On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.     

Synthesis,Crystal Structure and Magnetic Behaviour of {[Co(dimb)2(H2O)2]·(NO3)2·(H2O)2}n

The title complex {[Co(dimb)₂(H₂O)₂]·(NO₃)₂·(H₂O)₂}_n ( 1 ) (dimb = 1,3‐di(imidazol‐1‐ylmethyl)‐5‐methylbenzene) has been hydrothermally synthesized by the reaction of dimb with Co(NO₃)₂·6H₂O in aqueous solution. The cobalt(II) atoms are linked by bridging dimb ligands to form 2D corrugated and wavy networks containing Co₄(dimb)₄ macrocyclic motifs. Two neighboring independent layers interlinked each other in a parallel fashion to construct three‐dimensional structure by O–H···O, N–H···O and C–H···O hydrogen bonds. Magnetic measurement shows the weak antiferromagnetic interaction with a one‐dimensional chain model in the range of 5–300 K, with J of –0.68 cm⁻¹.     

拟共形映射和John域

本文研究了(R)∫ΩBn中的John域与一致域和线性局部连通域的关系.利用平面中John域和拟圆的关系,获得了(R)∫ΩBn中的John域成为一致域和线性局部连通域的几个充分条件,它们是(R)2的推广.     

A covalent attraction between two molecular cation TTF·+

The optimized structure of the tetrathiafulvalence radical-cation dimer (TTF·⁺-TTF·⁺) with all-real frequencies is obtained at MP2/6-311G level, which exhibits the attraction between two molecular cation TTF·⁺. The new attraction interaction is a 20-center-2-electron intermolecular covalent π/π bonding with a telescope shape. The covalent π/π bonding has the bonding energy of about ?21 kcal·mol^?1 and is concealed by the Coulombic repulsion between two TTF·⁺ cations. This intermolecular covalent attraction also influences the structure of the TTF·⁺ subunit, i.e., its molecular plane is bent by an angle θ = 5.6°. This work provides new knowledge on intermolecular interaction.

     

Synthesis and Structure of E-2-(2,4,6-tri tert butylphenylphosphinyl)-2-〔N-(tert-butyldimethylsilyl)-N-(p-chrolophenyl)〕amino-1-(2,4,6-tri tert-butyl-phenyl)phosphacthylene

1　INTRODUCTIONItwaswellknown thatelementsofthesecondary and higherrow are in generaldifficulty to form multiplebondsin which apπ hybridized stateisinvolved〔1〕.Thus,simple compounds containing multiple phosphorus carbon bonds,such as methyl dynephosphine( HC≡P) 〔2 - 3〕 and methylenephosphine( H2 C=PH〔4〕,are notstableat room temperature.Three methods to stabilize compounds containing double ormultiple bond involving phosphorusatom in the pπ hybridized state are often used.The f…     

面向创新教育的经济数学建模教学研究

本文较深刻地分析了经济数学建模教学在高校人才培养中的作用；明确了经济数学建模教学是经济数学课程教学改革的突破口、切入点；同时，对如何开展经济数学建模教学提出了建议．     

关于Hayman问题与分担值

设 f 为非常数亚纯函数, n(≥ 4)为正整数, a 为非零有穷复数. 若a 为f ⁿ与 (f ⁿ)′ 的CM分担值, 则nf ’=f.     

A cubically convergent Newton-type method under weak conditions

Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f^′(x)=0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method.