On the entropy of a product endomorphism in infinite measure spaces

Summary In this note, a relationship is established between the entropy, defined by Krengel for an endomorphism of a -finite measure space, and the notion of a spreading partition. This relationship is used to answer in the quasi-finite case a question raised by Krengel concerning the entropy of the product endomorphism on the direct product of a finite and -finite measure space.     

Distribution of metal-free sulfonated phthalocyanine in subcutaneously transplanted murine tumors

Metal-free sulfonated phthalocyanine with the average number of sulfonate groups per molecule 2.4 (H(2)PcS(2.4)) was recently proved to be an efficient photosensitizer for the photodynamic therapy. Fluorescence spectral imaging microscopy was applied here to study localization and relative concentration of H(2)PcS(2.4) with micron-scale resolution in subcutaneously transplanted murine tumors: Ehrlich mammary gland carcinoma (EC), Lewis lung carcinoma (LLC), P388 lymphoid leukemia (P388) and B16 melanoma (B16). The study of cryogenic tissue sections prepared 24 h after H(2)PcS(2.4) intravenous injection revealed that H(2)PcS(2.4) was present in all tissue structures in the monomeric photoactive state. The preferential accumulation of H(2)PcS(2.4) was documented in tumor cells and adjacent non-tumor tissues (skin structures, fatty tissue, connective tissue enriched in fibrous component and infiltrated with fibroblasts and macrophages) for all the studied tumor models. P388 and B16 were stained with H(2)PcS(2.4) less than adjacent skin structures, whereas EC and LLC accumulated H(2)PcS(2.4) alike or higher than particular skin structures. Staining of EC and LLC was similar and ca. 1.4 and 2 times higher than that of B16 and P388, respectively, thus revealing the differences in ability of particular tumor strains to H(2)PcS(2.4) accumulation. The H(2)PcS(2.4) concentration in remote healthy tissues (skin, muscles and connective tissue) was 2-3 times lower as compared with the analogous tissue structures from the tumor area, whereas subcutaneous fatty tissue staining did not depend on the tissue-to-tumor distance. The tissue distribution of H(2)PcS(2.4) predefines the combined action of two photodynamic damage mechanisms: eradication of tumor due to the direct tumor cell destruction and suppression of tumor growth due to the injury of growth supporting system.     

Monoalkyl,chiral-at-metal 'constrained geometry' complexes as efficient alpha-olefin and methyl methacrylate polymerisation catalysts

A new class of monoalkyl or monochloro constrained geometry group 4 complexes has been synthesized; upon activation with aluminium activators they serve as efficient catalysts for olefin polymerisation and for polymerisation of methyl methacrylate.     

Theoretical vibrational analysis of monohalogenated phenols

Harmonic vibrational frequencies of a representative series of X-phenols (X = F, Cl, Br) in ortho, meta and para positions are determined using density functional theory (B3LYP) in conjunction with 6-311 + + G(d,p), 6-311 + + G(2d,2p), and 6-311 + + G(2df,2p) basis sets. Their complete and clear-cut vibrational assignment based on the concept of the potential energy distribution is carried out. Such assignment allows to resolve a number of uncertainties appeared in the previous studies and to propose a new explanation of frequency alterations of particular vibrational modes in this series.     

Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.