A trajectory-following method for unconstrained optimization

A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

非线性光学材料──水草酸铵

一水草酸铵（简称ＡＯＭ）是一种优良的电光晶体￣［１］。文献￣［１，２］报道了该晶体的晶体结构，化学式为（ＮＨ＿４）＿２Ｃ＿２Ｏ＿２·Ｈ＿２Ｏ，属正交晶系，Ｐ２２２空间群，晶胞参数ａ＝０．８０３５ｎｍ，ｂ＝１。０３１ｎｍ，ｃ＝０．３８０１ｎｍ，ｚ＝２。本文拟报道ＡＯＭ单晶生长，热化学分析，透过波段以及非线性光学性质的初步研究。     

A supported gold catalyst for the elimination of hydrogen from CO2 feed gas in the production of urea

Supported gold catalyst for eliminating hydrogen from CO₂ feed gas in the production of urea is found to be superior to other industrial catalysts (e.g. Pt/Al₂O₃ and PdPt/Al₂O₃) in catalytic activity and resistance to sulfur poisoning.     

Tree-gel and loop-gel conversions in nonlinear polymerization

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SYNTHESIS AND PHOTOCHROMISM OF ACRYLIC ESTER COPOLYMERS BEARING PENDANT VIOLOGEN GROUPS

A series of acrylic ester copolymers with viologen group as pendant were synthesizedthrough the reaction of MMA-EBA (Ethenyl bromoacetate) copolymer with 4-(4'-pyridyl)-N-alkyl (or arylalkyl) pyridiniums. These viologen copolymers can exchange their anionwith NH_4PF_6 in methanol to improve their solubility in organic solvents such as DMFand acetone. Compared with the corresponding low molecular viologens, these viologencopolymers have relatively lower color development rate under UV light and fade fasterin air due to less affinity to photo-reductant and deficiency of association between theircation radicals. Their photofatigue resistant ability is also slightly better than that of lowmolecular vinlogens.     

A scratch-resistant single-layer antireflective coating by a low temperature sol-gel route

A novel quarterwave-thick narrow-bandwidth antireflective coating has been developed for both plastic and vitreous substrates by a sol-gel route. This coating has revealed pronounced scratch- and climatic-resistance under adverse conditions. The single-layer coating consists basically of a composite material made of silica as the discontinuous phase and of a polytetrafluoroethylene-derived (Teflon¹) organic polymer as the continuous phase. This leads to fluorine-containing colloidal silica product, or a so-called Flucosil coating. The coating is applied by spinning or dipping from specific solutions at room temperature followed by a mild and short heat treatment. In addition to remarkable abrasion and environmental resistance properties, such coatings have displayed excellent laser-induced damage threshold levels, surpassing uncoated substrates.We hope such a product might open new perspectives concerning household articles, architectural optical thin-films, ophthalmic uses, and so on.     

Toward breast cancer resistance protein (BCRP) inhibitors: design, synthesis of a series of new simplified fumitremorgin C analogues

In this study, we report the design and synthesis of a series of new simplified fumitremorgin C analogues. The preliminary biological study indicated some of these simplified fumitremorgin C might be developed into breast cancer resistance inhibitors.     

Crystal Structure of Dimethylamine 3,5-Dinitrobenzoic Acid Organic Adduct

1 INTRODUCTION Nonlinear optics (NLO) is at the forefront of cur- rent researches because of its importance in provi- ding the key functions of frequency shifting, optical modulation, optical switching, optical logic and op- tical memory for the emerging …