Primal Central Paths and Riemannian Distances for Convex Sets

In this paper, we study the Riemannian length of the primal central path in a convex set computed with respect to the local metric defined by a self-concordant function. Despite some negative examples, in many important situations, the length of this path is quite close to the length of a geodesic curve. We show that in the case of a bounded convex set endowed with a ν-self-concordant barrier, the length of the central path is within a factor O(ν ^1/4) of the length of the shortest geodesic curve. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming.     

关于Bloch函数的性质

研究了Bloch函数族B中的两个子族Bα与B0,给出了它们的函数之间的关系;作为应用建立了Bα与B0中函数的偏差定理,从而刻画了Bα与B0中函数的有关性质.     

Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems

This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103–116, 2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation approach for the case where the sample space is noncompact. This work was supported in part by Project 10771025 supported by NSFC and SRFDP 20070141063 of China.     

Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

The problem of the boundedness of the Riesz potential I _α , 0 < α < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted L _p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones. V. Guliyev’s research was partially supported by the grant of the Azerbaijan-U. S. Bilateral Grants Program II (project ANSF Award / AZM1-3110-BA-08) and the Turkish Scientific and Technological Research Council (TUBITAK, programme 2221, no. 220.01-619-4889).     

SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN Cn

Some previous results on convergence of Taylor series in Cn [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cn are constructed and the Taylor series expansion is deduced.     

The role of a radial ion-track distribution in semiconductors studied by numerical simulations

The effect of radial ion-track distribution on the transient current in semiconductors caused by a high-energy heavy ion strike was studied. Reasonable agreement was observed in experimental and calculated transient currents for ion energies ranging from several to several hundred MeV when the radius of the ion track used in the numerical simulations was shorter or equivalent to that of the penumbra radius.     

亚纯函数与其微分多项式的分担函数与正规族

设${\cal F}$为开平面内的区域$D$上的亚纯函数族, ${\cal F}$中任何函数$f(z)\in{\cal F}$, $f$的零点竽数至少为$k+1$.对于$D$内不等于零的解析函数$a(z)$.若$f(z)$与其微分多项式$D(f)$ IM分担$a(z)$,本文不仅得到${\cal F}$在$D$上正规, 而且得到相应于正规函数的结果.     

Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm⁻¹ and above 1800 cm⁻¹ are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner. Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001     

On convergence properties of a least-distance programming procedure for minimization problems under linear constraints

In Ref. 1, Bazaraa and Goode provided an algorithm for solving a nonlinear programming problem with linear constraints. In this paper, we show that this algorithm possesses good convergence properties.This paper was written under the guidance of Associate Professor C. Y. Wang. The author takes great pleasure in thanking him.     

The wall theorem for elastic moduli

New expressions for the elastic moduli of a classical system are derived. They involve only the two-point correlation function and the derivative of the onepoint correlation function, both only on the boundary of the system. These expressions, valid for any interaction derivable from a potential, are proved from a mechanical point of view by generalizing the virial theorem of Clausius, and from a statistical point of view by a direct method that constitutes an alternative to Green's dilatation method.