共查询到20条相似文献,搜索用时 15 毫秒
1.
Peter Bürgisser 《Foundations of Computational Mathematics》2004,4(4):369-396
The existence of string functions, which are not polynomial time
computable, but whose graph is checkable in polynomial time, is a basic
assumption in cryptography.
We prove that in the framework of algebraic complexity, there are no such
families of polynomial functions of polynomially bounded degree over
fields of characteristic zero.
The proof relies on a polynomial upper bound on the approximative complexity of
a factor g of a polynomial f in terms of the (approximative) complexity of f
and the degree of the factor g. This extends a result by Kaltofen.
The concept of approximative complexity allows us to cope with the case that a factor has
an exponential multiplicity, by using a perturbation argument.
Our result extends to randomized (two-sided error) decision complexity. 相似文献
2.
In this paper we address the problem of stability of flows associated to a sequence of vector fields under minimal regularity requirements on the limit vector field, that is supposed to be a gradient. We apply this stability result to show the convergence of iterated compositions of optimal transport maps arising in the implicit time discretization (with respect to the Wasserstein distance) of nonlinear evolution equations of a diffusion type. Finally, we use these convergence results to study the gradient flow of a particular class of polyconvex functionals recently considered by Gangbo, Evans and Savin. We solve some open problems raised in their paper and obtain existence and uniqueness of solutions under weaker regularity requirements and with no upper bound on the jacobian determinant of the initial datum.This work was partially supported by grants of M.I.U.R. and of IMATI-CNR, Pavia, Italy. 相似文献
3.
N. G. Mazur 《Theoretical and Mathematical Physics》1996,106(1):35-49
We consider an initial value problem for the KdV equation in the limit of weak dispersion. This model describes the formation and evolution in time of a nondissipative shock wave in plasma. Using the perturbation theory in power series of a small dispersion parameter, we arrive at the Riemann simple wave equation. Once the simple wave is overturned, we arrive at the system of Whitham modulation equations that describes the evolution of the resulting nondissipative shock wave. The idea of the approach developed in this paper is to study the asymptotic behavior of the exact solution in the limit of weak dispersion, using the solution given by the inverse scattering problem technique. In the study of the problem, we use the WKB approach to the direct scattering problem and use the formulas for the exact multisoliton solution of the inverse scattering problem. By passing to the limit, we obtain a finite set of relations that connects the space-time parameters x, t and the modulation parameters of the nondissipative shock wave.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 44–61, January, 1996. 相似文献
4.
5.
John A. D. Applelby David W. Reynolds 《Journal of Difference Equations and Applications》2013,19(12):1257-1275
The asymptotic behaviour of the solution of general linear Volterra non-convolution difference equations on a finite dimensional space, is investigated. It is proved under appropriate assumptions that the solution converges to a limit, which is in general non-trivial. These results are then used to obtain the exact rate of decay of solutions of a class of convolution Volterra difference equations, which have no characteristic roots. In particular, we obtain the exact rate of convergence of the solution of equations whose kernel does not converge exponentially. A useful formula for the weighted limit of a discrete convolution is also obtained. 相似文献
6.
Anca Capatina 《Numerical Functional Analysis & Optimization》2013,34(7-8):817-828
We are interested in finding the coefficient of friction which leads us to a given displacement on the contact surface between an elastic solid body and a rigid foundation. The mathematical formulation of the problem is an optimal control problem governed by a quasivariational inequality. We obtain an approximative caracterization, by using two families of penalized and regularized problems, for a given optimal control. 相似文献
7.
We present an exact formula for moments and cumulants of several real compound Wishart matrices in terms of an Euler characteristic
expansion, similar to the genus expansion for complex random matrices. We consider their asymptotic values in the large matrix
limit: as in a genus expansion, the terms which survive in the large matrix limit are those with the greatest Euler characteristic,
that is, either spheres or collections of spheres. This topological construction motivates an algebraic expression for the
moments and cumulants in terms of the symmetric group. We examine the combinatorial properties distinguishing the leading
order terms. By considering higher cumulants, we give a central-limit-type theorem for the asymptotic distribution around
the expected value. 相似文献
8.
We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces l M . 相似文献
9.
V. Zh. Sakbaeva 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):253-261
We study the Cauchy problem for an equation whose generating operator is degenerate on some subset of the coordinate space. To approximate a solution of the degenerate problem by solutions of well-posed problems, we define a class of regularizations of the degenerate operator in terms of conditions on the spectral properties of approximating operators. We show that the behavior (convergence, compactness, and the set of partial limits in some topology) of the sequence of solutions of regularized problems is determined by the deficiency indices of the degenerate operator. We define an approximative solution of the degenerate problem as the limit of the sequence of solutions of regularized problems and analyze the dependence of the approximative solution on the choice of an admissible regularization. 相似文献
10.
Delayed feedbacks are quite common in many physical and biological systems and in particular many physiological systems. Delay can cause a stable system to become unstable and vice versa. One of the well-studied non-biological chemical oscillators is the Belousov-Zhabotinsky(BZ) reaction. This paper presents an investigation of stability and Hopf bifurcation of the Oregonator model with delay. We analyze the stability of the equilibrium by using linear stability method. When the eigenvalues of the characteristic equation associated with the linear part are pure imaginary, we obtain the corresponding delay value. We find that stability of the steady state changes when the delay passes through the critical value. Then, we calculate the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states, by using the normal form theory and the center manifold theorem. Finally, numerical simulations results are given to support the theoretical predictions by using Matlab and DDE-Biftool. 相似文献
11.
《数学物理学报(B辑英文版)》2020,(3)
In this article, we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation. This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem. We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule. Some numerical results in one-dimensional case and two-dimensional case show that our method is effcient and stable. 相似文献
12.
The aim of this work is to establish the results for a particular class of inhomogeneous processes, the McKean–Vlasov diffusions. Such diffusions correspond to the hydrodynamical limit of an interacting particle system. In convex landscapes, existence and uniqueness of the invariant probability is a well-known result. However, previous results state the nonuniqueness of the invariant probabilities under nonconvexity assumptions. Here, we prove that there exists a phase transition. Below a critical value, there are exactly three invariant probabilities and above another critical value, there is exactly one. Under simple assumptions, these critical values coincide and it is characterized by a simple implicit equation. We also investigate other cases in which phase transitions occur. Finally, we provide numerical estimations of the critical values. 相似文献
13.
14.
主要考虑如下三阶两点边值问题通过对非线性项f作适当的限制,利用上下解方法,获得三阶两点边值问题解的存在性结果.特别之处是,一个截断技巧和Nagumo条件的引入和使用.同时得到了解的唯一性结果. 相似文献
15.
We consider multiple objective 0–1 programming problems in the situation where parameters of objective functions and linear constraints are exposed to independent perturbations. We study quantitative characteristics of stability (stability radii) of problem solutions. An approach to deriving formulae and estimations of stability radii is presented. This approach is applied to stability analysis of the linear 0–1 programming problem and problems with two types of nonlinear objective functions: linear absolute value and quadratic. 相似文献
16.
17.
通过上下解和单调迭代技术讨论了二阶脉冲泛函微分方程非线性边值问题极值解的存在性,推广了相关文献的结果. 相似文献
18.
The Zakharov–Shabat inverse spectral problem is constructed for a potential with support on the half-line and with a boundary value at the origin. This prescribed value is shown to produce a Jost solution with an essential singularity at large values of the spectral parameter; this requires particular attention when solving the related Hilbert boundary value problem. The method is then used to illustrate the sine-Gordon equation (in the light cone) and is discussed using a singular limit of the stimulated Raman scattering equations. 相似文献
19.
J. C. Sun & Tony F. Chan 《计算数学(英文版)》1995,13(4):325-336
1.IntroductionWeconsiderthefollowingsecondorderellipticboundaryvalueproblem:Lu=f,infl,(1)u=o,onOfl,(2)whereLisaselfadjointpositiveoperatorandflCnd(15dS3)isapolyhedraldomain.Aweaksolutionhasthefollowingform:FinduEHf(fl)suchthat:LetVh:=M=Span{rki},where{ghi}couldbenodalbasisconsistingofpiece-wiselinearfunctionsorothersplinefunctions-Substitutingthefollowingsolutionuh=Zui4iintotheaboveweakformleadstoadiscreteequationAu=f,(3)whereA=(crij),oij=A(ofi,rkj).(4)Itiswellknownthatthec0efficientmat… 相似文献
20.
A. Gopaul M.S. Sunhaloo R. Boojhawon M. Bhuruth 《Journal of Computational and Applied Mathematics》2009
We study the stability of zero-fill incomplete LU factorizations of a nine-point coefficient matrix arising from a high-order compact discretisation of a two-dimensional constant-coefficient convection–diffusion problem. Nonlinear recurrences for computing entries of the lower and upper triangular matrices are derived and we show that the sequence of diagonal entries of the lower triangular factor is unconditionally convergent. A theoretical estimate of the limiting value is derived and we show that this estimate is a good predictor of the computed value. The unconditional convergence of the diagonal sequence of the lower triangular factor to a positive limit implies that the incomplete factorization process never encounters a zero pivot and that the other diagonal sequences are also convergent. The characteristic polynomials associated with the lower and upper triangular solves that occur during the preconditioning step are studied and conditions for the stability of the triangular solves are derived in terms of the entries of the tridiagonal matrices appearing in the lower and upper subdiagonals of the block triangular system matrix and a triplet of parameters which completely determines the solution of the nonlinear recursions. Results of ILU-preconditioned GMRES iterations and the effects of orderings on their convergence are also described. 相似文献