ON THE RATE OF WEIGHTED L_p CONVERGENCE BY THE GRNWALD INTERPOLATORY OPERATORS

Abstract This paper gives the weighetd L_p convergence rate estimations of the Grunwald interpolatory polynomi-als based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estima-tions is optimal for p≥1.     

ESTIMATION OF THE MEAN LIFETIME IN NON-PARAMETRIC MODEL UNDER MODIFIED TYPE Ⅰ CENSORING

The methods to estimate the mean,s of the lifetimes under modified Type I Censoring arediscussed, in which case the distribution function of the lifetimes is unknown and the informationabout the individuals is cut by the fixed time C. As a slight modincation, we suggest observingsmall percentage of the lifetimes to construct the estimations. These estimations are unbiasedand consistent.     

ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION

The object of this paper is to establish the pointwise estimations of approximation of functions in C~1 andtheir derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-eral.     

INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.     

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-II Censoring

In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.     

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-Ⅱ Censoring

In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.     

多元线性模型回归系数的混合估计和Bayes估计

In this paper,the mixed estimations of regression coefficient in multivariate linear model is giyen on the condition of expanding sample data and their optimalities are considered.It is shown that GLSE is equivalent to the above mentioned mixed estimations.Furthermore,Bayes estimation in multivariate normal model,which is the same as the mixed estimations,is also improved.     

ABOUT THE FOURIER TRANSFORMS OF NON-SMOOTH MEASURES ON HYPERSPHERES

If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.     

分布函数的非参数最小二乘估计

By using the non-parametric least square method, the strong consistent estimations of distribution function and failure function are established, where the distribution function F(x)after logist transformation is assumed to be approximated by a polynomial. The performance of simulation shows that the estimations are highly satisfactory.     

数值积分的可选择误差界(英文)

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> Extemal Polynomials Associated with Generalized Jacobi Weights

Asymptotic estimations of the Christoffel type functions for Lm extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros of the Lm extremal polynomials and the Cotes numbers of the corresponding Turan quadrature formula is given.     

Kostka-Foulkes Polynomials Cyclage Graphs and Charge Statistic for the Root System <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

We establish a Morris type recurrence formula for the root system C_n. Next we introduce cyclage graphs for the corresponding Kashiwara-Nakashimas tableaux and use them to define a charge statistic. Finally we conjecture that this charge may be used to compute the Kostka-Foulkes polynomials for type C_n.     

Graded central polynomials for the algebra <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(<Emphasis Type="Italic">K</Emphasis>)

Let M _n (K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ _n -grading and a natural ℤ-grading. Finite bases for its ℤ _n -graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ _n -graded and for the ℤ-graded central polynomials for M _n (K) Partially supported by CNPq 620025/2006-9     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x(d))=x1^2k1…xd^2kd on S^(d-1).We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in,and can be regarded as an extension of under the weighted case.     

On the Relation between Piecewise Polynomial and Rational Approximation in <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>(<Emphasis Type="Bold">R</Emphasis><Superscript>2</Superscript>)

In the univariate case there are certain equivalences between the nonlinear approximation methods that use piecewise polynomials and those that use rational functions. It is known that for certain parameters the respective approximation spaces are identical and may be described as Besov spaces. The characterization of the approximation spaces of the multivariate nonlinear approximation by piecewise polynomials and by rational functions is not known. In this work we compare between the two methods in the bivariate case. We show some relations between the approximation spaces of piecewise polynomials defined on n triangles and those of bivariate rational functions of total degree n which are described by n parameters. Thus we compare two classes of approximants with the same number Cn of parameters. We consider this the proper comparison between the two methods.     

The F<Subscript>4</Subscript>-algorithm for Euclidean rings

In this short note, we extend Faugére’s F₄-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F₄-algorithm is based on the simultaneous reduction of several polynomials.     

Rectangular superpolynomials for the figure-eight knot 4<Subscript>1</Subscript>

We rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot 4₁ in an arbitrary rectangular representation R = [r^s] as a sum over all Young subdiagrams λ of R with surprisingly simple coefficients of the Z factors. Intriguingly, these coefficients are constructed from the quantum dimensions of symmetric representations of the groups SL(r) and SL(s) and restrict the summation to diagrams with no more than s rows and r columns. Moreover, the β-deformation to Macdonald dimensions yields polynomials with positive integer coefficients, which are plausible candidates for the role of superpolynomials for rectangular representations. Both the polynomiality and the positivity of the coefficients are nonobvious, nevertheless true. This generalizes the previously known formulas for symmetric representations to arbitrary rectangular representations. The differential expansion allows introducing additional gradings. For the trefoil knot 3₁, to which our results for the knot 4₁ are immediately extended, we obtain the so-called fourth grading of hyperpolynomials. The property of factorization in roots of unity is preserved even in the five-graded case.     

Regularity for weakly (K<Subscript>1</Subscript>, K<Subscript>2</Subscript>)-quasiregular mappings

In this paper, we first give the definition of weakly (K₁,K₂-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Hölder inequality, we obtain their regularity property: For anyq ₁ that satisfies\(0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1\), there existsp ₁=p ₁(n,q ₁,K ₁,K ₂)>n, such that any (K₁, K₂)-quasiregular mapping\(f \in W_{loc}^{1,q_1 } (\Omega ,R^n )\) is in fact in\(W_{loc}^{1,p_1 } (\Omega , R^n )\). That is, f is (K₁,K₂)-quasiregular in the usual sense.     

Inequality of the Turan type for trigonometric polynomials and conjugate trigonometric polynomials in <Emphasis Type="Italic">L</Emphasis><Subscript>0</Subscript>

We study inequalities of the Turan type for trigonometric polynomials and conjugate trigonometric polynomials in the quasinorm of L ₀ and derivatives of any order. We present expressions for constants in these inequalities and obtain double-sided estimates for them.