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Abstract: Abstract In this paper, we introduce a variant of the Lambek calculus allowing empty antecedents. This variant uses two connectives: the left division and a unary modality that occurs only with negative polarity and allows weakening in antecedents of sequents. We define the notion of a proof net for this calculus, which is similar to those for the ordinary Lambek calculus and multiplicative linear logic. We prove that a sequent is derivable in the calculus under consideration if and only if there exists a proof net for it. Thus, we establish a derivability criterion for this calculus in terms of the existence of a graph with certain properties. The size of the graph is bounded by the length of the sequent. PubDate: 2022-05-20

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Abstract: Abstract Gaussian random processes whose variances reach their maximum values at unique points are considered. Exact asymptotic behavior of probabilities of large absolute maximums of their trajectories have been evaluated using the double sum method under the widest possible conditions. PubDate: 2022-05-18

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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.

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: Abstract Limit distributions of the maximum of independent copies of a transformation of a Gaussian random variable are studied. Sufficient and necessary conditions are found for the transformations belonging to Fréchet and Weibull maximum domains of attraction. Simple sufficient conditions are also given. PubDate: 2022-05-16

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Abstract: Abstract The extremal problem of hypergraph colorings related to the Erdős–Hajnal property B-problem is considered. Let k be a natural number. The problem is to find the value of mk(n) equal to the minimal number of edges in an n-uniform hypergraph that does not admit 2-colorings of the vertex set such that every edge of the hypergraph contains at least k vertices of each color. In this paper, we obtain new lower bounds for mk(n). PubDate: 2022-05-16

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Abstract: Abstract Exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are found, in the case where all working and repair times are bounded by an exponential random variable (upper and lower), and working and repair times can be dependent. The convergence rate of the availability factor is estimated. PubDate: 2022-05-16

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Abstract: We study wavelet decompositions of information flows connected with trajectories in the space of distributions. We obtain an embedding criterion and the wavelet decomposition for the space of distributions and the space of dipoles. We show that it is possible to pass from the continual to the discrete case. PubDate: 2022-05-10

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Abstract: Abstract A numerical solution of the system of linear Volterra–Stieltjes integral equations of the second kind has been found and analyzed using the so-called generalized trapezoid rule. Conditions for estimating the error have also been determined and justified. A solution of an example obtained using the proposed method is given. PubDate: 2022-05-10

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Abstract: Abstract The linear Beltrami equation on the Riemann sphere is studied under the assumption that its measurable complex-valued coefficient μ(z) has a compact support in ℂ and ‖μ‖∞ = 1 Sufficient conditions for the existence of regular homeomorphic \( {W}_{\mathrm{loc}}^{1,1} \) solutions to the Beltrami equation with hydrodynamic normalization at infinity are given, in particular, provided that either the dilatation Kμ has the boundedmean- oscillation majorant or the so-called tangent dilatations \( {K}_{\mu}^T \) satisfy the integral divergence conditions of the Lehto type. The corresponding applications to the degenerate A-harmonic equation associated with the Beltrami equation have also been formulated. PubDate: 2022-05-10

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Abstract: Abstract A class of H-analytic (differentiable by Hausdorff) functions in a three-dimensional noncommutative algebra e \( {\overset{\sim }{\mathbbm{A}}}_2 \) over the field ℂ is considered. All H-analytic functions are described in the explicit form. The obtained description is applied to the integral representation of these functions, and the mentioned functions are also applied when solving some PDEs. PubDate: 2022-05-10

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Abstract: Abstract In contrast to finite dimensional Teichmüller spaces, all non-expanding invariant metrics on the universal Teichmüller space coincide. This important fact found various applications. We give its new, simplified proof based on some deep features of the Grunsky operator, which intrinsically relate to the universal Teichmüller space. This approach also yields a quantitative answer to Ahlfors’ question. PubDate: 2022-05-07

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Abstract: We consider the Dirichlet problem for the Hamilton–Jacobi equation in the three-dimensional Euclidean space with boundary condition on a smooth parametrized curve Γ. The minimax solution to the boundary value problem loses its smoothness on the bisector of the curve Γ. We propose an analytic-numerical approach to construction of minimax solutions. The approach is based on the procedure for finding boundary of singular surfaces and numerical construction of the singular set Γ. PubDate: 2022-05-06

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Abstract: We prove counterparts of the Lindelöf theorem in the spaces of entire functions and analytic functions in a half-plane the growth of which is determined by the proximate order in the sense of Boutroux. PubDate: 2022-05-06

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Abstract: We prove the Harnack inequality for nonnegative solutions to an equation with p(x)-Laplacian and partially Muckenhoupt weight, where p(x) takes two constant values p and q, the phase interface is a hyperplane, and the weight satisfies the Muckenhoupt Ap-condition in one part and the Muckenhoupt Aq-condition in another part of the domain PubDate: 2022-05-06

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Abstract: We study the influence of oscillatory perturbations on nonlinear nonisochronous oscillatory systems in the plane. We assume that the perturbation amplitude decays and the frequency is unboundedly increasing in time. We study capture into resonance in the case where the amplitude of the system unboundedly increases and the frequency adjusts to the perturbation frequency. We discuss the existence, stability, and asymptotic behavior of resonance solutions at long times. We propose the technique based on averaging method and construction of the Lyapunov functions. The results obtained are applied to the Duffing oscillator with decaying parametric perturbations. PubDate: 2022-05-05

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Abstract: We consider a waveguide that occupies a domain G with several cylindrical ends and is descried by the nonstationary equation where is a selfadjoint second order elliptic operator with variable coefficients. For the boundary condition we consider the Dirichlet, Neumann, or Robin ones. For the stationary problem with parameter we describe eigenfunctions of the continuous spectrum and a scattering matrix. Based on the limiting absorption principle, we obtain an expansion in eigenfunctions of the continuous spectrum. We compute wave operators and prove their completeness. We define a scattering operator and describe its connection with the scattering matrix. As a consequence, we construct scattering theory for the wave equation PubDate: 2022-05-05

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Abstract: Several mean value identities for harmonic and panharmonic functions are reviewed along with the corresponding inverse properties. The latter characterize balls, annuli, and strips analytically via these functions. PubDate: 2022-05-05

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Abstract: Abstract The result of M.A. Lavrentiev on the product of conformal radii of two non-overlapping simply connected domains has been generalized and strengthened. A method that allowed new estimates for the products of the inner radii of mutually non-overlapping domains to be obtained has been proposed. PubDate: 2022-05-02

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Abstract: Abstract Continued fraction and quasi-reciprocal continued fraction expansions of the generating function of Bernoulli numbers have been obtained. The convergence and uniform convergence of continued fraction expansions have been proved. Representations of the generating function of Bernoulli polynomials in the form of the product of three continued fractions, as well as the product of three quasi-reciprocal continued fractions, have been found. PubDate: 2022-04-30