Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The \(n \) -simplex equation was introduced by Zamolodchikov as a generalization of the Yang–Baxter equation which becomes the \(2 \) -simplex equation in this terms. In the present article, we suggest general approaches to construction of solutions of the \(n \) -simplex equation, describe certain types of solutions, and introduce an operation that allows us to construct, under certain conditions, a solution of the \((n + m + k)\) -simplex equation from solutions of the \((n + k) \) -simplex equation and \((m + k) \) -simplex equation. We consider the tropicalization of rational solutions and discuss its generalizations. We prove that a solution of the \(n \) -simplex equation on \(G \) can be constructed from solutions of this equation on \(H \) and \(K \) if \(G \) is an extension of a group \(H \) by a group \(K \) . We also find solutions of the parametric Yang–Baxter equation on \(H\) with parameters in \(K \) . We introduce ternary algebras for studying the 3-simplex equation and present examples of such algebras that provide us with solutions of the 3-simplex equation. We find all elementary verbal solutions of the 3-simplex equation on a free group. \( \) PubDate: 2024-03-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We describe constructions that are used in the proof of the main result of the first part of the article. They are based on automorphisms and properties of the Cantor space. PubDate: 2024-03-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We prove a sub-Lorentzian analog of the area formula for intrinsically Lipschitz mappings of open subsets of Carnot groups of arbitrary depth with a sub-Lorentzian structure introduced on the image space. PubDate: 2024-03-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider the problem on optimal quadrature formulas for curvilinear integrals of the first kind that are exact for constant functions. This problem is reduced to the minimization problem for a quadratic form in many variables whose matrix is symmetric and positive definite. We prove that the objective quadratic function attains its minimum at a single point of the corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there exists a unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the least possible norm of the error functional in the conjugate space. We show that the tuple of weights of the optimal quadrature formula is a solution of a special nondegenerate system of linear algebraic equations. PubDate: 2024-03-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider local sharply transitive representations of the algebra \(sl_3(\mathbb {R}) \) in the space of local vector fields with analytic coefficients in \( \mathbb {R}^{8}\) that are defined in a neighborhood of the origin. We find a system of differential equations that describes such representations. PubDate: 2023-12-01 DOI: 10.1134/S1055134423040077

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We study solvability questions for the problem on realization of operator functions for an invariant polylinear regulator of a higher-order differential system in an infinite-dimensional separable Hilbert space. This is a nonstationary coefficient-operator inverse problem for multilinear evolution equations whose dynamic order is higher than one (notice that nonautomonous hyperbolic systems belong to this class of problems). We analyze semiadditivity and continuity for a nonlinear Rayleigh–Ritz functional operator and obtain an analytic model of an invariant polylinear regulator. This model allows us to combine two bundles of trajectory curves induced by different invariant polylinear regulators in a differential system and obtain a family of admissible solutions of the initial differential system in terms of an invariant polylinear action. The obtained results can be applied in the general qualitative theory of nonlinear infinite-dimensional adaptive control systems described by higher-order multilinear nonautonomous differential systems (including neuromodelling). PubDate: 2023-12-01 DOI: 10.1134/S1055134423040053

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider a series of related extremal problems for holomorphic functions in a polydisc \(\mathbb {D}^m \) , \(m\in \mathbb {N}\) . The sharp inequality \( f(z) \le \mathscr {C}\, \ f\ ^{\alpha _1}_{L^{p_1}_{\phi _1}(G_1)}\, \ f\ ^{\alpha _0}_{L^{p_0}_{\phi _0}(G_0)} \) , with \(0<p_0,p_1\le \infty \) , is established between the value of a function holomorphic in \( \mathbb {D}^m\) and the norms of its limit values on measurable sets \(G_1 \) and \(G_0 \) , where \(G_0=\mathbb {S}^m\setminus G_1 \) and \(\mathbb {S}^m \) is the skeleton (the Shilov boundary) of \(\mathbb {D}^m \) . This result is an analog of the two-constant theorem by the Nevanlinna brothers. We study conditions under which the above inequality provides us with the value of the modulus of continuity of the functional for holomorphic extension of a function on \( G_1\) at a prescribed point of the polydisc. In these cases, a solution was obtained of the problem of optimal recovery of a function from approximately given values on a part of the skeleton \(G_1\) and the related problem of the best approximation of the functional of the continuation of a function into a polydisk from \( G_1.\) PubDate: 2023-12-01 DOI: 10.1134/S1055134423040016

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We construct an admissible set \(\mathbb {A}\) such that the family of all \( \mathbb {A}\) -computably enumerable sets possesses a negative computable \(\mathbb {A}\) -numbering but lacks positive computable \(\mathbb {A}\) -numberings. We also discuss the question on existence of minimal negative \(\mathbb {A} \) -numberings. PubDate: 2023-12-01 DOI: 10.1134/S105513442304003X

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider the problem of constructing explicit consistent estimators of finite-dimensional parameters of nonlinear regression models using various nonparametric kernel estimators. PubDate: 2023-12-01 DOI: 10.1134/S1055134423040065

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Within the framework of geometric tomography, inverse problems of photometry, wave optics, and discrete tomography, we study questions on reconstruction of the spatial location and luminosity of a discrete distribution of radiant sources from its images obtained with the use of a small number of optical systems. We analyze the problem on finding geometric parameters of such a distribution and describe sources of ambiguity. We consider the inverse problem on reconstruction of a discrete distribution that consists of incoherent and monochromatic sources and suggest uniqueness criteria for its solution. We also suggest a constructive approach to numerical solution of the inverse problem on reconstruction of the coordinates and luminosity of a family of radiant pinpoint sources from their images. PubDate: 2023-12-01 DOI: 10.1134/S1055134423040028

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider a model of antiviral immune response suggested by G.I. Marchuk. The model is described by a system of differential equations with several delays. We study asymptotic stability for a stationary solution of the system that corresponds to a completely healthy organism. We estimate the attraction set of this stationary solution. We also find estimates of solutions characterizing the stabilization rate at infinity. A Lyapunov–Krasovskiĭ functional is used in the proof. PubDate: 2023-12-01 DOI: 10.1134/S1055134423040089

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider the generating function \(\Phi \) for the number \(f_{\Gamma }(n) \) of rooted spanning forests in the circulant graph \(\Gamma \) , where \(\Phi (x)= \sum _{n=1}^{\infty } f_{\Gamma }(n) x^n\) and either \(\Gamma =C_n(s_1,s_2,\dots ,s_k) \) or \(\Gamma =C_{2n}(s_1,s_2,\dots ,s_k,n) \) . We show that \(\Phi \) is a rational function with integer coefficients that satisfies the condition \(\Phi (x)=-\Phi (1/x) \) . We illustrate this result by a series of examples. PubDate: 2023-12-01 DOI: 10.1134/S1055134423040041

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In the present article, we prove that every countable infinite group \(G \) is embeddable into a countable infinite simple group \(\overline {G}\) such that every equation of the form $$ w(x_1,\dots ,x_n) = g $$ is solvable in \(\overline {G} \) , where \(w \) is a nontrivial reduced group word in variables \(x_1,\dots ,x_n \) and \(g\in G \) . PubDate: 2023-08-01 DOI: 10.1134/S1055134423030045

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In the present article, we consider a mixed boundary value problem in a quarter-space for a pseudohyperbolic equation. We find conditions on the right-hand side of the equation that guarantee existence of solutions of this problem in Sobolev spaces with exponential weight. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030082

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In the present article, we consider a class of systems of linear differential equations with infinite distributed delay and periodic coefficients. We use the Lyapunov–Krasovskiĭ functional and obtain sufficient conditions for exponential stability of the zero solution, find conditions on perturbation of the coefficients of the system that guarantee preservation of exponential stability, and establish estimates for the norms of solutions of the initial and perturbed systems that characterize exponential decay at infinity. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030094

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In the present article, we study universal, minimal, and complete numberings of families of arithmetic sets. We show that, for every \(m\in {\mathbb N}\) and every nontrivial \( \Sigma ^0_{m+2}\) -computable family \(\mathcal S \) , there exists a \(\Sigma ^0_{m+2} \) -computable numbering that is not universal with respect to positive reducibilities and is complete with respect to each element \(B\in \mathcal S \) . For finite families of computably enumerable sets, we obtain necessary and sufficient conditions for existence of numberings that are complete, computable, and not universal with respect to positive reducibilities. For every infinite \(\Sigma ^0_{m+3} \) -computable family \(\mathcal S \) and every element \(B\in \mathcal S \) , we construct a \(\Sigma ^0_{m+3} \) -computable numbering that is complete with respect to \(B \) and minimal with respect to classical and positive reducibilities. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030057

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: For contact mappings of Carnot groups of depth two whose image is endowed with a sub-Lorentzian structure, we prove local properties of the surfaces-images and explicitly deduce a sub-Lorentzian analog of the area formula. The result in particular also holds for Lipschitz mappings in the sub-Riemannian sense. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030069

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Let \(R_n \) be the centered and normalized number of cycles of fixed length contained in a generalized random graph with \(n \) vertices. We obtain a Höffding-type exponential inequality for the tail probability of \(R_n\) . PubDate: 2023-08-01 DOI: 10.1134/S1055134423030021

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: For systems of linear autonomous delay differential equations, we develop a method for studying stability, which consists in constructing an auxiliary system whose asymptotic properties are close to those of the original system. Alongside new signs of stability, we find sharp estimates for the rate at which solutions tend to zero. The effectiveness of the results obtained is illustrated by a number of examples. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030070

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In the present article, we consider the problem on location of the matrix spectrum with respect to a parabola. In terms of solvability of a matrix Lyapunov type equation, we prove theorems on location of the matrix spectrum in certain domains \({\cal P}_i \) (bounded by a parabola) and \({\cal P}_e \) (lying outside the closure of \({\cal P}_i \) ). A solution to the matrix equation is constructed. We use this equation and prove an analog of the Lyapunov–Krein theorem on dichotomy of the matrix spectrum with respect to a parabola. PubDate: 2023-08-01 DOI: 10.1134/S1055134423030033