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1.
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.  相似文献   

2.
Based on the Boolean sum technique, we introduce and analyze in this paper a class of multi-level iterative corrections for finite dimensional approximations. This type of multi-level corrections is adaptive and can produce highly accurate approximations. For illustration, we present some old and new finite element correction schemes for an elliptic boundary value problem.  相似文献   

3.
This paper deals with maximum norm error estimates of conforming finite element approximate solutions for the stationary and nonstationary Navier-Stokes problems in a plane bounded domain, using the so-called velocity-pressure mixed variational formulation. Quasi-optimal maximum norm error estimates of the velocity and its first derivatives, and the pressure are obtained for conforming finite element approximations of the stationary Navier-Stokes problem by some estimates of the Green function and their finite element approximations for Stokes problem. Moreover, with the method of Navier-Stokes projection, quasi-optimal maximum norm error estimate results are shown for semidiscrete conforming finite element approximations of the nonstationary Navier-Stokes problem.  相似文献   

4.
Abstract The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr(VTAV)/tr(VTBV)+tr(VTCV)over the Stiefel manifold{V∈Rm×l |VTV=Il}(lm),naturally leads to a self-consistent-field(SCF)iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.  相似文献   

5.
This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions.Several properties for the approximating set(?)such that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced.Under the very mild conditions,we prove that these properties are equivalent that(?)is a Haar subspce.  相似文献   

6.
In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations, converge strongly in L^2([0, T]; Lloc^2(R^3)) provided that they have strong convergence in the region away from the symmetry axis. This result has been proved by the authors for the approximate solutions generated by smoothing the initial data,with no restriction of the sign of the initial data. Then we discuss the decay rate for maximal vorticity function, which is established for both approximate solutions generated by smoothing the initial data and viscous approximations respectively. One sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given, and a decay rate for maximal vorticity function in the region away from the symmetry axis is obtained for non-negative initial vorticity.  相似文献   

7.
This paper provides an analysis of the rotational form of the pressure-correction methods by spectral approximations for the unsteady Stokes equations. Error estimates in finite time for the fully discrete case are given. Numerical experiences using both spectral and spectral element methods are carried out to confirm the theoretical results.  相似文献   

8.
In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.  相似文献   

9.
This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method.  相似文献   

10.
The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume:If |A| =|B| > 0 and |A + B|1/n =(2 + δ)|A|1/n for some small δ,then,up to a translation,both A and B are close (in terms of δ) to a convex set K.Although this result was already proved by the authors in a previous paper,the present paper provides a more elementary proof that the authors believe has its own interest.Also,the result here provides a stronger estimate for the stability exponent than the previous result of the authors.  相似文献   

11.
Abstract We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q 1/2+∈. Similar results are obtained for the distribution of ordered pairs (x, x −1) with x a primitive λ-root, and for the number of primitive λ-roots satisfying inequalities such as |xx −1| ≤ B. (Dedicated to Professor Wang Yuan on the occasion of his 75th birthday) *Project supported by the National Natural Science Foundation of China (No.19625102) and the 973 Project of the Ministry of Science and Technology of China.  相似文献   

12.
An explicit integral formula is obtained for the Green function of the weighted biharmonic operator Δ(1−∣z∣2)−αΔ in the unit disk of the complex plane for the case α ∈ (−1, 0). The formula shows the positivity of the Green function. This is a basis for a theorem on factorization of analytic functions in the weighted Bergman spaces with the weights ω(z)=(1−∣z∣2)α as products of a nonvanishing function and a function of special form responsible for the zeros. Bibliography: 16 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 203–221.  相似文献   

13.
It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus of continuity of the form exp(−∣logt σ ) for some 0 < σ < 1.  相似文献   

14.
 We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory.  相似文献   

15.
We study the asymptotic behaviour of the transition density of a Brownian motion in ?, killed at ∂?, where ? c is a compact non polar set. Our main result concern dimension d = 2, where we show that the transition density p ? t (x, y) behaves, for large t, as u(x)u(y)(t(log t)2)−1 for x, y∈?, where u is the unique positive harmonic function vanishing on (∂?) r , such that u(x) ∼ log ∣x∣. Received: 29 January 1999 / Revised version: 11 May 1999  相似文献   

16.
 We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory. Received October 18, 2001; in final form April 11, 2002  相似文献   

17.
Let K be either the rational number field \Bbb Q{\Bbb Q} or an imaginary quadratic field. We give irrationality results for the number q = ?n=1rn/(qn-rl)\theta=\sum_{n=1}^{\infty}{r^n}/(q^n-r^l), where q (∣q∣ > 1) is an integer in K, rK × (∣r∣ < ∣q∣), and 1 £ l ? \Bbb Z1\le l\in{\Bbb Z} with q n r l (n ≥ 1).  相似文献   

18.
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment [–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫–11 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞).  相似文献   

19.
Let K be either the rational number field or an imaginary quadratic field. We give irrationality results for the number , where q (∣q∣ > 1) is an integer in K, rK × (∣r∣ < ∣q∣), and with q n r l (n ≥ 1). Authors’ addresses: Kenji Amano, NS solutions Corporation, 2-27-1 Shinkawa, Chuo-ku, Tokyo 104-0033, Japan; Yohei Tachiya, Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan  相似文献   

20.
The present paper first establishes a decomposition result for f(x)∈ C r C r+1. By using this decomposition we thus can obtain an estimate of ∣f(x) - L n (f,x)∣ which reflects the influence of the position of the x's and ω(f (r+1),δ)j, j = 0,1,...,s, on the error of approximation. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

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