非平衡态/不可逆过程的热力学理论(Ⅱ)

<正> 7 解的唯一性 如果不考虑非平衡态和不可逆性,则等能密度理论中的基本命题与经典弹性理论中的在形式上完全相同。无论整个系统的动能是大还是小,图6中(sumform)_o上的面力T_i和在(sumform)_c和在的位移u_i将始终在空间坐标系x_i和时刻i下给出。与一般力学中相同,必须知道有关位移u_i及其时间导数的初始条件。它们的影响则可通过(38)和(39)向等能面转化,从而得到     

Cinchona alkaloids in the asymmetric synthesis of 2-(phenylsulfanyl)aziridines

Enantioselective aza-Michael initiated ring closure (MIRC) additions of ethyl nosyloxycarbamate to 2-(phenylsulfanyl)-2-cycloalkenones catalysed by Cinchona alkaloids were studied. The results suggest that the enantioselectivity obtained is influenced by the structure of the catalyst and the different amination conditions. Substrate ring size also plays an important role.     

Synthesis of optically active trifluoromethyl substituted diaziridines and oxaziridines

(E)-Trifluoromethyl imines were considered as ideal substrates to be transformed into the corresponding diaziridines by a direct amination reaction with nosyloxycarbamates. The diastereoselective induction was strongly controlled by the N-substituent. Similar results were obtained in the epoxidation reactions performed on the same substrates using m-CPBA as oxidant. Starting from enantiopure imines chiral diaziridines or oxaziridines were obtained with very high enantiopurity.     

Existence and sum decomposition of vertex polyhedral convex envelopes

Convex envelopes are a very useful tool in global optimization. However finding the exact convex envelope of a function is a difficult task in general. This task becomes considerably simpler in the case where the domain is a polyhedron and the convex envelope is vertex polyhedral, i.e., has a polyhedral epigraph whose vertices correspond to the vertices of the domain. A further simplification is possible when the convex envelope is sum decomposable, i.e., the convex envelope of a sum of functions coincides with the sum of the convex envelopes of the summands. In this paper we provide characterizations and sufficient conditions for the existence of a vertex polyhedral convex envelope. Our results extend and unify several results previously obtained for special cases of this problem. We then characterize sum decomposability of vertex polyhedral convex envelopes, and we show, among else, that the vertex polyhedral convex envelope of a sum of functions coincides with the sum of the vertex polyhedral convex envelopes of the summands if and only if the latter sum is vertex polyhedral.     

Asymmetric addition of ethyl azidoformate to optically active enamines. Reversal of facial selectivity compared with (ethoxycarbonyl)nitrene

Thermal reaction of ethyl azidoformate with proline-derived optically active enamines of cyclohexanone, followed by photolysis, proceeds with opposite facial selectivity to that observed using (ethoxycarbonyl)nitrene. A tentative explanation is proposed. The absolute configuration of the main product, 2-(ethoxycarbonylamino)cyclohexanone (6), was deduced by chemical correlation.