The representation type of rational normal scrolls

The goal of this paper is to demonstrate that all non-singular rational normal scrolls \(S(a_0,\ldots ,a_k)\subseteq \mathbb P ^N\), \(N =\sum _{i=0}^k(a_i)+k\), (unless \(\mathbb P ^{k+1}=S(0,\ldots ,0,1)\), the rational normal curve \(S(a)\) in \(\mathbb P ^a\), the quadric surface \(S(1,1)\) in \(\mathbb P ^3\) and the cubic scroll \(S(1,2)\) in \(\mathbb P ^4\)) support families of arbitrarily large rank and dimension of simple Ulrich (and hence indecomposable ACM) vector bundles. Therefore, they are all of wild representation type unless \(\mathbb P ^{k+1}\), \(S(a)\), \(S(1,1)\) and \(S(1,2)\) which are of finite representation type.     

On the origin of the cation templated self-assembly of uranyl-peroxide nanoclusters

Uranyl-peroxide nanoclusters display different topologies based on square, pentagonal and hexagonal building blocks. Computed complexation energies of different cations (Li(+), Na(+), K(+), Rb(+), and Cs(+)) with [UO(2)(O(2))(H(2)O)](n) (n = 4, 5, and 6) macrocycles suggest a strong cation templating effect. The inherent bent structure of a U-O(2)-U model dimer is demonstrated and justified through the analysis of its electronic structure, as well as of the inherent curvature of the four-, five-, and six-uranyl macrocyles. The curvature is enhaced by cation coordination, which is suggested to be the driving force for the self-assembly of the nanocapsules.     

A simple and rapid dispersive liquid-liquid microextraction method followed by GC-FID for determination of N-methylpyrrolidine in cefepime

A simple, rapid and efficient sample preparation technique, dispersive liquid-liquid microextraction, coupled with gas chromatography-flame ionization detection has been developed to determine N-methylpyrrolidine in cefepime. The effect of various experimental factors on the preparation procedure, such as the nature and volume of extraction and disperser solvents, extraction time, the nature of buffer and its pH, and salt effect, was investigated, optimized and the following results were obtained: extraction solvent, chloroform; dispersive solvent and solvent for dissolving cefepime, a mixture of methanol/water (88:12, v/v); salting out agent, NaCl; and buffer, carbonate/bicarbonate (C=0.5?M, pH=12). The optimized conditions were applied to the real sample (cefepime) for the extraction and determination of N-methylpyrrolidine. The calibration graph is linear from 0.02 to 850?mg/L with the square of correlation coefficient 0.999. LOD and LOQ are 6.4 and 21.2?μg/L in solution, respectively, and 0.2 (2×10(-5) ) and 0.6 (6×10(-5) ) μg/g (%, w/w) in cefepime powder, respectively, using sample size 50?mg. Repeatability of the method is good and RSD% for six repeated experiments (C=170?mg/L) is 6.35%.     

A superspace formulation of the BV action for higher derivative theories

We first analyse the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under shift symmetry in the Batalin–Vilkovisky (BV) formalism. We show that the action for this theory can be written in a manifestly extended BRST invariant manner in superspace formalism using one Grassmann coordinate. It can also be written in a manifestly extended BRST invariant manner and on-shell manifestly extended anti-BRST invariant manner in superspace formalism using two Grassmann coordinates.     

On Some Inequalities Concerning Rate of Growth of Polynomials

In this paper we consider a class of polynomials P(z) = a0+∑n v=t a v z v, t ≥ 1not vanishing in |z|k, k≥1 and investigate the dependence of max|z|=1|P(Rz)-P(rz)on max|z|=1|P(z)|, where 1 ≤ r R. Our result generalizes and refines some know polynomial inequalities.     

2000 Vol.11 No.8 P.Preparation of AChE Inhibitors From Jujubogenin

A dammarane derivative dihydrojujubogenin-2-en-1-one, which possesses a skeleton and pharmacophore partially similar to those of Territrem B, a potent AChE inhibitor, was synthesized via three different paths. The anti-AChE activity of this compound and related analogue was measured.