Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron NumberSCI北大核心CSCD

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.     

On universal Korovkin sets w.r.t. positive spectral contractions

We prove that there exists a finite universal Korovkin set with respect to positive spectral contraction operators for a Segal algebra on a locally compact abelian groupG if and only ifĜ is finite dimensional separable metrizable space.     

Correction to: ‘The UCT, the Milnor Sequence, and a Canonical Decomposition of the Kasparov Groups’

In this note we correct a mistake in K-Theory 10 (1996), 49–72. In that paper we asserted that under bootstrap hypotheses the short exact sequence

Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues

We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian,

     

Universal forms over $\mathbb{Q}(\sqrt{5})$

In this paper, we find all quaternary universal positive definite integral quadratic forms over and prove an analogue of Conway and Schneeberger’s 15-Theorem. This work was partially supported by KRF(2003-070-C00001). This work was supported by the Brain Korea 21 project in 2004.     

滴定分析模型的统一、MATLAB解析及曲线绘制

在将酸碱滴定、络合滴定、氧化还原滴定和沉淀滴定反应统一为M+L=N的基础上,将4种滴定曲线方程统一为两种数学模型。通过简单迭代法计算滴定过程中变化的副反应系数,利用接近数学表达式的自然化语言MATLAB解析4种滴定曲线方程,并绘制出精确的滴定曲线,方法简单易操作。     

Universal connections in Fréchet principal bundles

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector space, we endow the bundle J ¹ P of 1-jets of the sections of a Fréchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P.      

On finding a large number of 3D points with a small diameter

Given a set S of n points in R³, we wish to decide whether S has a subset of size at least k with Euclidean diameter at most r. It is unknown whether this decision problem is NP-hard. The two closely related optimization problems, (i) finding a largest subset of diameter at most r, and (ii) finding a subset of the smallest diameter of size at least k, were recently considered by Afshani and Chan. For maximizing the size, they presented several polynomial-time algorithms with constant approximation factors, the best of which has a factor of . For maximizing the diameter, they presented a polynomial-time approximation scheme. In this paper, we present improved approximation algorithms for both optimization problems. For maximizing the size, we present two algorithms: the first one improves the approximation factor to 2.5 and the running time by an O(n) factor; the second one improves the approximation factor to 2 and the running time by an O(n²) factor. For minimizing the diameter, we improve the running time of the PTAS from O(nlogn+2^O(1/ε3)n) to O(nlogn+2^{O(1/(ε1.5logε))}n).