An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

The Classification of Exponential Paths in Sp(2)

众所周知，四阶以上辛群中指数型道路的Ｍａｓｌｏｖ指标可以取任意整数．本文给出了二阶辛群中指数型道路的分类及其Ｍａｓｌｏｖ指标的取值范围，指出了与高阶情形的不同之处．     

Permanence and stability of a predator–prey system with stage structure for predator

A stage-structured predator–prey system with delays for prey and predator, respectively, is proposed and analyzed. Mathematical analysis of the model equations with regard to boundedness of solutions, permanence and stability are analyzed. Some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium, respectively, are obtained.     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, 34.gif" alt="infin" align="MIDDLE" border="0">). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Increase of Calcium Levels at Interphase in NIH 3T3 Cells

The fluorescent calcium ion indicator dye Fluo-3 and DNA-binding dye Hoechst 33342 were employed to determine, in a quantitative microspectrofluorometric study, the intracellular calcium ion concentration ([Ca~(2+)]_i) and the DNA content of individual living NIH3T3 cells. The well-separated excitation and emission properties of these dyes allowed us to establish for each cell both the phase of the cell cycle using DNA content and [Ca~(2+)]_i. We found that the transition from G_1, through S, to the G_2 phase is accompanied by a two-fold increase in [Ca~(2+)]_i. The [Ca~(2+)]_i was inhomologous in each phase of the interphase (G_1, S and G_2) although [Ca~(2+)]_i in the S and G_2 phases was never lower than certain threshold values in the G_1 and S phases respectively. [Ca~(2+)]_i in G_0 cells was lower than that in G_2 cells. These changes in [Ca~(2+)]_i suggest that [Ca~(2+)]_i may be an import regulator of cell cycle progression.     

Accreditation of reference material producers: the example of IRMM's Reference Materials Unit

The potential approaches for third-party assessment of reference material producers are revisited and the activities of the Reference Materials (RM) Unit of the Institute for Reference Materials and Measurements (IRMM) to obtain accreditation to ISO Guide 34 and ISO 17025 are described. Accreditation was related to the Unit as all matrix RM activities of the institute are concentrated there. A management system was established that allows sufficient flexibility to be applicable to a wide range of RMs while being precise enough to ensure compliance with ISO Guides 30, 31 and especially 34 and 35. Accreditation was achieved in 2004 with independent scopes for testing and RM production and was confirmed and extended in 2005. The key aspects of the RM Unit's management system for RM production are presented. Presented at BERM-10, April 2006, Charleston, SC, USA