Invariant Measure for Diffusions with Jumps

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established. Accepted 24 February 1998     

Isolated rational curves on K3-fibered Calabi–Yau threefolds

In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ ^{n 1}}×ℙ¹. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau variety in projective space. Received: 14 October 1997 / Revised version: 18 January 1998     

Connection coefficients, orthogonal polynomials and the WZ-algorithms

In this paper we explore the relationship between the coefficients in the expansion of a function f(x) in orthogonal polynomials and the coefficients for the expansion of (1-x) ^m f(x), with particular attention to the case of Jacobi polynomials. Such problems arise frequently in computational chemistry. The analysis of the situation is substantially assisted by the use of two of the so-called Wilf-Zeilberger algorithms: the algorithm zeil and the algorithm hyper. We explain these algorithms and give several examples. This revised version was published online in June 2006 with corrections to the Cover Date.     

The conjugate gradient method for linear ill-posed problems with operator perturbations

We consider an ill-posed problem Ta = f_* in Hilbert spaces and suppose that the linear bounded operator T is approximately available, with a known estimate for the operator perturbation at the solution. As a numerical scheme the CGNR-method is considered, that is, the classical method of conjugate gradients by Hestenes and Stiefel applied to the associated normal equations. Two a posteriori stopping rules are introduced, and convergence results are provided for the corresponding approximations, respectively. As a specific application, a parameter estimation problem is considered.     

Spectral radius properties for layer potentials associated with the elastostatics and hydrostatics equations in nonsmooth domains

By producing a L² convergent Neumann series, we prove the invertibility of the elastostatics and hydrostatics boundary layer potentials on arbitrary Lipschitz domains with small Lipschitz character and 3D polyhedra with large dihedral angles.     

通用智能数据采集系统的开发

通用智能数据采集系统以单片机为核心,控制模/数转换芯片AD 7715实现对数据的采集,使用串行接口大容量FLA SH存储芯片AT 45D 041对数据进行存储,通过RS232口实现与上微机的通讯,并用LCD实时显示运行状态、测量结果等,重点阐述了单片机对AD 7715以及AT 45D 041的控制.该系统可广泛应用于需要对大量的实时数据进行采集的场合.     

Quantization of formal classical dynamical r-matrices: the reductive case

In this paper we prove the existence of a formal dynamical twist quantization for any triangular and non-modified formal classical dynamical r-matrix in the reductive case. The dynamical twist is constructed as the image of the dynamical r-matrix by a L_∞-quasi-isomorphism. This quasi-isomorphism also allows us to classify formal dynamical twist quantizations up to gauge equivalence.     

A Precise Interplay Between BMO Space and A 2 Class in Dimension One

Sharp inequalities between weight bounds from A ₂-condition and the BMO norm or the distance from L ^∞ in the BMO norm are obtained in the one dimensional case.     

Challenges of back end of the line for sub 65 nm generation

This paper presents a review of interconnect challenges for sub 65 nm node. From this generation, porous ultra low K (ULK) dielectric materials (dielectric constant k<2.1) are required. Their porosity makes integration very difficult, due to the mechanical weakness and process interaction issues (especially during stripping, CVD metal barrier deposition…). To overcome these process incompatibilities and keep the ‘effective dielectric constant’ low, dual damascene architecture becomes more and more complex and requires additional steps (porosity sealing treatment, degas steps, supercritical CO₂ clean, low k dielectric barrier, self aligned barrier…). Possible contamination trapped in the porosity (moisture, metallic residues…), and lower thermo-mechanical properties of ULK will probably impede reliability. Copper resistivity increase with dimension shrinkage will also be an extra issue.     

On exterior boundary-value problems of the Helmholtz equation not deduced from waves

A boundary integral equation is applied to describe a special kind of exterior Helmholtz boundary-value problem that is not deduced from waves. Then the asymptotic property of O(r ^–2) decay at infinity and the uniqueness of the solution as well as its finite energy property are discussed.