Behavior of theta-series under modular substitutions

In this article we provide a transformation formula of certain theta series, and apply it to obtain non-holomorphic vector-valued modular forms.     

New formulation of Horava-Lifshitz quantum gravity as a master constraint theory

Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra scalar mode which can be problematic. A new formulation of non-projectable Horava-Lifshitz gravity, naturally realized as a representation of the master constraint algebra studied by loop quantum gravity researchers, is presented. This yields a consistent canonical theory with first class constraints. It captures the essence of Horava-Lifshitz gravity in retaining only spatial diffeomorphisms (instead of full space-time covariance) as the physically relevant non-trivial gauge symmetry; at the same time the local Hamiltonian constraint needed to eliminate the extra mode is equivalently enforced by the master constraint.     

2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions

We consider families of curves with extra automorphisms in ?₃, the moduli space of smooth hyperelliptic curves of genus g = 3. Such families of curves are explicitly determined in terms of the absolute invariants of binary octavics. For each family of positive dimension where |Aut (C)|>4, we determine the possible distributions of weights of 2-Weierstrass points.     

基于CSO-SVR的气膜钢筋混凝土储仓主体结构施工成本预测研究

为了较准确的预测气膜钢筋混凝土储仓主体结构施工成本,提出一种鸡群算法(CSO)和支持向量回归机(SVR)结合模型,即CSO-SVR,利用CSO算法对SVR进行寻优得到全局最优解,从而得到具有最佳参数的支持向量回归机模型,通过气膜钢筋混凝土储仓主体结构施工成本数据预测仿真,结果显示:CSO-SVR模型预测精度高于PSO-SVR,GA-SVR,SVR,BPNN等方法,是预测气膜钢筋混凝土储仓主体结构施工成本的有效工具.     

Persistence of Metal Residues in Sewage Sludge Treated Soils Over Seventeen Years

Abstract

Results from two long-term sewage sludge experiments conducted on different soil types are presented. Sewage sludges highly contaminated with Cr, Cu, Ni or Zn and a relatively uncontaminated sludge were applied at both sites at the same rates and metal contents in 1968. The Cr-rich sludge also had a high Cd content. Plot soils were sampled in 1972, 1976 or 1977, 1981 and 1985 and total and extractable metal contents determined. Metals added in sewage sludge may change their form but persist in soils in an extractable and plant available form for many years. There is little difference in soil extractable contents or plant uptake of Cu and Zn whether sludge is applied as one single application or as its equivalent in four separate annual applications of one quarter the amount. The percentages of the total chromium contents extractable by both EDTA and acetic acid were small and this was reflected in a low uptake of this element by pasture herbage species (<0.3 mg Cr/kg DM).     

Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials

In this paper the set of general polynomial sequences is considered. An elementary systematic approach is proposed. In fact a structure of group is given and for every element of this group recurrence relations and determinant forms are derived. Applications of the derived determinant forms are considered. In particular, the general linear interpolation and bounds of the zeros of each polynomial of the sequence are sketched. Finally, as an illustrative example, the shifted (with respect to the degree) Genocchi polynomial sequence is analyzed.     

Kinetic spectrophotometric determination of pravastatin in drug formulations via derivatization with 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl)

A simple and sensitive kinetic spectrophotometric method for the quantitative analysis of pravastatin sodium (PVS) in pure and pharmaceutical formulations has been described. The method is based on the formation of colored product between PVS and 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl) in acetone medium at 55 ± 2 °C. The reaction is followed spectrophotometrically by measuring the increase in absorbance at 462 nm as a function of time. The initial rate and fixed time methods were adopted for constructing the calibration curves. The linearity ranges were found to be 15.0–50.0 and 10.0–70.0 μg mL^?1 for initial rate and fixed time methods, respectively. The limits of detection for initial rate and fixed time methods are 0.029 and 0.086 μg mL^?1, respectively. Both methods have been applied successfully for the estimation of PVS in commercial dosage forms with no interference from the excipients. The results are compared with the HPLC pharmacopoeial method.