Photoemission study of the modification of the electronic structure of transition-metal overlayers on TiO2 surfaces II. Cr on TiO2(0 0 1)

The electronic states of the Cr overlayers on TiO₂(0 0 1) surfaces have been investigated using angle-resolved and resonant photoemission spectroscopy with synchrotron radiation. At lower coverages, Cr deposition on TiO₂(0 0 1) creates two well separated in-gap emissions due to the formation of surface Ti³⁺ (3d¹) ions and Cr³⁺ (3d³) ions. At higher coverages, the in-gap emission is developed into the 2-peak-structure emission of Cr 3d character. The corresponding state is considered to be of metallic nature from the viewpoint of the high ability of oxygen adsorption, but has no Fermi edge, indicating a possibility of forming small Cr clusters on TiO₂(0 0 1) at this stage.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

The Central Limit Problem for Random Vectors with Symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is treated by a variation of Stein’s method which is adapted for continuous symmetries. This work was done while at Stanford University.     

Sets of reflections defining twisted Bruhat orders

Twisted Bruhat orders are certain partial orders on a Coxeter system (W,S) associated to initial sections of reflection orders, which are certain subsets of the set of reflections T of a Coxeter system. We determine which subsets of T give rise to a partial order on W in the same way.     

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by David Brown and York (Phys. Rev. D 55, 1977–1984 1997; Phys. Rev. D 47, 1407–1419 1993). We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

同轴双无衍射光的理论与实验

提出同轴双无衍射光的概念。如果两束汇聚角略有不同的同轴无衍射光同时存在，则它们相互之间叠加干涉后产生一种纵向呈周期变化的光场结构，这是一种新的光束空间分布，这种光束在横向仍是一种同心环光斑，可用于精密对准。而在不同纵向位置，这些同心环的强度分布是不同的，且是周期性变化的。同轴双无衍射光的轴向周期性可用于沿光束传播方向的定位。文中提出了双环缝法、分段圆锥透镜法、正弦相位环光栅法等实现同轴双无衍射光的理论与实验方法，分析了同轴双无衍射光的横向与纵向传播的衍射光斑特性，理论计算与实验测量的结果基本相符合。     

Thermal analysis of renal stones

The chemical composition of 200 renal stones, collected from Taxila, Rawalpindi and Islamabad regions in Pakistan, was determined by thermogravimetric (TG) and differential thermal analysis (DTA) techniques. The thermal curves show weight losses at various temperatures indicating dehydration and decomposition phenomena of renal stones. Results were compared with qualitative data obtained by IR analysis which confirmed the chemical composition of various stones in the solid state. The thermal curves helped in the differentiation of various kinds of water held by stones and their chemical composition was obtained by weight loss during pyrolysis. It was found that 26.5% of the stones were pure whewellite, 3% weddellite, 13% uric acid anhydrous, 7.5% struvite, 2.5% ammonium acid urate, 0.5% cystine and 47% stones had mixed composition. In the mixed state the most frequent combinations were those of calcium oxalate with uric acid (14.5%) and with phosphates (27.5%).

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Zusammenfassung Mittels TG und DTA wurde die chemische Zusammensetzung von 200 Nierensteinen untersucht, die in den Gebieten Taxila, Rawalpindi und Islamabad in Indien gesammelt wurden. Die Thermogramme zeigen Masseverluste bei verschiedenen Temperaturen, die auf Dehydratation und Zersetzung der Nierensteine hinweisen. Die Ergebnisse wurden mit den qualitativen Resultaten aus der IR-Analyse verglichen, welche die chemische Zusammensetzung der verschiedenen Steine im festen Zustand bekräftigte. Die Thermogramme halfen bei der Unterscheidung von verschieden gebundenem Wasser, ihre chemische Zusammensetzung wurde durch Gewichtsverlust bei der Pyrolyse bestimmt. Man fand, daß 26.5 % der Steine aus reinem Whewellit bestanden, 3 % aus Weddellit, 13 % aus anhydrierter Harnsäure, 7.5 % aus Struvit, 2.5 % aus Ammmoniumhydrogenurat, 0.5 % aus Cystin und 47 % der Steine hatten eine gemischte Zusammensetzung. Die häufigsten Kombinationen der Mischzusammensetzungen waren Calciumoxalat mit Harnsäure (14.5 %) und mit Phosphaten (27.5 %).

     

Cauchy problem in the class of monotone increasing functions

The paper establishes some solvability conditions of the Cauchy problem for linear differential equation in the class of monotone increasing functions. The results are applied for clarifying the possibility of flight along a given trajectory under existence of braking forces.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.