Ground states of two-component attractive Bose–Einstein condensates I: Existence and uniqueness

We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in ${\mathbb{R}}^2$, where the intraspecies interaction $(?a_1,?a_2)$ and the interspecies interaction ?β are both attractive, $i.e$, $a_1$, $a_2$ and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\beta \nearrow {\beta }^{?}=a^{?}+\sqrt{(a^{?}?a_1)(a^{?}?a_2)}$, where $0<a_i<a^{?}:={6w6}_2^2$ ($i=1,2$) is fixed and w is the unique positive solution of $\mathrm{\Delta }w?w+w^3=0$ in ${\mathbb{R}}^2$. The semi-trivial limit behavior of ground states is tackled in the companion paper [12].     

Optical analysis of polymer powder materials for Selective Laser Sintering

This study increases the basic understanding of optical material properties of polymer powders used in selective laser sintering (SLS). Therefore, different polymer powder materials were analyzed regarding their optical material properties with an integration spheres measurement setup. By the measurements a direct connection between the absorption behavior of the solid material and the overall optical material characteristics of the same material in powdery form could be shown. The results were used to develop an advanced explanation model for the optical material properties of powders. At present, existing explanation models only consider the occurring of multiple reflections in the gaps between the particles to explain the overall optical material properties of powder materials. Thus, by also considering the absorption behavior of the single particles, the basic understanding of the beam-matter interaction and their effect on the optical material properties of powder materials can be expanded.     

均衡约束数学规划问题的一种新的约束规格

本文研究了均衡约束数学规划(MPEC)问题.利用其弱稳定点,获得了一种新的约束规格–MPEC的伪正规约束规格.用一种简单的方式,证明了该约束规格是介于MPEC-MFCQ(即MPEC,Mangasarian-Fromowitz约束规格)与MPEC-ACQ(即MPEC,Abadie约束规格)之间的约束规格,因此该约束规格也可以导出MPEC问题的M-稳定点.最后通过两个例子,说明了该约束规格与MPEC-MFCQ以及与MPEC-ACQ之间是严格的强弱关系.     

Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems

In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi e?ciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, su?cient conditions for local (weak) quasi e?cient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.     

Constraint-Based Representations of Statistical Graphs

Abstract

Pictor is an environment for statistical graphics that promotes simple commands for common uses and offers the ability to experiment with whole new paradigms. Pictor describes graphs as graphical objects whose component pieces are related by several sorts of constraints. This article describes in detail the constraint system that Pictor uses.     

Some results on regularity in vector optimization

In this paper we suggest an approach to regularity in, vector optimization which extends the one given in [9]; some necessary or sufficient regularity conditions are given for a wide class of nondifferentiable vector optimization problems which embraces the convex ones.     

A time-stepping procedure based on convolution for the mixed finite element approximation for porous media flow

A time-stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post-processed by the convolution with Bramble-Schatz kernel. Convergence analysis shows that the property of superconvergence, originally held for the approximation of velocity, can be retained for the approximation of concentration variable. Compared with the traditional results in references, the constraint conditions between parameters in this paper are improved essentially.     

A parametric view on the Mangasarian–Fromovitz constraint qualification

The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers. Received May 8, 1995 / Revised version received February 12, 1998 Published online February 25, 1999     

Characterization of Standard Reference Material 2942, Ce-ion-doped glass, spectral correction standard for UV fluorescence

Standard Reference Material (SRM) 2942 is a cuvette-shaped, Ce-ion-doped glass, recommended for use for relative spectral correction of emission from 320 to 430 nm and day-to-day performance verification of steady-state fluorescence spectrometers. Properties of this standard that influence its effective use or contribute to the uncertainty in its certified emission spectrum were explored here. These properties include its photostability, absorbance, dissolution rate in water, anisotropy and temperature coefficient of fluorescence intensity. The expanded uncertainties in the certified spectrum are about 9% around the peak maximum at 330 nm, using an excitation wavelength of 310 nm. The SRM also exhibits a strong resistance to photodegradation, with no measurable decrease in fluorescence intensity even after 25 h of irradiation with UV light>280 nm from a Xe lamp.     

Faddeev-Jackiw and the improved methods in quantization of the superconductive system

In this paper, we give the overview on Faddeev-Jackiw method and its improved one, as well as the relative studies recently and realize quantization of the superconductive system by the two methods, we get the same results by the two disposal methods. Furthermore, at convenience of the familiar study in this system, we take it as the application example and compare the two methods by dealing with this system from different aspects, demonstrate the improved Faddeev-Jackiw method is effective and significative, and represent the superiorities of the improved Faddeev-Jackiw method. We show that the improved method may simplify investigations of different complicated constrained systems.