集值映射图的广义相依导数与真有效解的最优性条件

本文提出了集值映射图的SP-相依导数的概念,利用这个概念,给出了集值向量优化问题两种真有效解的最优性条件.     

Generalized (η,ρ)-Invex Functions and Global Semiparametric Sufficient Efficiency Conditions for Multiobjective Fractional Programming Problems Containing Arbitrary Norms

The purpose of this paper is to develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (η, ρ)-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.     

Effect of boundary conditions on the invariant density of noisy maps at fully-developed chaos

The invariant density of one-dimensional maps in the regime of fully-developed chaos with uncorrelated additive noise is considered. Boundary conditions are shown to play a significant role in determining the precise form of the invariant density, via the manner in which they handle the spill-over, caused by the noise, of orbits beyond the interval. The known case of periodic boundary conditions is briefly recapitulated. Analytic solutions for the invariant density that are possible under certain conditions are presented with applications to specific well-known maps. The case of ‘sticky’ boundaries is generalized to ‘re-injection at the nearest boundary’, and the exact functional equations determining the invariant density are derived. Interesting boundary layer effects are shown to occur, that lead to significant modifications of the invariant density corresponding to the unperturbed (noise-free) case, even when the latter is a constant — as illustrated by an application of the formalism to the noisy tent map. All our results are non-perturbative, and hold good for any noise amplitude in the interval.     

Nonstandard Boundary Conditions in Quantum Mechanics

The class of boundary conditions for wave functions which follow from the quantum mechanical continuity equation for the probability density and the probability current is considered.     

具等式约束的最优性一阶条件研究

本把Botsko于1986年首先提出的关于多元函数f(x)于点x^#取极小值的一阶充分条件加以改进，并推广到具有等式约束的情形。得到的若干成果将为解决经济优化问题提供方便。     

CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS

The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.     

Multidimensional dependency measures

The problem of dependency between two random variables has been studied throughly in the literature. Many dependency measures have been proposed according to concepts such as concordance, quadrant dependency, etc. More recently, the development of the Theory of Copulas has had a great impact in the study of dependence of random variables specially in the case of continuous random variables. In the case of the multivariate setting, the study of the strong mixing conditions has lead to interesting results that extend some results like the central limit theorem to the case of dependent random variables.In this paper, we study the behavior of a multidimensional extension of two well-known dependency measures, finding their basic properties as well as several examples. The main difference between these measures and others previously proposed is that these ones are based on the definition of independence among n random elements or variables, therefore they provide a nice way to measure dependency.The main purpose of this paper is to present a sample version of one of these measures, find its properties, and based on this sample version to propose a test of independence of multivariate observations. We include several references of applications in Statistics.     

Optimization of conditions in static headspace GC

The precision and sensitivity of head-space GC can be improved by careful selection of the operating conditions: partitioning in the vapor phase can be promoted by altering the sample matrix; the ratio of the volumes of the gaseous and liquid phases, the sample temperature, the equilibration time, and the effect of sample mixing should also be considered. Most of the principles covered here can be applied to either manual headspace GC or to headspace GC utilizing an automated sampler.     

Existence results to elliptic systems with nonstandard growth conditions

Nonstandard growth conditions in partial differential equations have been the subject of recent developments in elastic mechanics and electrorheological fluid dynamics [Lecture Notes in Mathematics, vol. 1748, 2000; C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 393-398; Math. USSR Izv. 29 (1987) 33-66]. In this work, elliptic systems with nonstandard growth conditions are studied. Existence and multiplicity results, under growth conditions on the reaction terms, are established.     

Influence of the operating conditions and of the optical transition on non-spectral matrix effects in inductively coupled plasma-atomic emission spectrometry

In order to study in ICP-AES, the influence of the plasma operating conditions, power and carrier gas flow rate, and of the optical transition on non-spectral matrix interferences, line-rich elements such as Mn, Cr and Cu have been selected. Selection of a large pool of lines was possible because of the use of multichannel solid-state detection. An axially viewed plasma was used. Matrices were K, Na, Li, Ca and Mg. Matrix effect was evaluated by comparing the signals for test elements in water. Use of robust conditions led to an almost flat response, while non-robust conditions led to a significant scattering of the signal changes. In the case of Mn, the z⁷P Mn multiplet was exemplified as it contains not only the most Mn sensitive line, the Mn II 257.610 nm resonance line, but also the 259.372 and 260.568 nm resonance lines, and the non-resonant Mn II 343.897 nm line. Even under robust conditions, the non-resonant line exhibited a different behavior. The difference with the other resonance lines was reduced by using an axially viewed ICP with a large injector id, or suppressed by using a radially viewed ICP. In the case of Cr, the z⁶D Cr II multiplet was selected as it contains three resonant lines linked to the a⁶S fundamental, and other non-resonant lines. The behavior was identical under robust conditions, while an abnormal behavior was observed for the Cr II 334.78 nm line under non-robust conditions, depending on the extent of these non-robust conditions. Cu was an interesting element as ionic lines lie in the energy sum range 15.96–16.26 eV, i.e. slightly above the Ar ionization energy. It was shown that, under robust conditions, the line behavior was not similar although the energy range was small. Moreover, this behavior was depending on the ICP system used for the experiment. It was concluded that not only the magnitude of matrix effects depends on the operating conditions but also may depend on the optical transition, illustrating the complexity of these effects.