Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

Dynamic Release of Propranolol HCl from Cationic Ion–Exchanger–Loaded Calcium Alginate Beads

The dynamic release of drug propranolol HCl from the propranolol HCl–resin complex (PRC) loaded calcium alginate beads has been studied in the buffer media of pH 1.2 at the physiological temperature 37°C. The PRC encapsulated beads demonstrated nearly 58.04% release while naked PRC particles released 98.00% drug in 24 h in the gastric fluid. The amount of drug released was found to increase with and decrease in the amount of sodium alginate in the beads. Similarly, with the increase in the amount of entrapped PRC particles within the beads, the quantity of drug released was also observed to increase. The degree of crosslinking of beads also affected the release kinetics. Interestingly, the release from naked PRC particles followed ‘first‐order’ kinetics while PRC particles, entrapped in calcium–alginate beads, exhibited ‘diffusion controlled’ release behavior as indicated by liner nature of fractional release vs. √t plot.     

Flow Through Diffusion Cell Method: A Better Approach to Study Drug Release Behavior as Compared to Traditional Dissolution Test Method

Co‐polymeric hydrogels consisting of N‐vinyl‐2‐pyrrolidone (NVP) and acrylic acid (AAc) were synthesized and evaluated for release of a model drug, i.e., vitamin B₁₂. Release studies in simulated gastric fluid (pH 1.2) and intestinal fluid (pH 7.4), at 37°C, showed the hydrogels to be pH sensitive. An in vitro release study by ‘traditional dissolution test’ (TDT) showed that percent drug released from the hydrogel was nearly 8.6±2.1 and 83.2±4.8 in the media of pH 1.2 and 6.8, respectively. However, in order to incorporate in vivo GI conditions such as acidic pH and high water content in the stomach, low water content and the presence of a semi–solid mass in the large intestine, a new test model, called flow through diffusion cell (FTDC) was also used. The two approaches yielded almost different release profiles. The gels were characterized by thermogravimetric analysis and FTIR spectroscopy.     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.     

First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions

The investigation of electron transport processes in nano-scale architectures plays a crucial role in the development of surface chemistry and nano-technology. Experimentally, an important driving force within this research area has been the concurrent refinements of scanning tunneling microscopy (STM) techniques. The theoretical treatment of the STM operation has traditionally been based on the Bardeen and Tersoff–Hamann methods which take as input the single-particle wave functions and eigenvalues obtained from finite cluster or slabs models of the surface-tip interface. Here, we present a novel STM simulation scheme based on non-equilibrium Green’s functions (NEGF) and Wannier functions which is both accurate and very efficient. The main novelty of the scheme compared to the Bardeen and Tersoff–Hamann approaches is that the coupling to the infinite (macroscopic) electrodes is taken into account. As an illustrating example we apply the NEGF-STM method to the Si(001)-(2×1):H surface with sub-surface P doping and discuss the results in comparison to the Bardeen and Tersoff–Hamann methods.     

Inequalities for Humbert functions

This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications.     

基于不均衡数据的小企业信用风险评价

小企业信用风险评价既是银行风险管理问题,又事关经济社会稳定。针对小企业贷款实践中,违约样本远少于非违约样本、且违约客户误判对银行影响较大的现实,采用不均衡支持向量机对小企业信用风险评价指标进行赋权,进而构建了能有效区分违约客户、非违约客户的评价模型。根据有无特定评价指标、特定评价指标数值变化对贷款小企业违约状态的影响程度赋权;反映了对违约状态影响越大、评价指标权重越大的赋权思路。将违约样本正确识别率、违约样本的准确率与查全率等因素作为支持向量机赋权模型中客户识别率的度量标准,改变了样本数据不均衡所导致的样本总体精度很高、违约样本精度反而不高的现象。研究结果表明:行业景气指数、资本固定化比率、净利润现金含量、恩格尔系数、营业利润率等评价指标对小企业信用风险的影响较大。     

Hall’s and Kőnig’s theorem in graphs and hypergraphs

We investigate the relation between Hall’s theorem and K?nig’s theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall’s theorem, thereby showing that this class strictly contains all K?nig–Egerváry graphs. Furthermore, we give a generalization of Hall’s theorem to normal hypergraphs.     

Dumbbell-Shaped 2,2’-Bipyridines: Controlled Metal Monochelation and Application to Ni-Catalyzed Cross-Couplings

2,2’-Bipyridine ligands (dsbpys) with dumbbell-like shapes and differently substituted triarylmethyl groups at the C5 and C5’ positions showed high ligand performance in the Ni-catalyzed cross-electrophile coupling and the Ni/photoredox-synergistically catalyzed decarboxylative coupling reactions. The superior ligand effects of dsbpys compared to the conventional bpy ligands were attributed to the monochelating nature of dsbpys.     

On a partial integrodifferential equation of Seal’s type

In this paper we generalize a partial integrodifferential equation satisfied by the finite time ruin probability in the classical Poisson risk model. The generalization also includes the bivariate distribution function of the time of and the deficit at ruin. We solve the partial integrodifferential equation by Laplace transforms with the help of Lagrange’s implicit function theorem. The assumption of mixed Erlang claim sizes is then shown to result in tractable computational formulas for the finite time ruin probability as well as the bivariate distribution function of the time of and the deficit at ruin. A more general partial integrodifferential equation is then briefly considered.