Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

Antinociceptive and anti-inflammatory effects of a lectin-like substance from Clitoria fairchildiana R. Howard seeds

Lectins are proteins that have the ability to bind specifically and reversibly to carbohydrates and glycoconjugates, without altering the structure of the glycosyl ligand. They are found in organisms such as viruses, plants and humans, and they have been shown to possess important biological activities. The objective of this study was to purify and characterize lectins in the seeds of Clitoria fairchildiana, as well as to verify their biological activities. The results indicated the presence of a lectin (CFAL) in the glutelin acid protein fraction, which agglutinated native rabbit erythrocytes. CFAL was purified by column chromatography ion-exchange, DEAE-Sephacel, which was obtained from a peak of protein retained in the matrix by applying 0.5 M NaCl using the step-wise method. Electrophoretic analysis of this lectin in SDS-PAGE indicated a two band pattern protein molecular mass of approximately 100 and 116 kDa. CFAL proved to be unspecific to all carbohydrates/glycoconjugates in common use for the sugar inhibition test. This lectin showed no significant cytotoxicity to human red blood cells. It was observed that CFAL has anti-inflammatory activity in the paw edema induced by carrageenan model, in which a 64% diminution in edema was observed. Antinociceptive effects were observed for CFAL in the abdominal writhing test (induced by acetic acid), in which increasing doses of the lectin caused reduction in the number of contortions by up to 72%. It was concluded that the purified and characterized lectin from the seeds of Clitoria fairchildiana has anti-inflammatory and antinociceptive activity, and is not cytotoxic to human erythrocytes.     

Purification,Partial Characterization,and CNBr-Sepharose Immobilization of a Vasorelaxant Glucose/Mannose Lectin from Canavalia virosa Seeds

A novel mannose/glucose-binding lectin from Canavalia virosa (designated as ConV) has been purified from seeds of C. virosa by affinity chromatography on a mannose-Sepharose 4B column. ConV strongly agglutinates rabbit erythrocytes and was inhibited by monosaccharides (D-mannose, D-glucose, and α-methyl-D-mannoside) and glycoproteins (ovalbumin and fetuin). SDS-PAGE revealed three bands corresponding to three subunits (α, β, and γ) confirmed by ESI mass spectrometry with exact mass of 25,480?±?2 Da, 12,864?±?1 Da, and 12,633?±?1 Da, respectively. The purified lectin was more stable in pH ranging from 7.0 to 9.0, supported up to 80?ºC without any loss in activity and unaffected by EDTA. ConV showed no toxicity against Artemia sp. nauplii and relaxed endothelized rat aorta, with the participation of the lectin domain. In our tests, the lectin immobilized on CNBr-Sepharose was capable of binding 0.8 mg of ovalbumin per chromatography, allowing the use of ConV as a tool for capture and purification of glycoproteins.     

Molecular characterization and tandem mass spectrometry of the lectin extracted from the seeds of Dioclea sclerocarpa Ducke

Lectin from the seeds of Dioclea sclerocarpa (DSL) was purified in a single step by affinity chromatography on a Sephadex G-50 column. The primary sequence, as determined by tandem mass spectrometry, revealed a protein with 237 amino acids and 81% of identity with ConA. DSL has a molecular mass of 25,606 Da. The β and γ chains weigh 12,873 Da and 12,752 Da, respectively. DSL hemagglutinated rabbit erythrocytes (both native and treated with proteolytic enzymes), showing stability even after one hour of exposure to a specific pH range. The hemagglutinating activity of DSL was optimal between pH 6.0 and 8.0, but was inhibited after incubation with D-galactose and D-glucose. The pure protein possesses a molecular mass of 25 kDa by SDS-PAGE and 25,606 Da by mass spectrometry. The secondary structure content was estimated using the software SELCON3. The results indicate that b-sheet secondary structures are predominant in DSL (approximately 42.3% antiparallel b-sheet and 6.7% parallel b-sheet). In addition to the b-sheet, the predicted secondary structure of DSL features 4.1% a-helices, 15.8% turns and 31.3% other contributions. Upon thermal denaturation, evaluated by measuring changes in ellipticity at 218 nm induced by a temperature increase from 20 °C to 98 °C, DSL displayed cooperative sigmoidal behavior with transition midpoint at 84 °C and permitted the observation of two-state model (native and denatured).