Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for ``infinite-dimensional second-order cone programs.' We consider as an example a long-step primal-dual algorithm based on the Nesterov-Todd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration. An application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator. The calculation of the Nesterov-Todd direction requires in this case solving one matrix differential Riccati equation plus solving a finite-dimensional system of linear algebraic equations on each iteration. The number of equations and unknown variables of this algebraic system is m+1, where m is a number of quadratic performance criteria. Key words.polynomial-time primal-dual interior-point methods – JB-algebras – infinite-dimensional problems – optimal control problemsThis author was supported in part by DMS98-03191 and DMS01-02698.This author was supported in part by the Grant-in-Aid for Scientific Research (C) 11680463 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.Mathematics Subject Classification (1991):90C51, 90C48, 34H05, 49N05     

Pulsed-laser crystallization and epitaxial growth of metal-organic films of Ca-doped LaMnO3 on STO and LSAT substrates

Ca-doped LaMnO₃ (LCMO) thin films have been successfully prepared on SrTiO₃ (STO) and [(LaAlO₃)_0.3-(SrAlTaO₆)_0.7] (LSAT) substrates using the excimer laser assisted metal-organic deposition (ELAMOD) process. The crystallization and the epitaxial growth of the amorphous metal-organic LCMO thin films have been achieved using a KrF excimer laser irradiation while the substrates were kept at constant temperature of 500 °C. Epitaxial films were obtained using laser fluence in the interval of 50-120 mJ/cm². The microstructure of the LCMO films was studied using cross-section transmission electron microscopy. High quality of LCMO films having smooth surfaces and sharp interfaces were obtained on both the STO and the LSAT substrates. The effect of the laser fluence on the temperature coefficient of resistance (TCR) was investigated. The largest values of TCR of the LCMO grown on the LSAT and the STO substrates of 8.3% K⁻¹ and 7.46% K⁻¹ were obtained at different laser fluence of 80 mJ/cm² and 70 mJ/cm², respectively.     

Synthesis of poly(p‐phenylene)‐poly(4‐diphenylaminostyrene) bipolar block copolymers with a well‐controlled and defined polymer chain structure

A poly(p‐phenylene) (PPP)‐poly(4‐diphenylaminostyrene) (PDAS) bipolar block copolymer was synthesized for the first time. A prerequisite prepolymer, poly(1,3‐cyclohexadiene) (PCHD)‐PDAS binary block copolymer, in which the PCHD block consisted solely of 1,4‐cyclohexadiene (1,4‐CHD) units, was synthesized by living anionic block copolymerization of 1,3‐cyclohexadiene and 4‐diphenylaminostyrene. To obtain the PPP‐PDAS bipolar block copolymer, the dehydrogenation of this prepolymer with quinones was examined, and tetrachloro‐1,2‐(o)‐benzoquinone was found to be an appropriate dehydrogenation reagent. This dehydrogenation reaction was remarkably accelerated by ultrasonic irradiation, effectively yielding the target PPP‐PDAS bipolar block copolymer. The hole and electron drift mobilities for PPP‐PDAS bipolar block copolymer were both on the order of 10^?3 to 10^?4 cm²/V·s, with a negative slope when plotted against the square root of the applied field. Therefore, this bipolar block copolymer was found to act as a bipolar semi‐conducting copolymer. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Annealing effect on performance and morphology of photovoltaic devices based on poly(3‐hexylthiophene)‐b‐poly(ethylene oxide)

Novel block copolymers, poly(3‐hexylthiophene)‐b‐poly(ethylene oxide) (P3HT‐b‐PEO) were synthesized via Suzuki coupling reaction of P3HT and PEO homopolymers. The copolymers were characterized by NMR, gel permeation chromatography, differential scanning calorimeter, and UV–vis measurements. A series of devices based on the block copolymers with a fullerene derivative were evaluated after thermal or solvent annealing. The device using P3HT‐b‐PEO showed higher efficiency than using P3HT blend after thermal annealing. Phase‐separated structures in the thin films of block copolymer blends were investigated by atomic force microscopy to clarify the relationship between morphologies constructed by annealing and the device performance. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Synthesis of porphyrin‐end‐functionalized polycyclohexane with well‐controlled and defined polymer chain structure

Tetraphenylporphyrin‐end‐functionalized polycyclohexane (H₂TPP‐PCHE) and its metal complexes (MTPP‐PCHE) were synthesized as the first successful example of porphyrin‐end‐functionalized transparent and stable polymers with a well‐controlled and defined polymer chain structure. Chloromethyl‐end‐functionalized poly(1,3‐cyclohexadiene) (CM‐PCHD) was synthesized as prerequisite prepolymer by the postpolymerization reaction of poly(1,3‐cyclohexadienyl)lithium and chloro(chloromethyl)dimethylsilane. CM‐end‐functionalized PCHE (CM‐PCHE) was prepared by the complete hydrogenation of CM‐PCHD with p‐toluenesulfonyl hydrazide. H₂TPP was incorporated onto the polymer chain end by the addition of 5‐(4‐hydroxyphenyl)‐10,15,20‐triphenylporphyrin to CM‐PCHE. The complexation of H₂TPP‐PCHE and Zn(OAc)₂ (or PtCl₂) yielded a zinc (or platinum) complex of H₂TPP‐PCHE. H₂TPP‐PCHE and MTPP‐PCHE were readily soluble in common organic solvents, and PCHE did not inhibit the optical properties of the H₂TPP, ZnTPP, and PtTPP end groups. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Mathematical analogy of a beam on elastic supports as a beam on elastic foundation

This paper presents the mathematical hypothesis that a beam on equidistant elastic supports (BOES) can be considered as a beam on an elastic foundation (BOEF) in static and free vibration problems. This modeling of BOES as BOEF is presumed to be applicable to a limited range of support stiffness, spacing and flexural rigidity of the beam. The authors investigate the applicability of the modeling of BOEF from the property of characteristic solutions obtained from governing equations of both BOES and BOEF. In this study, the formulation of BOES leads to governing difference equations, and the motions of BOEF are expressed by differential equations. This is because exact solutions must be employed in order to verify their analogy accurately. The characteristic solutions obtained from these two governing equations are compared to each other in order to investigate the relationship between them.     

New approach of semiconductor laser related technologies for ultrafast photonics

Ultrashort laser pulses offer new jump in information and communication technology. Especially semiconductor laser based ultrafast photonic devices and systems are promising. We review our new approaches for femtosecond pulse generation, and thin film technology for broad band semiconductor optical amplifiers.     

Thermogravimetric Analysis of Aromatic Polyamides with Benzimidazolyl Side Group

The TG studies are presented for isomers of benzimidazolyl-substituted polyamides (BIPA). The TG data are compared with those polyamides (PA) of identical backbones without substitution, in view of the mechanism of thermal degradation. The TG mass loss curves divided to three temperature ranges reflect the decomposition reactions in the respective temperature ranges: (1) cleavage of single bonds of nitrogen to aromatic ring, (2) random scission of single bonds, (3) condensation of the remained rings. Liberation of benzimidazole rings occurs in the temperature range (2). The final product, char, contains benzimidazole rings. Terephthaloyl-rich BIPA's retard liberation of benzimidazole from the decomposed polymer. This revised version was published online in August 2006 with corrections to the Cover Date.     

A note on chordal bound graphs and posets

We study relations between induced subgraphs and (n,m)-subposets. Using properties of (n,m)-subposets, we consider a characterization of chordal double bound graphs in terms of forbidden subposets. Furthermore, we deal with properties of a poset whose double bound graph is isomorphic to its upper bound graph or its comparability graph, etc.