城镇职工养老保险随机模型研究

构建了包含个人、企业、政府等市场参与者相互制衡的城镇职工养老保险随机模型,该模型涉及了储蓄、工作期消费、个人养老金账户、工资、退休后消费共5个随机变量;利用ITo引理证明了随机微分方程解的存在性,唯一性,利用2010-2014年中国有关宏观数据,对5个变量进行了动态模拟,并对部分参数变动对模型的影响进行分析,得出了储蓄替代率和人口出生率与两期消费正相关,两者的小范围变动不会影响两期消费的趋势等结论.     

一类核具有连续横截面变换半群的秩

设X_n={1,2,…,n}并赋予自然数序,MCK_n是X_n上核具有连续横截面保序或反序变换所构成的半群.K_n是MCK_n的最大正则子半群.本文将考虑K_n的理想K(n,r)={α∈K_n:|im(α)|≤r}(3≤r≤n-1).证明了K(n,r)的秩为(n-r+1)(n-r+2)(n-r+3)/6.     

A Unified Continuous Flow Assembly-Line Synthesis of Highly Substituted Pyrazoles and Pyrazolines

A rapid and modular continuous flow synthesis of highly functionalized fluorinated pyrazoles and pyrazolines has been developed. Flowing fluorinated amines through sequential reactor coils mediates diazoalkane formation and [3+2] cycloaddition to generate more than 30 azoles in a telescoped fashion. Pyrazole cores are then sequentially modified through additional reactor modules performing N-alkylation and arylation, deprotection, and amidation to install broad molecular diversity in short order. Continuous flow synthesis enables the safe handling of diazoalkanes at elevated temperatures, and the use of aryl alkyne dipolarphiles under catalyst-free conditions. This assembly-line synthesis provides a flexible approach for the synthesis of agrochemicals and pharmaceuticals, as demonstrated by a four-step, telescoped synthesis of measles therapeutic, AS-136A, in a total residence time of 31.7 min (1.76 g h⁻¹).     

Three‐dimensional printed magnetophoretic system for the continuous flow separation of avian influenza H5N1 viruses

As a result of the low concentration of avian influenza viruses in samples for routine screening, the separation and concentration of these viruses are vital for their sensitive detection. We present a novel three‐dimensional printed magnetophoretic system for the continuous flow separation of the viruses using aptamer‐modified magnetic nanoparticles, a magnetophoretic chip, a magnetic field, and a fluidic controller. The magnetic field was designed based on finite element magnetic simulation and developed using neodymium magnets with a maximum intensity of 0.65 T and a gradient of 32 T/m for dragging the nanoparticle–virus complexes. The magnetophoretic chip was designed by SOLIDWORKS and fabricated by a three‐dimensional printer with a magnetophoretic channel for the continuous flow separation of the viruses using phosphate‐buffered saline as carrier flow. The fluidic controller was developed using a microcontroller and peristaltic pumps to inject the carrier flow and the viruses. The trajectory of the virus–nanoparticle complexes was simulated using COMSOL for optimization of the carrier flow and the magnetic field, respectively. The results showed that the H5N1 viruses could be captured, separated, and concentrated using the proposed magnetophoretic system with the separation efficiency up to 88% in a continuous flow separation time of 2 min for a sample volume of 200 μL.     

Investigation of the continuous flow of the sample solution on the performance of electromembrane extraction: Comparison with conventional procedure

In this study, electromembrane extraction from a flowing sample solution, termed as continuous‐flow electromembrane extraction, was developed and compared with conventional procedures for the determination of four basic drugs in real samples. Experimental parameters affecting the extraction efficiency were further studied and optimized. Under optimum conditions, linearity of continuous‐flow procedure was within 8.0–500 ng/mL, while it was wider for conventional procedures (2.0–500 ng/mL). Moreover, repeatability (percentage relative standard deviation) was found to range between 5.6 and 10.4% (n  = 3) for the continuous‐flow procedure, with a better repeatability than that of conventional procedures (2.3–5.5% (n  = 3)). Also, for the continuous‐flow procedure, the estimated detection limit (signal‐to‐noise ratio = 3) was less than 2.4 ng/mL and extraction recoveries were within 8–10%, while the corresponding figures for conventional procedures were less than 0.6 ng/mL and 42–60%, respectively. Thus, the results showed that both continuous flow and conventional procedures were applicable for the extraction of model compounds. However, the conventional procedure was more convenient to use, and thus it was applied to determine sample drugs in real urine and wastewater samples.     

Structures of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra

In this paper, we determine the universal central extension, derivation algebra and automorphism group of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra. Furthermore, we generalize these results to the generalized twisted N = 1 Schrödinger–Neveu–Schwarz algebra in the final section.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Hypergeometric approach to Apéry-like series

By reformulating four hypergeometric series formulae, we derive 36 Apéry-like series expressions for the Riemann zeta function, including a couple of identities conjectured by Sun [New series for some special values of L-functions. Nanjing Univ J Math. 2015;32(2): 189–218].     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.