Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

不同光滑度立方体氧化铁对液晶电光性能的改善

向列相液晶被广泛应用于液晶显示中,但是由于杂质的存在,会导致液晶的驱动电压变大,增加能耗。 为了降低阈值电压和饱和电压,通常向液晶中添加纳米颗粒来提高电光性能。 本文利用水热法制备了表面粗糙和光滑的两种立方体Fe₂O₃纳米颗粒,其形貌均匀,尺寸约550 nm。 将二者分别掺杂到向列相液晶E7中,结果表明,粗糙立方体Fe₂O₃/E7复合体系具有比光滑立方体Fe₂O₃/E7复合体系和向列相液晶E7更优的电光性能,且在掺杂质量分数为0.4%时,其电光性能达到最优,阈值电压和饱和电压分别降低9.9%和11.6%,对比度增大80%,响应时间降低至6.0 ms。 这归因于粗糙立方体Fe₂O₃具有足够的表面积和表面所带电荷更多,所以会更易吸附体系中的杂质离子和减弱杂质离子的屏蔽作用,从而提高了电光性能。     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

鞘磷脂和神经节苷脂对磷脂酰乙醇胺混合脂超分子体系液晶态立方相Im3m和Pn3m结构影响的研究

用磷脂酰乙醇胺(DEPE)、鞘磷脂(Sphingomyeline, Sph)、神经节苷脂(Gm1)和胆固醇(Chol)模拟了生物膜超分子体系液晶态结构, 通过用小角X射线衍射(SAXD)对混合脂体系液晶态结构进行了研究, 鉴定出了两种立方相: 即Im3m(Q²²⁹)和Pn3m(Q²²⁴)结构. 实验发现, 鞘磷脂的含量对DEPE膜的结构有一定的影响, 随着鞘磷脂浓度的增加, 混合脂体系的液晶态结构发生了由Im3m(Q²²⁹)到Pn3m(Q²²⁴)的变化. 神经节苷脂(Gm1)的含量对混合脂体系的液晶态结构也有一定的影响, 当神经节苷脂(Gm1)含量达到某一临界值时, 混合脂体系的液晶态结构发生了从Im3m(Q²²⁹)到Pn3m(Q²²⁴) 的变化. 当DEPE-Shp-Gm1超分子聚集体中含有胆固醇时, 胆固醇的极性头部(—OH)与磷脂酰乙醇胺(DEPE)、鞘磷脂(Shp)、神经节苷脂(Gm1)的极性头部通过氢键相互作用形成液晶态立方相Im3m(Q²²⁹)结构, 再通过疏水/亲水相互作用形成稳定的Pn3m (Q²²⁴)结构.     

Efficient algorithms for solving rank two and rank three bilinear programming problems

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaacaWFTbGaa8% xAaiaa-5gacaWFPbGaa8xBaiaa-LgacaWF6bGaa8xzaiaa-bcacaWF% 7bacbiGaa43yamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+Hhaca% GFRaGaa4hzamaaDaaaleaacaGFWaaabaGaa4hDaaaakiaa+LhacaGF% RaWaaabuaeaacaGFJbWaa0baaSqaaiaa+PgaaeaacaGF0baaaOGaam% iEaiabl+y6NjaadsgadaqhaaWcbaGaamOAaaqaaiaadshaaaGccaWG% 5bGaaiiFaaWcbaGaa8NAaiaa-1dacaWFXaaabeqdcqGHris5aOGaa4% hEaiabgIGiolaa+HfacaGFSaGaa4xEaiabgIGiolaa+LfacaWF9bGa% a8hlaaaa!5D2E!\[minimize \{ c_0^t x + d_0^t y + \sum\limits_{j = 1} {c_j^t xd_j^t y|} x \in X,y \in Y\} ,\]where X Rⁿ¹ and Y R ⁿ² are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.This research was supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 63490010.     

Use of Local Lagrange Interpolation for calculation of retention indices in linear temperature-programmed gas chromatrography

Summary The influence of the isothermal temperature, program rate, initial temperature and flow rate on retention indices was studied. The methods of Kováts, Van Den Dool and Local Lagrange Interpolation are compared. Ten experimental measurements were carried out on a capillary column coated with OV-101 stationary phase.     

Functional Janus dendrimers containing carbazole with liquid crystalline,optical and electrochemical properties

ABSTRACT

Novel liquid crystalline Janus dendrimers that combine a mesogenic block and an electroactive block have been synthesised. The mesogenic block is based on two third-generation Percec-type dendrons bearing six or eight terminal dodecyloxy alkyl chains, whereas the electroactive blocks are formed by one or two carbazole units. The liquid crystal behaviour was investigated by polarised-light optical microscopy, differential scanning microscopy and X-ray diffraction. The Janus dendrimers with one electroactive unit exhibited cubic or columnar liquid crystal phases, whereas the Janus dendrimers with two electroactive units did not show liquid crystalline behaviour. The UV-vis absorption and emission properties of the Janus dendrimers were investigated. The spectra suggested the existence of π-π stacking and the formation of aggregates in the solid state. Electrodeposition of the carbazole-containing dendrimers afforded semi-globular particles in which the number of electropolymerizable units and the flexible or rigid character of the linker have a decisive influence in the particle size.     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.