Given graph G=(V,E) with vertex set V and edge set E, the max k-cut problem seeks to partition the vertex set V into at most k subsets that maximize the weight (number) of edges with endpoints in different parts. This...
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Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the se...
The paper presents a survey of the results obtained by the members of the department of Mathematical Statistics in the field of analytic and asymptotic properties of mixture probability models. Much attention is paid ...
The paper presents a survey of the results obtained by the members of the department of Mathematical Statistics in the field of analytic and asymptotic properties of mixture probability models. Much attention is paid to the representation of some widely applied absolutely continuous probability distributions (gamma, Weibull, Student, Snedecor–Fisher, Mittag-Leffler, Burr, etc.) as mixtures of distributions possessing maximum differential entropy (normal and exponential). Some useful discrete distributions that are representable as mixed Poisson distributions are discussed as well. Examples are presented of limit theorems for statistics constructed from samples with random sizes in which the distributions mentioned above are limit laws. Also, the estimates of convergence rate in these theorems are presented. Some problems related to the application of methods of intellectual analysis of big arrays of dynamically accumulated data based on mixture probability models are discussed.
In this paper, we present discontinuous Galerkin (DG) finite element discretizations for a class of linear hyperbolic port-Hamiltonian dynamical systems. The key point in constructing a port-Hamiltonian system is a St...
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This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains...
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Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for s...
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We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems. The exact time integration algorithm fo...
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We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of t...
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Point cloud is a crucial data format for 3D vision, but its irregularity makes it challenging to comprehend the associated geometric information. Although some previous research has attempted to improve deep learning ...
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This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆...
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This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆ of the nonlinear wave equation ☆□☆g☆u☆+☆q☆u☆m☆=☆0☆, ☆m☆≥☆4☆, from the Dirichlet-to-Neumann map. Our proof is based on the recent higher-order linearization method and use of Gaussian beams. We also extend earlier uniqueness results by removing the assumptions of convex boundary and that pairs of light-like geodesics can intersect only once. For this, we construct special light-like geodesics and other general constructions in Lorentzian geometry. We expect these constructions to be applicable in studies of related problems as well.
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