Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients

The Ramanujan Journal - The Gauss summation theorem and an extended $$_3F_2$$ -series of Watson and Whipple type are examined by means of power series expansions. Numerous Ramanujan-like series...     

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].     

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education     

广义Maxwell黏弹性流体在两平板间的非定常流动

将分数阶微积分运算引入Maxwell黏弹性流体的本构方程，研究了黏弹性流体在两平板问的非定常流动．对于广义Maxwell黏弹性流体的分数阶导数模型，导出了对时间具有分数阶导数的特殊运动方程，利用分数阶微积分的Laplace变换理论，得到了流动的解析解．     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education     

Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

氧化镓纳米材料的制备及其在光电探测方面的应用研究进展

近年来,半导体的纳米材料凭借其奇特的介观物理特性,成为当前研究的热点,特别是纳米金属氧化物。氧化镓纳米材料具备优异的光电、气敏、耐压且低损耗等特性,为材料学、电子学和化学等多个研究领域带来了新的机遇。本文概述了氧化镓纳米结构的制备方法,并展望了其在光电探测方面的应用。     

Common extension of bilateral series for Andrews’ q-Bailey and q-Gauss sums

By means of the modified Abel lemma on summation by parts, we establish a common bilateral series extension of the q-Bailey and q-Gauss sums discovered by Andrews (Duke Math. J. 40 (1973), 525–528).     

Synthesis of titanium nitride thin films deposited by a new shielded arc ion plating

Thin films of titanium nitride (TiN) were deposited on stainless steel substrates by a modified deposition technique, double-layered shielded arc ion plating with vicarious circular holes (DL-SAIP). The results show that the TiN film with the distance of 10 mm between the double-layered shield plates had the least droplets. The deposition rate of the films prepared with the new technique was more homogeneous than that of all the other shielded arc ion plating. The film/substrate adhesion and microhardness values of the TiN films were higher than 40 N and 18 GPa, respectively. Thus such TiN thin films can be expected in applications.     

Further determinant identities related to classical root systems

By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.