We introduce a priori Sobolev-space error estimates for the solution of arbitrary nonlinear, and possibly parametric, PDEs that are defined in the strong sense, using Gaussian process and kernel based methods. The pri...
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We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-...
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In this study, I compute the static dipole polarizability of main-group elements using the finite-field method combined with relativistic coupled-cluster and configuration interaction simulations. The computational re...
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Let P be a simple polygon with n vertices, and let A be a set of m points or line segments inside P. We develop data structures that can efficiently count the objects from A that are visible to a query point or a quer...
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A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimen...
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A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space, problem, is approximated by a polynomial ansatz and its convergence is analyzed. An ℓ1 penalty term is employed, which combined with the proximal point method, allows to find sparse solutions for the learning problem. The approach requires multiple evaluations of the elements of the polynomial basis and of their derivatives. In order to do this efficiently a graph-theoretic algorithm is devised. Several examples underline that the proposed methodology provides a promising approach for mitigating the curse of dimensionality which would be involved in case the optimal feedback law was obtained by solving the Hamilton Jacobi Bellman equation.
The current analysis executes a numerical exploration of Magnetohydrodynamic (MHD) free convective heat transmission in a square enclosure filled with copper–water nanofluid by considering the effect of heat absorpti...
The current analysis executes a numerical exploration of Magnetohydrodynamic (MHD) free convective heat transmission in a square enclosure filled with copper–water nanofluid by considering the effect of heat absorption/generation. The left and right walls are kept as adiabatic, the top wall is presumed to be hot, and the bottom wall is adiabatic which has a cold slit in the center. Using a two-dimensional Navier–Stokes equation in Cartesian form, the present analysis is theoretically modeled. To solve the governing constitutive equations in non-dimensional form, the Marker and Cell (MAC) approach is used. The MAC method employs a staggered grid where velocity components are stored at the cell faces, and pressure is stored at the cell centers. This arrangement helps in accurately enforcing the incompressibility condition (i.e., the divergence-free condition of the velocity field). The impact of the Rayleigh number, Hartmann number, heat absorption/generation coefficient, and nanoparticle volume fraction are examined to explore the features of free convective heat transmission within the enclosure. Results of these parameters have been graphically visualized by means of streamlines, isotherms contours, as well as local and mean Nusselt numbers. According to findings, the performance of heat transmission within the cavity is substantially influenced by the variations in the magnetic field’s strength, the volume fraction of Cu-nanoparticles, and heat absorption/generation. The average rate of heat transmission within the enclosure can be magnified by replacing the internal heat absorption with internal heat generation. The suspension of $$5\%$$ Cu nanoparticles into water boosts the mean rate of heat transmission of water by $$19.314\%.$$
The separating Noether number βsep(G) of a finite group G is the minimal positive integer d such that for every G-module V there is a separating set of degree ≤ d. In this manuscript, we investigate the separating N...
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Reconstructing signals which are embedding spatial patterns such as Electrical resistivity tomography, is a process that should require to reconstruct first the spatial correlation of the damaged signals. This paper p...
Reconstructing signals which are embedding spatial patterns such as Electrical resistivity tomography, is a process that should require to reconstruct first the spatial correlation of the damaged signals. This paper proposes an approach that implements an Unstationary Kriging (UNK) to reconstruct the experimental variogram of a damaged synthetic pseudo section within a set of pseudo sections coming from the same survey. We used and compared 02 other simple methods which are Linear Regression (LR) and Ordinary Kriging (OK), to test the hypothesis we formulate to link the experimental variograms coming from the same ERT survey. We implemented the UNK using Discrete Fourier Transforms (DFT) for trend modeling. After an implementation of the hybrid process (UNK) on 02 sets of data which are synthetics, we observed that the LR and the UNK methods present an interest. They both reconstruct signals with a +90% rate of accuracy, but when there is no structure or spatial correlation within the data, the LR is unstable. DFT was also tested alone for reconstruction but was mainly used in this study to help in computing the trends for each set of variographic signals. In the end, we conclude on an evidence that is: the proposed hybrid process is a promising way to reconstruct variographic signals, since we can improve it after more time invested to dig deep into the modeling of each of his components.
作者：
Liu, HaixiaSchool of Mathematics and Statistics
Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China
Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the L-extended unco...
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This paper introduces and explores the concept of fuzzy ϕ-contraction to establish the existence of n-tupled coincidence points in partially ordered GV-fuzzy metric spaces. Using the unique properties of the H-type tr...
This paper introduces and explores the concept of fuzzy ϕ-contraction to establish the existence of n-tupled coincidence points in partially ordered GV-fuzzy metric spaces. Using the unique properties of the H-type triangular norm, we integrate this norm into GV-fuzzy metric spaces. The mappings under consideration exhibit the mixed monotone property with respect to partial ordering. Furthermore, we employ the mixed g-monotone property of mappings to analyze their behavior within the given framework. To validate our theoretical findings, we present an illustrative example, which demonstrates the higher-dimensional analysis of the ϕ-contraction principle used in our primary results. As an application, we investigate the existence of solutions for a system of second-kind Fredholm nonlinear integral equations. Employing the developed fixed-point results, we establish sufficient conditions that guarantee the solvability of such integral equations within the GV-fuzzy metric space setting.
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