compact set so that the gradient
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Slow Convergences of Ergodic Averages Math. Notes (IF 0.6) Pub Date : 2023-06-20 V. V. Ryzhikov
Abstract Birkhoff’s theorem asserts that, for an ergodic automorphism, time averages converge to the space average. Krengel showed that, for a given sequence \(\psi(n)\to+0\) and any ergodic automorphism, there exists an indicator function such that the corresponding time means converge a.e. slower than \(\psi\). We give a new proof of the absence of estimates for rates of convergence, answering a
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On the Question of the Definability of Certain Classes of Completely Decomposable Abelian Torsion-Free Groups by Their Homomorphism Groups Math. Notes (IF 0.6) Pub Date : 2023-06-20 T. A. Pushkova, A. M. Sebel’din
Abstract Let \(C\) be an Abelian group. A class \(X\) is said to be a \(_{C}H\)-class if, for any groups \(A,B\in X\), a group isomorphism of \(\operatorname{Hom}(C,A)\) and \(\operatorname{Hom}(C,B)\) implies an isomorphism of the groups \(A\) and \(B\). In the paper, conditions on a completely decomposable Abelian group \(C\) are investigated under which a class of certain completely decomposable
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Improvement of Nonmonotone Complexity Estimates of $$k$$ -Valued Logic Functions Math. Notes (IF 0.6) Pub Date : 2023-06-20 V. V. Kochergin, A. V. Mikhailovich
Abstract The problem of determining the nonmonotone complexity of the implementation of \(k\)-valued logic functions by logic circuits in bases consisting of all monotone (with respect to the standard order) functions and finitely many nonmonotone functions is investigated. In calculating the complexity measure under examination only those elements of the circuit which are assigned nonmonotone basis
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On Nonfree Actions of Commuting Involutions on Manifolds Math. Notes (IF 0.6) Pub Date : 2023-06-20 D. V. Gugnin
Abstract A new lower bound is obtained relating the rational cup-length of the base and that of the total space of branched coverings of orientable manifolds for the case in which the branched covering is a projection onto the quotient space by the action of commuting involutions on the total space. This bound is much stronger than the classical Berstein–Edmonds 1978 bound which holds for arbitrary
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Landweber Exactness of the Formal Group Law in $$c_1$$ -Spherical Bordism Math. Notes (IF 0.6) Pub Date : 2023-06-20 G. S. Chernykh
Abstract We describe the structure of the coefficient ring \(W^*(pt)=\varOmega_W^*\) of the \(c_1\)-spherical bordism theory for an arbitrary \(SU\)-bilinear multiplication. We prove that for any \(SU\)-bilinear multiplication the formal group of the theory \(W^*\) is Landweber exact. Also we show that after inverting the set \(\mathcal{P}\) of Fermat primes there exists a complex orientation of the
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Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time Math. Notes (IF 0.6) Pub Date : 2023-06-20 A. G. Kachurovskii, I. V. Podvigin, A. Zh. Khakimbaev
Abstract We consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic theorem with discrete time. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and the complete description of all such subspaces is obtained. Uniform convergence
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Close Turning Points and the Harper Operator Math. Notes (IF 0.6) Pub Date : 2023-06-20 A. A. Fedotov
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On the Solvability of Nonlinear Parabolic Functional-Differential Equations with Shifts in the Spatial Variables Math. Notes (IF 0.6) Pub Date : 2023-06-20 O. V. Solonukha
Abstract The first mixed boundary value problem for a nonlinear functional-differential equation of parabolic type with shifts in the spatial variables is considered. Sufficient conditions are proved under which a nonlinear differential-difference operator is demicontinuous, coercive, and pseudomonotone on the domain of the operator \(\partial_t\). Based on these properties, existence theorems for
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Estimate of the Second Coefficient of Holomorphic Mappings of a Disk into Itself with Two Fixed Points Math. Notes (IF 0.6) Pub Date : 2023-06-20 O. S. Kudryavtseva, A. P. Solodov
Abstract On the class of holomorphic self-mappings of the unit disk with an internal and a boundary fixed point, we consider the problem of describing the domains of Taylor coefficients depending on the values of the angular derivative at the boundary fixed point. An optimal horocycle containing the domain of the second coefficient is found.