Approximating the integral of a multifunction

Given a weakly converging sequence of measures, we study the convergence of the corresponding integrals of a continuous unbounded multifunction. We also study the implication of these results to variational problems, and provide further approximating results for the integral of a multifunction, involving both truncation of the multifunction and measure approximation.     

On the existence of special depth first search trees

The Depth First Search (DFS) algorithm is one of the basic techniques that is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depth-first spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total-DFS-Graphs. We prove that Total-DFS-Graphs are closed under minors. It follows by the work of Robertson and Seymour on graph minors that there is a finite set of forbidden minors of these graphs and that there is a polynomial algorithm for their recognition. We also provide explicit characterizations of these graphs in terms of forbidden minors and forbidden topological minors. The complete characterization implies explicit linear algorithm for their recognition. In some problems the degree of some vertices in the DFS tree obtained in a certain run are crucial and therefore we also consider the following problem: Let G = (V,E) be a connected undirected graph where |V| = n and let d ? Nⁿ be a degree sequence upper bound vector. Is there any DFS tree T with degree sequence d _T that violates d (i.e., d _T ≤ d , which means: E j such that d _T(j) > d (j))? We show that this problem is NP-complete even for the case where we restrict the degree of only on specific vertex to be less than or equal to k for a fixed k ≥ 2 (i.e., d = (n - 1, ?, n - 1, k, n - 1, ?, n - 1)). 0 1995 John Wiley & Sons, Inc.     

Spectrally Resolved Imaging of Cabot Rings and Howell-Jolly Bodies

The spectral characteristics of erythropoietic cellular inclusions stained by May-Grunwald Giemsa (MGG) were determined by spectrally resolved imaging. Multipixel spectra were obtained from Cabot rings and Howell-Jolly (HJ) bodies, displaying a range of wavelengths of transmitted light. The spectral characteristics of these inclusions were compared with those of isolated DNA, his-tones (type II) and arginine-rich histones (type VI), all stained by MGG. Results of single-cell spectroscopy show that the spectra of Cabot rings and HJ bodies share spectral characteristics with the type II and type VI histones. However, no resemblance was found between Cabot rings and DNA spectra. The spectral analysis of hetero-chromatin displayed a spectral pattern with characteristics of both DNA and histones, while the euchromatin showed a major contribution of the DNA component.     

Subcellular Localization of Sulfonated Tetraphenyl Porphines in Colon Carcinoma Cells by Spectrally Resolved Imaging

Subcellular localization of the dye, 5,10,15,20-tetra(4-sul-fonatophenyl)porphine (TPPS₄) and the more hydrophobic dye, 5,10,15,20-tetra(1-sulfonatophenyl)porphine (TPPS₁), in murine colon carcinoma cells was studied by spectrally resolved imaging (SRI) combined with image processing techniques. Spectrally resolved imaging enabled the acquisition of multipixel fluorescence spectra (>10⁴) from a single cell. Demarcation of specific localization sites and segregation of the irrelevant fluorescence were based on the pixel spectra and by operating the functions of spectral similarity mapping (SSM), principal component analysis (PCA) and spectral classification. The SRI revealed the fine details of the photochemical process that clarify some aspects of subcellular damage. The SRI depicted the differences between TPPS₄ and TPPS, with respect to their initial localization and their fate at the end of the photochemical effect. The dye TPPS₄ was localized initially in lysosomal vesicles, and upon irradiation fluorescence was seen in the nucleus as well as in vesicles. Some of the vesicles were closely related to the nucleus, as resolved by SSM, PCA and spectral classification. Additional light exposure stimulated relocalization of TPPS₄ into the nucleus as well as into the nucleolus, which was clearly depicted by SSM and PCA. Spectral classification showed a third, weak residual cytoplasmic array around the nucleus. The dye TPPS, concentrated in a Golgi-like complex and was resolved in the nuclear envelope and in small vesicles: it was not redistributed into other compartments upon photosensitization. Serum supplementation to the incubation media of colon carcinoma cells treated with TPPS₄ or TPPS, did not change the localization patterns. Pixel spectra of the two dyes in the cells showed spectral shifts and expanded shoulders due to microenvironmental effects. Thus, the chemical nature of the sulfonated phenyl porphines, and not their interaction with serum proteins, was the main determinant of their binding to the lysosomes, nucleus, nucleolus, nuclear envelope or Golgi.     

The kBr/kCl element effect for nucleophilic vinylic substitution of the highly reactive tricyanovinyl-x system by substituted anilines

The element effects for the substitution of tricyanovinyl chloride and bromide by the $\text{p}$-position of three dialkylanilines are k_Br/k_Cl=2.37±0.18. An early transition state for the expulsion of the halide ion from the intermediate zwitterion is indicated.     

Zum massenspektroskopischen Fragmentierungsverhalten von Arylalkylphosphonaten

Zusammenfassung Der Einfluß verschiedener Substituenten auf das Fragmentierungsverhalten von Arylalkylphosphonaten wird diskutiert. Während einige der beobachteten Zerfallsreaktionen analog zu den bei Carbonsäureestern gefundenen verlaufen (z. B.McLafferty-Umlagerung, doppelte Wasserstoffumlagerung bei Estern mit höheren Alkoholen), treten zusätzliche Umlagerungen auf, die für Ester der phosphorigen und der Phosphorsäure typisch zu sein scheinen (z. B. Eliminierung der Phosphor- und Sauerstoffatome unter Rekombination von Kohlenstoffresten).

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The influence of various substituents on the fragmentation behavior of aryl alkyl phosphonates is discussed. Several fragmentation reactions occur as observed with carbonic acid esters (e. g.,McLafferty rearrangement and double hydrogen transfer with esters of higher alcohols). In addition, rearrangements may take place which seem to be typical for esters of the phosphorous and phosphoric acid (e. g., expulsion of the phosphorus and oxygen atoms accompanied by recombination of carbon residues). *** DIRECT SUPPORT *** A3615112 00008

     

A new local search for continuous location problems

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation space search. The local search is applied to the multi-source Weber problem where encouraging results are obtained. This local search is also embedded within Variable Neighbourhood Search producing excellent results.     

Locating a service facility with some unserviced demand

^** Email: zdrezner{at}exchange.fullerton.edu The location of a facility in the plane when service availabilityis a convex decreasing function of the distance (distance decay)is considered. The total cost of the system consists of threecomponents: (i) the cost of waiting in line for service, (ii)the cost of providing the service and (iii) the cost of lostdemand. A generalized Weiszfeld algorithm and a global optimizationtechnique are constructed and tested on problems of up to 10000demand points assuming exponential decay in service. Both algorithmsare very efficient.