Concerning the possible values of upper and lower derivatives

In this paper, the behavior of the upper and lower derivatives of integrals with respect to differential bases formed from intervals is studied. The main result consists in proving the fact that there are, in general, no analogs of the well-known Besicovitch theorem for translation-invariant Busemann-Feller bases formed from intervals.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 107–114, July, 1998.     

Band-limited refinable functions for wavelets and framelets

Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and biframes with desirable time-frequency localization.     

偏序集上的测度拓扑与稠拓扑

In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.     

Entropy and the Uncertainty Principle

We generalize, improve and unify theorems of Rumin, and Maassen–Uffink about classical entropies associated with quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different bases. Thus, they provide a kind of uncertainty principle. Our inequalities are sharp because they are exact in the high-temperature or semi-classical limit.     

A Weyl type formula for Fourier spectra and frames

We prove qualitative and quantitative results concerning the asymptotic density in dilates of centered convex bodies of the frequency vectors of orthogonal exponential bases and frames associated to bounded domains in Euclidean space.

     

Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function

The paper deals with homogenization of a spectral problem for a second order self-adjoint elliptic operator stated in a thin cylinder with homogeneous Neumann boundary condition on the lateral boundary and Dirichlet condition on the bases of the cylinder. We assume that the operator coefficients and the spectral density function are locally periodic in the axial direction of the cylinder, and that the spectral density function changes sign. We show that the behavior of the spectrum depends essentially on whether the average of the density function is zero or not. In both cases we construct the effective 1-dimensional spectral problem and prove the convergence of spectra.     

On Differential Bases Formed of Intervals

Translation invariant subbases of the differential basis B ₂ (formed of all intervals), which differentiates the same class of all non-negative functions as B ₂ does, are described. A possibility for extending the results obtained to bases of more general type is discussed.     

核估计在医疗费用分布研究中的应用

医疗费用的分布是健康保险的精算基础之一.本文研究了某团体一年的住院医疗费用记录,运用非参数模型中的核密度估计方法,对每次住院费用对数的分布密度进行了估计,并用它进一步估计了每次住院费用的均值和方差,取得了较好的效果.在此基础上,本文对拟合结果及其对健康保险的启示作了一些讨论.     

Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.     

Construction of many- particle spin entangled states and signature

Using the collective rotational transformation,R _x(π we construct two types of many-particle spin entangled states in terms of the bases of angular momentum uncoupling and coupling representations. The concept of signature is introduced. The entanglement properties of a four-particle system is investigated by analyzing various subsystem reduced density matrices.     

On the Differential Properties of Temlyakov-Type and Temlyakov-Bavrin-Type Integrals

We establish a formula that expresses the value of the density of the Temlyakov-type integral with defining domain of type A in terms of the integral itself by means of a differential operator. We extend this operator connection to the Temlyakov–Bavrin-type integral of order k. Our study bases on the method of linear differential operators with variable coefficients which is developed by A. V. Nelaev.     

Hyperbolic Wavelet Approximation

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of periodic functions [DPT]. October 16, 1995. Date revised: August 28, 1996.     

Construction of regular solutions of Schrödinger and Faddeev equations in the linear three-particle configuration limit

We study the six-dimensional Schrödinger and Faddeev equations for a three-particle system with central pairwise interactions more general than the Coulomb interactions. The regular general and particular physical solutions of such equations are represented by infinite series in integer powers of the distance from one of the particles to the center of mass of the other two particles and in some functions of the other three-particle coordinates. Constructing such functions in the angular bases formed by spherical and bispherical harmonics or by symmetrized Wigner D-functions reduces to solving simple algebraic recurrence relations. For the projections of physical solutions on the angular basis functions, we introduce the boundary conditions in the linear three-particle configuration limit.     

Pivoting for Size and Sparsity in Linear Programming Inversion Routes

^* Present address: The Operations Research Department, Stanford University, Stanford, California 94305, U.S.A. This note reports some experimental results on the inversionof real linear programming bases, with particular emphasis onthe compromise between minimum density and maximum numericalstability. The general features of a linear programming inversionroutine are outlined and the special structure of linear programsconsidered. The main result is a suitable and apparently safe"pivot tolerance" level, together with more general data onthe nature and behaviour of the problems.     

A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures

A theory of generalized statical bases is developed for usein the flexibility methods as applied to skeletal structuralproblems. It is shown that any maximal linearly independentset of cycles of the integral cycle group of a linear graphmodel of the structure may be used in the formation of a staticalbasis. Such a set of simple cycles is found by embedding thisgraph into a two-dimensional polyhedron. Cell complexes areformed so that the simple cycles bounding the 2-cells correspondto substructures on which a statical basis may be constructed.Two methods are given for the construction of the embeddings.In one a collapsible complex is formed from a union of a setof disks; while in the other the embedding is into an orientablemanifold which is modified to form an admissible complex.     

周期B样条基转换矩阵的表示和计算

周期B样条基以一种简洁的形式表示闭B样条曲线.周期B样条基转换矩阵为闭B样条曲线及相关曲面的不同表示间的转换提供了一个数学模型.本文给出了周期B样条基转换矩阵的存在性条件,给出并证明了周期B样条基转换矩阵的一个简单的递归表示式.在此基础上,本文进一步给出了周期B样条基转换矩阵的计算公式和高效算法.周期B样条基转换矩阵为闭B样条曲线的节点插入、升阶、节点删除和降阶等基本运算提供了一个统一而简单的解决方法,本文给出了一些应用例子.     

Basis property of eigenfunctions of nonselfadjoint operator pencils generated by the equation of nonhomogeneous damped string

We consider a class of nonselfadjoint quadratic operator pencils generated by the equation, which governs the vibrations of a string with nonconstant bounded density subject to viscous damping with a nonconstant damping coefficient. These pencils depend on a complex parameterh, which enters the boundary conditions. Depending on the values ofh, the eigenvalues of the above pencils may describe the resonances in the scattering of elastic waves on an infinite string or the eingenmodes of a finite string. We obtain the 7asymptotic representations for these eigenvalues. Assuming that the proper multiplicity of each eigenvalue is equal to one, we prove that the eigenfunctions of these pencils form Riesz bases in the weightedL ²-space, whose weight function is exactly the density of the string. The general case of multiple eigenvalues will be treated in another paper, based on the results of the present work.     

Biorthogonal bases of compactly supported wavelets

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets. We give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions, and we present a sufficient conditions for the decay of their Fourier transforms. We study the regularity of these biorthogonal bases. We provide several families of examples, all symmetric (corresponding to “linear phase” filters). In particular we can construct symmetric biorthogonal wavelet bases with arbitraily high preassigned regularity; we also show how to construct symmetric biorthogonal wavelet bases “close” to a (nonsymmetric) orthonormal basis.     

On Computing Gröbner Bases in Rings of Differential Operators with Coefficients in a Ring

Following the definition of Gr?bner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some computational properties of Gr?bner bases arising when the coefficient set is a ring. First we give examples to show that the generalization of S-polynomials is necessary for computation of Gr?bner bases. Then we prove that under certain conditions the G-S-polynomials can be reduced to be simpler than the original one. Especially for some simple case it is enough to consider S-polynomials in the computation of Gr?bner bases. The algorithm for computation of Gr?bner bases can thus be simplified. Last we discuss the elimination property of Gr?bner bases in rings of differential operators and give some examples of solving PDE by elimination using Gr?bner bases. This work was supported by the NSFC project 60473019.     

Electron-microscopic examination of a splat-cooled silver-germanium alloy

Extremely rapid solidification of a Ag-15 at.% Ge alloy results in the formation of a highly irregular structure. The individual grains consist of a lamellar mixture of close-packed structures with different stacking sequences (f.c.c. and h.c.p. phases as well as long-period stacking structures), superposed with a high density of randomly arranged stacking faults. It is concluded that the structure observed at room temperature may have formed by martensitic transformation of a metastable b.c.c. phase which is formed first upon solidification.