Stability radii of positive linear Volterra-Stieltjes equations

We study stability radii of linear Volterra-Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer functions. Then, the class of positive linear Volterra-Stieltjes equations is studied in detail. It is shown that for this class, complex, real and positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices. As direct consequences of the obtained results, we get some results on robust stability of positive linear integro-differential equations and of positive linear functional differential equations. To the best of our knowledge, most of the results of this paper are new.     

The Level-split of the Two-level Entangled Atom in an Optical Field

The behavior of a two-level entangled atom in an optical field with circular polarization is studied in this paper. The interaction of an optical field and one of the entangled atoms is analyzed in detail. A general solution of the SchrAo¨Gdinger equation about the motion of the entangled atom is obtained. The properties of the action are dependent on the initial state of the atom. By detecting the entangled atom out of the field, we can obtain the state of the other atom moving in the field. It is shown that the state of the atom out of the field will influence the energies of the split-levels of the atom in the field.     

Facile preparation of new unsymmetrical curcumin derivatives by solid-phase synthesis strategy

Seventeen unsymmetrical curcumin derivatives were synthesized in good yield and purity by a facile solid phase synthesis strategy.     

Quantification problems in depth profiling of pwr steels using Ar+ ion sputtering and XPS analysis.

The oxide scales of AISI 304 formed in boric acid solutions at 300 degrees C and pH = 4.5 have been studied using X-ray photoelectron spectroscopy (XPS) depth profiling. The present focus is depth profile quantification both in depth and chemical composition on a molecular level. The roughness of the samples is studied by atomic force microscopy before and after sputtering, and the erosion rate is determined by measuring the crater depth with a surface profilometer and vertical scanning interferometry. The resulting roughness (20-30 nm), being an order of magnitude lower than the crater depth (0.2-0.5 microm), allows layer-by-layer profiling, although the ion-induced effects result in an uncertainty of the depth calibration of a factor of 2. The XPS spectrum deconvolution and data evaluation applying target factor analysis allows chemical speciation on a molecular level. The elemental distribution as a function of the sputtering time is obtained, and the formation of two layers is observed-one hydroxide (mainly iron-nickel based) on top and a second one deeper, mainly consisting of iron-chromium oxides.     

Chemical analysis and distribution investigation of trace elements in indium matrix by spark source mass spectrometry

Summary High-purity indium was analysed by spark source mass spectrometry, using electrical and photoplate detection. For the calibration of the differences in elemental sensitivity, a standard sample was prepared in which 10 impurities were determined by graphite furnace atomic absorption spectrometry. In this way accuracies of less than 40% were obtained for relatively homogeneous elements at ppm and sub-ppm level. About 40 elements could be determined with detection limits of 10 to 30 ppb. Two pattern recognition methods, principal component analysis and clustering analysis, were applied to obtain information on trace element distribution, which indicated that a number of elements were strongly spatially correlated in the analysed sample.

---

Chemische Analyse und Verteilungsbestimmung von Spurenelementen in Indium-Matrix durch Funkenquellen-Massenspektrometrie

---

On leave from: Department of Chemistry, Nanjing Normal University, Nanjing, People's Republic of China     

Periodic solutions for a Lotka–Volterra mutualism system with several delays

In the present paper, a Lotka–Volterra type mutualism system with several delays is studied. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions of the mutualism system. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions. Our results are different from the existing ones such as those in of Yang et al. [F. Yang, D. Jiang, A. Ying, Existence of positive solution of multidelays facultative mutualism system, J. Eng. Math. 3 (2002) 64–68] and Chen et al. [F. Chen, J. Shi, X. Chen, Periodicity in a Lotka–Volterra facultative mutualism system with several delays, J. Eng. Math. 21 (3) (2004) 403–409].     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

Lot-sizing with fixed charges on stocks: the convex hull

In this paper, we examine a variant of the uncapacitated lot-sizing model of Wagner–Whitin that includes fixed charges on the stocks. Such a model is natural in a production environment where stocking is a complex operation, and appears as a subproblem in more general network design problems.

Linear-programming formulations, a dynamic program, the convex hull of integer solutions and a separation algorithm are presented. All these turn out to be very natural extensions of the corresponding results of Barany et al. (Math. Programming Stud. 22 (1984) 32) for the uncapacitated lot-sizing problem. The convex hull proof is based on showing that an extended facility location formulation is tight and by projecting it onto the original space of variables.     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.