On the approximation by the mixed exponential type integral operators

In 1984, L. C. Hsu, X. J. Yang and the auther^[1] defined a class of summation-integral operators. Later, the author^[2]–[5], Mazhar-Totik^[6] and Sahai-Prased^[7] studied some specific exponential type integral operators, separately. The purpose of this paper is to introduce and study some more general mixed exponential type integral operators.     

Simultaneous approximation to values of exponential function at algebraic points

This paper applies the methods of Chudnovsky^[2], Osgood^[4] and Baker^[1] to give a simultaneous approximation theorem to the values of exponential function at algebraic points, which slightly sharpens and generalises the results of Chudnovsky^[2],[3]. This work is supported by the National Natural Science Foundation of China.     

Interpolation of nonlinear functionals by integral continued fractions

We constructively prove the theorem of existence of an interpolation integral chain fraction for a nonlinear functionalF:Q[0,1]→R ¹. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 364–375, March, 1999.     

k-valent maps on the surfaces

In this paper, the works of Kotzig^[1], Zaks^[3] and the author^[2] have been generalized and unified. A number of new results have also been obtained.     

D-optimality andD n -optimal designs for mixtures regression models with logarithmic terms

In this paper the authors put forward a new mixtures regression models with Logarithmic terms^[14] to generalize Draper's models^{[1, 2 or 6]} by using Kiefer-Wolfowitz's equivalence theorem^[3], Fedorov's and Wynn's method^[5]. And we also suggest a method for computer-aided design of combinatorial search^[13].In this study, we have proved and constructed the approximateD-optimal (measure) andD _n -optimal (exact) designs by the use of the first and second order mixtures regression models with logarithmic terms in three and four components.Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

On the mean curvatures sharp estimates of hypersurfaces

Sharp estimates for the mean curvatures of hypersurfaces in Riemannian manifolds are known from the works of Jorge-Xavier ^[3], Markvorsen ^[6] and Vlachos ^[11]. We first give a simplified proof of these estimates. This proof shows that a similar original result holds for hypersurfaces in Einstein manifolds which are warped product of by Ricci-flat manifolds.     

Gaussian series and daubechies operators

The subspace [Mtilde] of L²(Cⁿ) which is composed of Gaussian series and contains the subspace M spanned by Gaussian functions given in the paper [6] by Du and Wong has the proporety that the product of two Daubechies operators with symbols in [Mtilde] is a Daubechies operator with symbol H in [Mtilde]. Furthermore, an explicit expression for the symbol H is given     

一类随机游动上确界的密度的渐近性

Kluppelberg^[1], Asmussen 等^[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等^[3], 程东亚和王岳宝^[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质.     

Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

We characterize finite codimensional linear isometries on two spaces, C ⁽ⁿ⁾[0; 1] and Lip [0; 1], where C ⁽ⁿ⁾[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C ⁽ⁿ⁾[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.     

The Category of Directed Systems in a Category

We present two related categorical constructions. Given a category C, we construct a category C^[d], the category of directed systems in C. C embeds into C^[d], and if C has enough colimits, then C is monadic over C^[d]. Also, if E,M is a factorization structure for C, then C^[d] has a related factorization structure E_d M_d such that if E consists entirely of monic arrows, then so does E_d and the E_d-quotient poset of an object A is naturally the poset of directed downsets of the E-quotient poset of A. Similarly, if M consists entirely of monicarrows, then so does M_d and the M_d-subobject poset of an object A is naturally the poset of directed downsets of the M-subobject poset. C^[d] has completeness and cocompleteness properties at least as good as those of C, and it is abelian if C is. Dualization gives the other construction: a category C^[i], the category of inverse systems in C, into which C also embeds and which satisfies similar properties, except that directed downsets in the E-quotient and M-subobject posets are replaced by directed upsets.     

Hirzebruch Xy genera of the Hilbert schemes of surfaces by localization formula

We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula to calculate the Hirzebruch ?_y genus X_y(S^[n]), where S^[n] is the Hilbert scheme of points of length n of a surface S. Combinatorial interpretation of the weights of the fixed points of the natural torus action on ( ²)^[n] is used. This is the first step to prove a conjectural formula about the elliptic genus of the Hilbert schemes.     

The cup product of Hilbert schemes for K3 surfaces

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A ^[n] so that there is canonical isomorphism of rings (H ^*(X;ℚ)[2]) ^[n] ≅H ^*(X ^[n] ;ℚ)[2n] for the Hilbert scheme X ^[n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle. Oblatum 25-I-2001 & 18-IX-2002?Published online: 24 February 2003     

On the existence of positive solutions for a class of singular boundary value problems

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C¹[0,1]∩C²(0,1) or C[0,1]∩C²(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.     

Transition distributions of young diagrams under periodically weighted plancherel measures

Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.     

nth order Stieltjes differential boundary operators and Stieltjes differential boundary systems

This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in $\text{L}$_n^p[0,1] × $\text{L}$_n^p[0,1], 1 ? p < ∞. The adjoint relation in $\text{L}$_n^q[0,1] × $\text{L}$_n^q[0,1], $\text{1}\text{p}\text{+}\text{1}\text{q}\text{= 1}$, is derived. Green's formula is also found. Self-adjoint relations are found in $\text{L}$_n²[0,1] × $\text{L}$_n²[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of $\text{L}$_n^p[0,1] × $\text{L}$_n²[0,1] is established.     

On principal submatrices

It is shown that if A[ω] is a principal submatrix of the positive definite Hermitian matrix A, then A ^?1[ω] ?(A[ω])^?1is a positive semidefinite hermitian matrix. This fact is used to give a brief proof of a result of Saburou Saitoh concerning Hadamard products.     

Some results on L1-approximation

The new inequalities for L¹-Approximation are obtained; J. W. Garrett, C. S. Ress and Č. V. Stanojevic's Theorem^[2] and T. Xie's Theorem^[3] are modified.