On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

Estrogen receptor ligands. 12. Synthesis of the major metabolites of an ERalpha-selective, dihydrobenzoxathiin antagonist for osteoporosis

[reaction: see text] During the course of drug metabolism studies, a major metabolite of compound 1 was detected in rhesus monkeys and assigned structure 4. The intriguing biotransformation of 1 leading to 4 was confirmed by a 19-step total synthesis starting from resorcinol (11), the key feature of which was the construction of the oxygen bridge utilizing a phenolic oxidation and trapping sequence. In addition, the synthesis of a related metabolite (5) is described.     

Catalytic enantioselective Conia-ene reaction

An enantioselective intramolecular Conia-ene reaction of beta-dicarbonyl compounds and alkynes to afford methylene cyclopentanes is described. The reaction employs a DTBMSegphos-Pd(II)/Yb(III) dual catalyst system that allows for the asymmetric synthesis of all-carbon quaternary centers and generates a product containing an alkene that can be further manipulated.     

Evidence against the occurrence of artifacts due to carrier ampholyte-protein binding during isoelectric focusing.

The formation of irreversible complexes between carrier ampholyte components and proteins was investigated by gel filtration of mixtures of proteins and radioactively labelled ampholytes. Experiments were performed both with purified proteins (albumin, ferritin, beta-glucuronidase) and with a complex mixture of proteins (serum); in no case was binding of ampholytes to proteins detected. Thus the results argue against the occurrence in isoelectric focusing of proteins of artifacts due to such complex formation.     

Seasonal fluctuation of DNA photodamage in marine plankton assemblages at Palmer Station, Antarctica

Ultraviolet radiation-induced DNA damage frequencies were measured in DNA dosimeters and natural plankton communities during the austral spring at Palmer Station, Antarctica, during the 1999-2000 field season. We found that the fluence of solar ultraviolet-B radiation (UV-B) at the earth's surface correlated with stratospheric ozone concentrations, with significant ozone depletion observed because of "ozone hole" conditions. To verify the interdependence of ozone depletion and DNA damage in natural microbial communities, seawater was collected daily or weekly from Arthur Harbor at Palmer Station, Antarctica, throughout "ozone season," exposed to ambient sunlight between 0600 and 1800 h and fractionated using membrane filtration to separate phytoplankton and bacterioplankton populations. DNA from these fractions was isolated and DNA damage measured using radioimmunoassay. Under low-ozone conditions cyclobutane dimer concentrations in bacterioplankton and phytoplankton communities were maximal. DNA damage measured in dosimeters correlated closely with ozone concentrations and UV-B fluence. Our studies offer further support to the theory that stratospheric deozonation is detrimental to marine planktonic organisms in the Southern Ocean.     

Efficient synthesis of tertiary amines from secondary amines

Reliable N-alkylations of secondary amines have been developed. By using DIAD and TPP (or PS-TPP) a variety of secondary amines can be converted to the corresponding tertiary amines in good to excellent yields with diverse alkylhalides; no formation of quaternary amine salts are observed. These protocols are amenable to combinatorial chemistry libraries, and are also useful for the syntheses of secondary amines by an acid lysis of the cleavable tertiary amino resins.     

Linear free energy relationship of the energy of the CTTS transition of Halide ions with the solvatochromic parameter α

A linear free energy relationship was found betweenv _max, the energy of the absorption maximum of chloride, bromide, or iodide ion in various solvents, and the solvatochromic parameter which is a measure of the hydrogen bond donor ability of the solvent. The relationships are: for chloride,v _max=6.99+50.16 kK; for bromide,v _max=5.52+45.20 kK; for iodide,v _max=5.02+40.33 kK. The correlation ofv _max for iodide ion with gave a larger correlation coefficient and smaller standard deviation than a correlation with the E _T (30) parameter of Dimroth. From the values ofv _max for iodide ion and the solvated electron in liquid ammonia at 25°C, these correlations indicate a preliminary value of 0.00 for the parameter of liquid ammonia. This had not been reported before and is lower than expected from a general knowledge of the physical and chemical properties of liquid ammonia but is consistent with a more detailed consideration and recent gas phase measurements of hydrogen bond donor strength.