查看更多>>摘要：We prove that any mu rth order derivatives of degree -n Bernstein polynomials are linearly independent if and only if mu <= n - r + 1, where r is an element of {1, 2, ... , n}. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Understanding fluid phase behavior, like VLE, in high P & T conditions is crucial for developing high-fidelity simulations of chemically reacting flows in liquid-fueled combustion systems and also forms an integral part of the design-modeling of the control processes in chemical industries. Two data-driven models have been proposed in this study, each of which was competent in estimating VLE for the Type III binary systems of C-10/N-2 and C-12/N-2, at pressures ranging up to 50-60 MPa. Both models showed better performance in predicting equilibrium pressure as compared to VLE modeled using PREOS. A modified model has also been proposed, capable of estimating the full phase envelope for the binary systems of C-10/N-2 and C-12/N-2 across a wide range of temperatures, and thus exhibit the mixture critical pressure at the concerned temperature. The diverse applicability of the proposed network architecture was further exhibited while estimating the VLE of a ternary system of C-1/C-10/N-2. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we first establish a general Marsden's identity for Unified and Extended B-splines (UE B-splines or Omega B-splines for short). Then, by using this result, we construct univariate omega spline quasi-interpolants on a bounded interval and we study their approximation errors. For particular values of omega, we refind some already developed quasi-interpolants. As a practical side of these operators, we give some applications to numerical analysis especially quadrature formulas, differentiation and numerical solutions of linear Fredholm integral equations, which are illustrated by some numerical examples. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the "optimal "coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a generalized interval type-2 fuzzy random variable based algorithm under mean chance value at risk criterion. First, we introduce the interval type-2 fuzzy random variable and then we propose a scalar expected value of the interval type-2 fuzzy random variables. Also the new concepts of mean chance value at risk and mean chance conditional value at risk are discussed. An application to the inverse 1 median location problem on tree network with uncertain costs proves that this algorithm solves this problem in O(n(2) log n) time. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper shows the exponential convergence of the Sinc-collocation method based on the double exponential (DE) transformation applied to eighth-order boundary value problems (BVPs). Then using Kantorovich's theorem, we obtain the exponential convergence of the non-linear eighth-order ordinary differential equation (ODE). Furthermore, we extend the analytical results to the arbitrary even-order case. In the numerical experiment, several linear and nonlinear examples are provided to verify our theoretical analysis. Meanwhile, the solution yielded via DE transformation is compared with those obtained by single exponential (SE) transformation and existing method to demonstrate the high efficiency and accuracy of our method. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in the plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the symmetry group of the obtained trigonometric curve. The algorithm exploits the fact that the introduced unique assignment of the trigonometric curve to each closed discrete curve commutes with isometries. For understandable reasons, an essential part of the paper is devoted to determining rotational and axial symmetries of trigonometric curves. We also show that the formulated approach can be easily applied on unorganized clouds of points. A functionality of the designed detection method is presented on several examples. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward-backward-forward algorithm. Under the monotonicity assumption on the mapping F and other moderate conditions, we derive some asymptotic convergence properties and O(1/k) convergence rate in terms of the restricted gap function values for the proposed algorithms. Furthermore, under the bounded metric subregularity condition, we investigate the linear convergence rate and oracle complexity bounds for the proposed algorithms when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate of inverted right perpendiculark+1inverted left & nbsp;perpendicular(-s) with s > 0, the mean-squared distance of the iterates to the solution set decays at a corresponding polynomial rate, while the iterations and oracle complexities to obtain an epsilon-solution are O(1/epsilon(1/s)) and O(1/epsilon(1+1/s)) respectively. Finally, some numerical experiments on stochastic network games and traffic assignment problems indicate that the proposed algorithms are efficient. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
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