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.     

Treated Rice Bran for Scavenging Cr(III) and Hg(II) from Acidic Solution

The purpose of this study was to examine the efficiency with which rice bran (treated or untreated) removes heavy metals, especially Cr(III) and Hg(II), from acidic solution. Sorption assays were done in shaken flasks in the presence of rice bran. Different experimental conditions such as pH, volume of solution, bran weight, particle size, exchange time and stirring time were improved. The efficiency of bran was studied before and after treatments. For treatment, solutions of acid, alkali and salt were used. The results show that after treating with 4 M sodium chloride solution, its efficiency in removal of Cr(III) and Hg(II) was improved. Kinetic measurements of chromium and mercury removal by bran have revealed that sorption equilibrium was obtained after 10 min of contact. Sorption experiments done with various granulometric fractions of rice bran have shown that this sorbent has the same efficiencies in meshes higher than 20. Further research is necessary in order to determine a mechanism for cations removal by the bran. It is mentioned that the process of making polished rice from brown rice discharges rice bran; therefore, it is very inexpensive, with a cost of 1/50 ? 1/40 of that of synthetic sorbent, and thus its use would significantly lower the cost of wastewater treatment.