Twisted cubic theta hypergeometric series

The modified Abel lemma on summation by parts is employed to examine the “twisted” cubic theta hypergeometric series through three appropriately devised difference pairs. Several remarkable summation and transformation formulae are established. The associated reversal series are also evaluated in closed forms, that extend significantly the corresponding q‐series identities.     

工件延误和可拒绝下的单机重新排序问题的近似方案

研究工件延误产生干扰且延误工件可拒绝下的单机重新排序问题。在该问题中,给定计划在零时刻到达的一个工件集需在一台机器上加工,工件集中的每个工件有它的加工时间和权重,在工件正式开始加工前,按照最短赋权加工时间优先的初始排序已经给定,目标函数是极小化赋权完工时间和,据此每个工件的承诺交付截止时间也给定。然而,在工件正式开始加工时,工件集中的部分工件由于延误不能按时到达,这对初始排序的执行产生了干扰,所以需要对初始排序进行调整,即重新排序。为了保证服务水平,允许对延误工件拒绝加工,但需支付相应的拒绝费用。调整后的重新排序的目标是在保证接受工件集中工件的最大延误不超过给定的上界的约束下,使得接受工件集的赋权完工时间和,拒绝工件集的拒绝费用和以及接受工件集中工件的最大延误的赋权惩罚费用之和达到极小。对该问题,设计了一个伪多项式时间动态规划精确算法,并利用稀疏技术得到了一个完全多项式时间近似方案。     

Hidden q-analogues of Ramanujan-like $$\pi $$ π -series

The Ramanujan Journal - By examining known q-series identities, we derive q-analogues of several $$\pi $$ -related infinite series, including some of Ramanujan’s series for $$1/\pi $$ .     

Stability of wavelet frames with matrix dilations

Under certain assumptions we show that a wavelet frame

in remains a frame when the dilation matrices and the translation parameters are perturbed. As a special case of our result, we obtain that if is a frame for an expansive matrix and an invertible matrix , then is a frame if and for sufficiently small 0$">.

     

研究鼻道的分流作用对嗅觉反应的影响

考虑了中、下鼻道的分流作用,把总鼻道内气流的截面平均速度描述为轴向位置的函数,建立了不定常的二维嗅觉模型,并得到了该模型的精确解,精确解揭示了各生理参数之间的内在联系。计算结果表明理论结果与实验结果是一致的,这对进一步研究嗅觉机理具有一定的参考价值。     

杂多铌氧簇聚物的研究进展

多铌氧簇聚物是多金属氧簇聚物的重要组成部分,具有丰富多样的结构类型,在碱催化、光催化产氢等方面具有广泛的应用前景,吸引了越来越多化学工作者的关注。本文系统地综述了主族元素(ⅢA/ⅣA/ⅤA/ⅥA族)为杂原子的杂多铌氧簇聚物和过渡元素(V/Fe/Cu)为杂原子的杂多铌氧聚合物的研究进展,主要包括化合物的合成策略、结构调控、性质及应用的探索。此外,对当前杂多铌氧簇聚物的发展所面临的挑战进行了总结,并对其后续的发展进行了展望。     

Products of two 1ϕ1 series and implications

An expansion formula into bivariate formal power series is established that implies, as consequences, three remarkable identities of partial theta functions due to Warnaar (2003), Schilling–Warnaar (2002) and Andrews–Warnaar (2007).     

Restricted estimates of the fractional integral on the diagonal

For a function in a mixed-norm Lebesgue space, we study the restriction of its fractional integral on the diagonal. We show that the restriction is weakly bounded when the indices satisfy certain conditions. We give a complete characterization of such indices. To prove this result, we generalize a classical result on operators that commute with translations.