CONVERGENCE ANALYSIS AND MRALLEL IMPLEMENTION FOR THE DIRECTEDGRAPH -ALGORITHM

1IntroductionAssulliingX=(xl.T?'....:ltnItR",iff(X):Rn~Rcanbeformedasfollows:whereOdenotesabinaryopertion(suchas ,x,tnax,minetc.),wecallf(X)aspearablefun.ti.n[1].L.Cooperstated'thatmostoffunctionsmaybetransformedtoseparableformsbyincreasingassistantvariablesandconstraints[2].InPracticalapplications,multistageproduction-inventoryproblems,equipmentreplacementproblems,resouceallocationproblemsandsomeschedulingproblemsetc.,canallbeformulatedasthefollowingforms[3].wherefi,hi(15jSn):R~R.Appara…     

Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented.     

The Order Completion Method for Systems of Nonlinear PDEs: Pseudo-topological Perspectives

By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.      

Determination of sub-nanogram quantities of ruthenium by flameless atomic absorption spectrometry

Flameless atomic absorption spectrometry has been applied to the determination of subnanogram quantities of ruthenium in a variety of matrices encountered in the solidification of nuclear waste. Detection limits ranged to below 10^?10 g, depending on the sample matrix. Most matrix effects could be eliminated by proper selection of atomizer temperature program, allowing the use of a single set of standards in 0.1 N HCl. The one exception was the calcined solid matrix, where a fusion and extraction were used to dissolve the ruthenium and separate it from matrix constituents.     

Fuzzy network technique for technological forecasting

The stochastic network technique is known to be a powerful tool carrying out a technological forecast of complex systems. A network dealt with is characterized by a tetrad of essential elements: logical nodes with some inputs and outputs, probabilistics activity branches, feedback loops, and multiple sources and sinks. A set of network parameters is defined for each element and their values are estimated for practical analysis of the network. In the case where the system to be treated is very large and/or complex, it cannot always be represented by a definite network and therefore forecasted values of parameters are inevitably indefinite themselves. A conventional probabilistic approach is sometimes inadequate in such a case. In the light of these facts, the paper proposes a fuzzy network technique, in which among activity branches emanating from a node, a branch to be undertaken once the node is realized belongs to a fuzzy set; and the time required to complete an activity branch belongs to a fuzzy set. Operations of maximum and minimum for sum and product of fuzzy sets take the place of manipulations of addition and multiplication for probabilities, respectively. Although the operations are somewhat formal, the obtained results seem interesting. A numerical example is attached to show a comparison of the proposed technique with the conventional one.     

Intra-elemental photoelectron line intensities and their significance to quantitative analysis

Intraelemental relative photoelectron line intensities for 20 pure elements obtained under ultrahigh vacuum (5·10^?9 torr) and high resolution with cleaned surfaces are presented. Theoretical and experimental aspects of relative photoelectron line intensities as well as other characteristics of significance to quantitative analysis are discussed. Experimental data are related to theoretical results and compared with other recent work.     

三角债清理的模型与算法

本文用图论和网络的观点研究了三角债问题，建立了解决三角债问题的网络模型，给出了为解决三角债所需投入的最少资金的计算公式及具体操作方法，这一研究无疑具有很强的理论意义和实际意义，所提供的算法也具有较好的可操作性。     

Banach空间上非Lipschitz映射的渐近行为

设Ｃ是具Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间Ｅ的非空凸闭子集，Ｇ是定向集．｛Ｔ_ｔ：ｔ∈Ｇ｝是Ｃ上的渐近非扩张型映照．本文给出了｛Ｔ_ｔ：ｔ∈Ｇ｝的弱收敛定理．     

The Lattice of Completions of an Ordered Set

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind–MacNeille completion P. The lattice K(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closure operators on any complete lattice. In particular, if K(P) is finite, then it is an upper semimodular lattice and an upper bounded homomorphic image of a free lattice, and hence meet semidistributive.     

Dependence of the spectral width of the self-absorbed Sr 4607.33Åresonance line on Sr atomic density in a flame

Using a pressure-scanned Fabry-Pérot interferometer, we measured spectral profiles of the self-absorbed Sr resonance line at 4607.33Åemitted in a pre-mixed, laminar, shielded air-C₂H₂ flame at 1 atm for various Sr-solution concentrations. The dependence of the full width at one-half maximum (FWHM) on Sr atomic density in the flame was found to agree with a calculation based on the Voigt expression and Beer's law. It appears that one can derive the FWHM under optically thin conditions (i.e. at vanishing Sr atomic density) by linear extrapolation from measurements made at higher concentrations where the signal-to-noise ratio is good, but broadening due to self-absorption plays a role.