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1.
<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.  相似文献   

2.
<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.  相似文献   

3.
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.  相似文献   

4.
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions.  相似文献   

5.
<正>Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.  相似文献   

6.
本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.  相似文献   

7.
<正>The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J.Comput.Phys.,1999;2000],respectively.This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations,where an adaptive parameter 17 is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.  相似文献   

8.
In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.  相似文献   

9.
This paper is concerned with a singular second-order nonlinear boundary value problem with a time depending on derivative operator and posed on the positive half-line. The nonlinearity is derivative-dependent, which has singularities at t=0 and/or x=0, and may change sign. The method of the upper and lower solutions on unbounded domains combined with the topological degree theory are employed to prove the existence and multiplicity of solutions.  相似文献   

10.
<正>The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented.Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed.Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.  相似文献   

11.
Paul Levande 《Discrete Mathematics》2010,310(17-18):2460-2467
We give two combinatorial proofs and partition-theoretic interpretations of an identity from Ramanujan’s lost notebook. We prove a special case of the identity using the involution principle. We then extend this into a direct proof of the full identity using a generalization of the involution principle. We also show that the identity can be rewritten into a modified form that we prove bijectively. This fits the identity into Pak’s duality of partition identities proven using the involution principle and partition identities proven bijectively. The original identity was first proven algebraically by Andrews as a consequence of an identity of Rogers’ and combinatorially by Kim, while the modified form of the identity generalizes an identity recently found by Andrews and Warnaar related to the product of partial theta functions.  相似文献   

12.
In this paper, we prove an addition formula for the Jacobian theta function using the theory of elliptic functions. It turns out to be a fundamental identity in the theory of theta functions and elliptic function, and unifies many important results about theta functions and elliptic functions. From this identity we can derive the Ramanujan cubic theta function identity, Winquist's identity, a theta function identities with five parameters, and many other interesting theta function identities; and all of which are as striking as Winquist's identity. This identity allows us to give a new proof of the addition formula for the Weierstrass sigma function. A new identity about the Ramanujan cubic elliptic function is given. The proofs are self contained and elementary.  相似文献   

13.
The purpose of the present paper is to establish an identity involving invariant polynomials of two matrix arguments. This identity is a generalization of a well known identity that gives evaluation of the Gauss hypergeometric function when the argument matrix is identity. Applications of the identity derived in this article are also given.  相似文献   

14.
The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobás inequality for two set families can be lifted to an identity.In this paper, we show another generalization of the AZ identity. The new identity implies an identity which characterizes the deficiency of the Bollobás inequality for an intersecting Sperner family. We also give some consequences relating to Helly families and LYM-style inequalities.  相似文献   

15.
In this paper, we establish a three-term theta function identity using the complex variable theory of elliptic functions. This simple identity in form turns out to be quite useful and it is a common origin of many important theta function identities. From which the quintuple product identity and one general theta function identity related to the modular equations of the fifth order and many other interesting theta function identities are derived. We also give a new proof of the addition theorem for the Weierstrass elliptic function ℘. An identity involving the products of four theta functions is given and from which one theta function identity by McCullough and Shen is derived. The quintuple product identity is used to derive some Eisenstein series identities found in Ramanujan's lost notebook and our approach is different from that of Berndt and Yee. The proofs are self contained and elementary.  相似文献   

16.
In this paper we give a simple proof of the Jacobi triple product identity by using basic properties of cube roots of unity. Then we give a new proof of the quintuple product identity, the septuple product identity and Winquist’s identity by using the Jacobi triple product identity and basic properties of cube and fifth roots of unity. Furthermore, we derive some new product identities by this uniform method. Later, we give some generalizations of those identities. Lastly, we derive some modular equations.  相似文献   

17.
We analyze a two-parameter q-series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.  相似文献   

18.
Applications of residues to combinatorial identities   总被引:1,自引:0,他引:1  
A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon's master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.

  相似文献   


19.
The concept of a convolution identity for tensors is introduced and it is proved that any convolution identity for tensors on a finite-dimensional space follows from a convolution identity equivalent to the classical Cayley-Hamilton identity.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 211–214, 1982.  相似文献   

20.
We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of an arbitrary associative algebra. One is a consequence of the other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an algebra, then the multiplication operation in that algebra is associative. We find a generalization of the obtained results to the super case and give a generalization of the fundamental identity in the case of arbitrary elements. For nondegenerate even symplectic (super)manifolds, we discuss analogues of the fundamental identity.  相似文献   

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