工件有到达时间及可拒绝下的同类平行机排序问题的近似算法

本文研究工件有到达时间且可拒绝下的同类平行机排序问题。在该问题中, 给定一个待加工工件集, 每个工件在到达之后, 可以被选择安排到$m$台同类平行机器中的某一台机器上进行加工, 也可以被选择拒绝加工, 但需支付一定的拒绝惩罚费用。目标函数是最小化接受工件集的最大完工时间与拒绝工件集的总拒绝费用之和。当$m$为固定常数时, 设计了一个伪多项式时间动态规划精确算法; 当$m$为任意输入时, 设计了一个近似算法, 当接受工件个数大于$(m-1)$时, 该算法近似比为3, 当接受工件个数小于$(m-1)$时, 该算法近似比为$(2+\rho)$, 其中$\rho$为机器加工速度最大值和最小值的比值。最后通过算例演示了算法的运行。     

Note on the Bradley and Ramanujan summation

The hypergeometric series of Bradley and Ramanujan is evaluated by means of the binomial convolutions of Hagen and Rothe, which presents, alternatively, a short proof of the recent result of Bradley about Ramanujan's enigmatic claim.

     

Dominance method for plane partitions III-flagged skew plane partitions

This paper investigates the enumerative problems of flagged skew plane partitions in which each row (column) has an upper and a lower bounds on the entries. By means of dominance technique, a direct and elementary derivation for their generating functions is presented which may be more accessible to readers.     

Binomial convolutions and hypergeometric identities

By means of formal power series calculus, some new recurrences on the generating functions for the generalized Abel and Gould coefficients are derived from the Gould's work (1956–1961), which yield equivalently several convolution formulas of binomial coefficients. Alternatively, some of these can be verified either through a pair of relations due to Gould and Hsu (1973), from which some strange hypergeometric evaluations including one of Gessel and Stanton (1982) may be produced mechanically. By associating the binomial convolutions investigated in this paper with Whipple's transform (1926) on very well-poised series, a new family of the₇ F ₆-hypergeometric identities are established in a unified way.     

Synthesis of gold nano- and microplates in hexagonal liquid crystals

Single-crystalline gold nano- and microplates with triangular or hexagonal shapes are synthesized by reduction of HAuCl(4) in lyotropic liquid crystal (LLC) mainly made of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymers and water after adding a small amount of capping agents, cetyltrimethylammonium bromide (CTAB) or tetrabutylammonium bromide (TBAB). During the growth of such plates, capping agents play the crucial role. It is found that there is an optimal value of CTAB or TBAB concentration for producing microplates. The selective adsorption of CTAB or TBAB on certain crystallographic facets may be the key point of the supposed mechanism. Although LLC does not really act as a template, it provides an ordered structure confining CTAB as well as the nascent metal nuclei, which enhances the oriented attachment of nuclei and thus the consequent growth of single-crystal plates.     

Self-assembled structure in room-temperature ionic liquids

Self-assembled vesicles, structurally equivalent to some hydrotropes, have been obtained from a Zn2+-fluorous surfactant or in the mixture of Zn2+-fluorous surfactant/zwitterionic surfactant in room-temperature ionic liquids (RTILs). The existence of bilayers arranged in vesicles in RTILs would be very exciting, open several new possibilities as reaction media, and increase our understanding of the physical and chemical factors for self-assembling systems in RTILs.     

Supercapacitor performances of rich nitrogen-doped mesoporous graphene fabricated by a facile template-free copyrolysis process

Rich nitrogen-doped mesoporous graphene (NDMG) with a large specific surface area of 496.8 m² g^?1 and high electrical conductivity of 327.2 S cm^?1, and suitable pore size was synthesized by a facile co-thermal annealing of pre-prepared phenolic polymer and dicyandiamide. The NDMG has a high nitrogen content (7.9 wt%) and can act as promising electroactive materials for two-electrode symmetric supercapacitors. The NDMG cells displayed a high specific capacitance of ca. 316 F g^?1 at 0.5 A g^?1, which is much higher than that of the pristine graphene devices (ca. 123 F g^?1). Moreover, compared with the capacitance drop rate of pristine graphene devices (8.9 %), the specific capacitance of NDMG cells was decreased by only 3.2 % after 2000 cycles, exhibiting a good cycling performance and reversibility. In addition, the specific capacitance of the NDMG cells can reach 251 F g^?1 at 5.0 A g^?1, revealing an excellent rate capability and implying the ability to deliver a high energy density at a high power density. The good electrochemical performances of NDMG can be attributed to its high surface area, suitable mesopore size, and high electrical conductivity.