Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.     

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.     

具有急慢性阶段的MSIS流行病模型阈值和稳定性结果

系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.     

血液净化用吸附剂脱附过程的数学模型研究

对已吸附了低密度脂蛋白（ＬＤＬ）及极低密度脂蛋白（ＶＬＤＬ）达到饱和程度的吸附柱，用１ｍｏｌ／Ｌ的生理盐水进行脱附，采用修正Ｌａｎｇｍｕｉｒ吸附式建立了连续脱附过程的数学模型，计算结果与实验测定值吻合，表明该数学模型适用于描述类似于ＬＤＬ及ＶＬＤＬ这类蛋白质大分子的脱附过程。     

Oxazinins from toxic mussels: isolation of a novel oxazinin and reassignment of the C-2 configuration of oxazinin-1 and -2 on the basis of synthetic models

The analysis of a batch of toxic mussels (Mytilus galloprovincialis) from the Northern Adriatic Sea led to the isolation of a novel oxazinin, oxazinin-4. Its structure including the relative stereochemistry has been elucidated through extensive NMR analysis. A synthetic route to oxazinins has been crucial in establishing the absolute stereochemistry of oxazinin-4 and for reassigning the absolute C-2 configuration of oxazinin-1 and -2 previously isolated from toxic shellfish and stereostructurally characterized.     

A scheme related to the Brauer loop model

We introduce the Brauer loop scheme, where • is a certain degeneration of the ordinary matrix product. Its components of top dimension, ⌊N²/2⌋, correspond to involutions π∈SN having one or no fixed points. In the case N even, this scheme contains the upper-upper scheme from [A. Knutson, Some schemes related to the commuting variety, J. Algebraic Geom., in press, math.AG/0306275] as a union of (N/2)! of its components. One of those is a degeneration of the commuting variety of pairs of commuting matrices.The Brauer loop model is an integrable stochastic process studied in [J. de Gier, B. Nienhuis, Brauer loops and the commuting variety, J. Stat. Mech. (2005) P01006, math.AG/0410392], based on earlier related work in [M.J. Martins, B. Nienhuis, R. Rietman, An intersecting loop model as a solvable super spin chain, Phys. Rev. Lett. 81 (1998) 504-507, cond-mat/9709051], and some of the entries of its Perron-Frobenius eigenvector were observed (conjecturally) to equal the degrees of the components of the upper-upper scheme.Our proof of this equality follows the program outlined in [P. Di Francesco, P. Zinn-Justin, Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties, math-ph/0412031]. In that paper, the entries of the Perron-Frobenius eigenvector were generalized from numbers to polynomials, which allowed them to be calculated inductively using divided difference operators. We relate these polynomials to the multidegrees of the components of the Brauer loop scheme, defined using an evident torus action on E. As a consequence, we obtain a formula for the degree of the commuting variety, previously calculated up to 4×4 matrices.     

基于残差加权经验过程方法的自回归模型分布变点监测

Change monitoring of distribution in time series models is an important issue.This paper proposes a procedure for monitoring changes in the error distribution of autoregressive time series,which is based on a weighed empirical process of residuals with weights equal to the regressors.The asymptotic properties of our monitoring statistic are derived under the null hypothesis of no change in distribution.The finite sample properties are investigated by a simulation.As it turns out,the procedure is not only able to detect distributional changes but also changes in the regression coefficient and mean.Finally,we apply the statistic to a groups of financial data.     

Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation H=(RWL)² between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic () and deterministic () coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent which, for a saturated mound slope, yields . Received: 11 November 1997 / Revised in final form: 28 November 1997 / Accepted: 28 November 1997     

Theoretical Study on Mechanism of Cycloadditional Reaction Between Dichloro-Germylidene and Formaldehyde

用MP2/6-31G^*方法研究了单线态二氯亚甲基锗烯与甲醛环加成反应的反应机理,该反应有两条相互竞争的主反应通道,同时伴随着两中间体(INT3和INT4)副产物的生成. 第一条主反应通道所生成的物种为三员环中间体(INT1)和Ge-O顺位的四员环产物(P1);第二条主反应通道所生成的物种为Ge-O对位的扭曲四员环中间体(INT2)和氯迁移产物(P2);P1和INT2分别与甲醛(R2)的进一步作用而导致了两副产物的生成.     

New feature in the Auger peak of adsorbed oxygen

Recent joint theoretical and experimental investigations of Auger core-core-valence spectra of alkali adatoms on simple metals have revealed that such technique is capable to ascertain contributions from different adsorption environments in the signal [M.I. Trioni, S. Caravati, G.P. Brivio, L. Floreano, F. Bruno, A. Morgante, Phys. Rev. Lett. 93 (2004) 206802]. Consequently, to verify if such an effect is present also for other chemical species, we study theoretically the KLV transition of oxygen either as a bulk impurity or as an adsorbate in/on Al and Ag (jellium-like). We make use of the Fermi golden rule in which the matrix elements of the interaction are calculated within DFT. We verify that the relevant physical quantity of this phenomenon is the excited local density of states (LDOS), calculated within a region centered on the core ionized atom. The Auger rate for oxygen in Ag bulk displays a single asymmetric peak, while for adsorbed oxygen a second smaller feature at lower energies, and very close to the first one, appears. This unexpected result follows from the removal of the degeneracy of the m quantum number of the 2p states of oxygen at the surface. It is only displayed on the electronically less dense metal (Ag), but not on Al.