Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Quantum Chemical Studies of Intermolecular Interactions

This thesis studies the intermolecular interactions in (i) boron-nitrogen based systems for hydrogen splitting and storage, (ii) endohedral complexes, A@C60, and (iii) aurophilic dimers. We first present an introduction of intermolecular interactions. The theoretical background is then described. The research results are summarized in the following sections. In the boron-nitrogen systems, the electrostatic interaction is found to be the leading contribution, as 'Coulomb Pays for Heitler and London' (CHL). For the endohedral complex, the intermolecular interaction is formulated by a one-center expansion of the Coulomb operator 1/rab. For the aurophilic attraction between two C2v monomers, a London-type formula was derived by fully accounting for the anisotropy and point-group symmetry of the monomers.

Molecular Modelling of Estrogen-Producing Enzymes CYP450 Aromatase and 17beta-Hydroxysteroid Dehydrogenase Type 1

Breast cancer is the most common cancer in women in the western countries. Approximately two-thirds of breast cancer tumours are hormone dependent, requiring estrogens to grow. Estrogens are formed in the human body via a multistep route starting from cholesterol. The final steps in the biosynthesis include the CYP450 aromatase enzyme, converting the male hormones androgens (preferred substrate androstenedione ASD) into estrogens(estrone E1), and the 17beta-HSD1 enzyme, converting the biologically less active E1 into the active hormone 17beta-hydroxyestradiol E2. E2 is bound to the nuclear estrogen receptors causing a cascade of biochemical reactions leading to cell proliferation in normal tissue, and to tumour growth in cancer tissue. Aromatase and 17beta-HSD1 are expressed in or near the breast tumour, locally providing the tissue with estrogens. One approach in treating hormone dependent breast tumours is to block the local estrogen production by inhibiting these two enzymes. Aromatase inhibitors are already on the market in treating breast cancer, despite the lack of an experimentally solved structure. The structure of 17beta-HSD1, on the other hand, has been solved, but no commercial drugs have emerged from the drug discovery projects reported in the literature. Computer-assisted molecular modelling is an invaluable tool in modern drug design projects. Modelling techniques can be used to generate a model of the target protein and to design novel inhibitors for them even if the target protein structure is unknown. Molecular modelling has applications in predicting the activities of theoretical inhibitors and in finding possible active inhibitors from a compound database. Inhibitor binding at atomic level can also be studied with molecular modelling. To clarify the interactions between the aromatase enzyme and its substrate and inhibitors, we generated a homology model based on a mammalian CYP450 enzyme, rabbit progesterone 21-hydroxylase CYP2C5. The model was carefully validated using molecular dynamics simulations (MDS) with and without the natural substrate ASD. Binding orientation of the inhibitors was based on the hypothesis that the inhibitors coordinate to the heme iron, and were studied using MDS. The inhibitors were dietary phytoestrogens, which have been shown to reduce the risk for breast cancer. To further validate the model, the interactions of a commercial breast cancer drug were studied with MDS and ligand–protein docking. In the case of 17beta-HSD1, a 3D QSAR model was generated on the basis of MDS of an enzyme complex with active inhibitor and ligand–protein docking, employing a compound library synthesised in our laboratory. Furthermore, four pharmacophore hypotheses with and without a bound substrate or an inhibitor were developed and used in screening a commercial database of drug-like compounds. The homology model of aromatase showed stable behaviour in MDS and was capable of explaining most of the results from mutagenesis studies. We were able to identify the active site residues contributing to the inhibitor binding, and explain differences in coordination geometry corresponding to the inhibitory activity. Interactions between the inhibitors and aromatase were in agreement with the mutagenesis studies reported for aromatase. Simulations of 17beta-HSD1 with inhibitors revealed an inhibitor binding mode with hydrogen bond interactions previously not reported, and a hydrophobic pocket capable of accommodating a bulky side chain. Pharmacophore hypothesis generation, followed by virtual screening, was able to identify several compounds that can be used in lead compound generation. The visualisation of the interaction fields from the QSAR model and the pharmacophores provided us with novel ideas for inhibitor development in our drug discovery project.

Bernard Bernstein Archive, 1941-2008 (bulk bulk 1960-1984).

Bernard Bernstein collection documents professional activities of Bernard Bernstein, a jeweler, metal smith, writer, and teacher. The collection includes artifacts, correspondence, documents, manuscripts, printed materials, photographs, other visual materials, and sketches.The larger part of the collection includes materials dealing with the artistic side of Bernard Bernstein. These materials are found throughout the collection and consist of artifacts produced during his schooling at City College (Series I: Artifacts), various jewelry designs produced by Bernard Bernstein for commercial use (Series III: Designs), certificates and awards (Series V: General), and materials pertaining to a number of shows and exhibits that Bernard Bernstein was a part of (Series IV: Exhibitions and Art Catalogues).Other materials include documents pertaining to Bernard Bernstein education, professional carrier as a teacher ( Series II: City College of the City University of New York, Series V: General), and his articles in professional journals (Series VI: Printed Materials).In some cases materials are accompanied by Bernard Bernstein’s notes explaining the significance and provenance of the documents.

Digestion of forages in the rumen is increased by the amount but not the type of protein supplement

Three polyester bag experiments were conducted with fistulated Bos indicus steers to determine the effect of the amount and type of nitrogen (N) supplement on the digestion rate of forages different in quality. In Experiment 1, test substrates were incubated in polyester bags in the rumen of steers fed ryegrass, pangola grass, speargrass and Mitchell grass hays in a 4 by 4 Latin-square design. In Experiment 2, test substrates were incubated in polyester bags in the rumen of steers fed speargrass hay supplemented with urea and ammonium sulfate (US), branched-chain amino acids with US (USAA), casein, cottonseed meal, yeast and Chlorella algae in a 7 by 3 incomplete Latin-square design. In Experiment 3, test substrates were incubated in polyester bags in the rumen of steers fed Mitchell grass hay supplemented with increasing amounts of US or Spirulina algae (Spirulina platensis). The test substrates used in all experiments were speargrass, Mitchell grass, pangola grass or ryegrass hays. Digestion rate of the ryegrass substrate was higher than that of the speargrass substrate (P < 0.05) in Experiment 1. Supplementation with various N sources increased the degradation rate and effective degradability of all incubated substrates above that apparent in Control steers (P < 0.05; Experiment 2). Supplementation of US and Spirulina increased degradation rate and effective degradability of ryegrass, pangola grass and Mitchell grass substrates above that apparent in Control steers (P < 0.05; Experiment 3). However, there was no further response on digestion rate of the substrates in increasing supplementation levels either for US or Spirulina. In conclusion, rate of digestion was affected by forage physical and anatomical properties. Supplementation with various N sources increased rate of digestion when the Control forage ration was very low in N but once a minimum level of N supplementation was reached, irrespective of form of N or other potential growth factors, there was no further increase in rate of digestion.

Herman Bernstein 1897-1935

Correspondence, clippings, manuscripts, notes, reports, relating to Bernstein's journalistic, literary and diplomatic careers. Correspondence with well-known literary, political and communal, society personalities, 1908-1935. Includes Cyrus Adler, Viscount Allenby, Joseph Barondess, Bernard Baruch, Henri Bergson, Hayyim Nahman Bialik, Jacob Billikopf, Vladimir Bourtzeff, Louis Brandeis, Robert Cecil, Fyodor Chaliapin, Jacob de Haas, Albert Einstein, Henry Ford, Felix Frankfurter, Herbert Hoover, Vladimir Jabotinsky, Horace M. Kallen, Peretz Hirschbein, Peter Kropotkin, Herbert Lehman, Louis Lipsky, Judah L. Magnes, Louis Marshall, Henry Morgenthau, Max Nordau, Adolph Simon Ochs, David de Sola Pool, Bernard G. Richards, Theodore Roosevelt, Julius Rosenwald, Jacob Schiff, Harry Schneiderman, Maurice Schwartz, George Bernard Shaw, Sholem Aleichem, Nathan Straus, Henrietta Szold, Chaim Tchernowitz, Leo Tolstoy, Samuel Untermyer, Henry Van Dyke, Lillian Wald, Felix Warburg, Chaim Weizman n, Jefferson Williams, Stephen Wise, Israel Zangwill. Correspondence and other materials relating to Bernstein's post as U.S. ambassador to Albania. Materials pertaining to Bernstein's editorial work at *The Day*, *Jewish Tribune*, *New York Herald*, *Jewish Daily Bulletin*. Materials pertaining to Bernstein's involvement with the American Jewish Committee. Correspondence with organizations including American Jewish Congress, *American Hebrew*, HIAS, *Jewish Chronicle* (London), Jewish Community of New York, *Menorah Journal*, *New York American*, *New York Times*, ORT, U.S. Dept. of State, Yiddish Art Theater, Zionist Organization of America. Articles, clippings, correspondence and court materials relating to the Ford libel suit. Miscellaneous documents and reports relating to the Paris Peace Conference, the Jewish situation in Russia, 1917-1920, Russian revolutionary events of 1917. News dispatches from Russia, 1917-1920s. Translations by Bernstein of Russian wri Andre yev,

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Development of type I genetic markers from expressed sequence tags in highly polymorphic species

Expressed sequence tag (EST) databases provide a primary source of nuclear DNA sequences for genetic marker development in non-model organisms. To date, the process has been relatively inefficient for several reasons: - 1) priming site polymorphism in the template leads to inferior or erratic amplification; - 2) introns in the target amplicon are too large and/or numerous to allow effective amplification under standard screening conditions, and; - 3) at least occasionally, a PCR primer straddles an exon–intron junction and is unable to bind to genomic DNA template. The first is only a minor issue for species or strains with low heterozygosity but becomes a significant problem for species with high genomic variation, such as marine organisms with extremely large effective population sizes. Problems arising from unanticipated introns are unavoidable but are most pronounced in intron-rich species, such as vertebrates and lophotrochozoans. We present an approach to marker development in the Pacific oyster Crassostrea gigas, a highly polymorphic and intron-rich species, which minimizes these problems, and should be applicable to other non-model species for which EST databases are available. Placement of PCR primers in the 3′ end of coding sequence and 3′ UTR improved PCR success rate from 51% to 97%. Almost all (37 of 39) markers developed for the Pacific oyster were polymorphic in a small test panel of wild and domesticated oysters.