一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

等式与界约束非线性优化信赖域算法的全局收敛

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 ,　ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…     

Comparative studies of the colony-promoting activity of porcine kidney extract with several interleukins and colony-stimulating factors.

Porcine kidney extracts (PKE) possess colony-promoting activity (CPA) which stimulates primitive hematopoietic cells in the presence of granulocyte/macrophage colony-stimulating factor (GM-CSF), but PKE itself does not stimulate colony formation on murine bone marrow cells. We have compared the CPA of PKE with that of recombinant cytokines or CSFs such as interleukin-1 alpha (IL-1 alpha), IL-3, IL-6, granulocyte colony-stimulating factor (G-CSF), GM-CSF and macrophage colony-stimulating factor (CSF-1). All of these factors were less potent than PKE. Furthermore, the combinations of IL-1 alpha or PKE with G-CSF, GM-CSF, IL-3 or IL-6 were examined in the presence of one of these factors such as CSF. It is found that PKE acts synergistically with G-CSF, GM-CSF, IL-3 and IL-6, showing enhancement ratios of 10, 2.5, 4.2 and 30, respectively. The combination of IL-1 alpha resulted in poor colony formation in contrast with those of PKE, except for CSF-1. These results suggest that the CPA of the factor(s) in PKE differ from the cytokines and CSFs tested in this study, and is significantly affected by various types of CSF.     

Partial purification and characterization of a factor for the enhancement of colony formation in vitro by myeloid progenitor cells.

We have purified a factor, hematopoietic promoting factor (HPF), from porcine kidney extract (PKE), which exhibits a promoting activity on granulocyte/macrophage (GM) colony and burst-forming-unit-erythroid (BFU-E)-derived colony formation by progenitors from murine bone marrow cells in vitro. The addition of HPF resulted in an enhancement of the GM colonies as well as BFU-E-derived colonies, but did not enhance the colony-forming-unit-erythroid (CFU-E)-derived colony formation. HPF was added to the BFU-E cultures together with cytokines, such as recombinant murine interleukin-3 (IL-3), recombinant murine GM colony-stimulating-factor (GM-CSF) and recombinant human G-CSF, which have all been shown to enhance BFU-E growth. The combination of HPF plus these cytokines resulted in an enhancement of benzidine negative colony formation in comparison to the case of each cytokine alone; however, no increase was found on BFU-E colony formation. HPF is able to enhance the granulopoiesis and erythropoiesis in vitro. And the synergistic activity of HPF is significantly affected by the presence of cytokines in the cultures.     

Photopolymerization of cyclohexene oxide by use of o-nitrobenzyl triphenylsilyl ether/aluminum compound catalyst. Dependence of catalyst activity on the structure of the silyl ether

o-Nitrobenzyl triphenylsilyl ehther/aluminum compound has been previously shown by the authors to act as catalyst in the photopolymerization of epoxides. The dependence of the structure of the silyl ether on the catalyst activity was examined. There were two steps in the photopolymerization. The first step (“Step 1”) is photodecomposition of the silyl ether to silanol. The second step (“Step 2”) is the initiation of polymerization by silanol and the aluminum compound. The introduction of an electron withdrawing group, Cl, CF₃, on the benzene ring bonded to Si made the quantum yield of Step 1 low, however, the rate of Step 2 was increased. The low quantum yield of Step 1 was explained in terms of the rate of electron transfer that is controlled by the relative electron density between the CH₂ and NO₂ in the o-nitrobenzyl group. The acceleration of Step 2 was explained in terms of an increase in silanol acidity that was promoted by the introduction of an electron withdrawing group. The overall rate of the photopolymerizatiol depends to a greater degree on the rate of Step 2 than on that of Step 1.     

Isomerization polymerization of β-propiolactones carrying side-chain ester groups

Based on our recent discovery of the isomerization polymerization of β-(2-acetoxyethyl)-β-propiolactone into poly-δ-ester,^1,2 we examined the generality of this phenomenon by using two related monomers. The catalysts were (EtAlO)_n and Et(ZnO)₂ZnEt. The side-chains in the monomers selected were the (CH₃)₂CHCOO? CH₂CH₂? (2) and (CH₃)CICHCOO? CH₂CH₂? (3) groups in which steric effects are almost identical but electronic effects are in opposition. The monomers yielded isomerized poly-δ-ester units, depending on the terminal substituent groups in the side-chain. These observations can be interpreted with the bicyclic intermediate proposed in the earlier work. Monomer (2) was reactive and produced a poly-δ-ester structure most readily, probably because of the higher electron density at the side-chain ester group which coordinated with the catalyst. In contrast, monomer (3) was less reactive, and the probability of isomerization was the lowest, i.e., the electron deficient side-chain ester group apparently interfered with the formation of the intermediate, especially in the Zn-catalysis. Equibinary random copolymers were prepared from (2) and (3) according to the catalyst and polymerization conditions chosen.     

Rhodium-Catalyzed Enantioselective Synthesis,Structures, and Properties of Single and Double Azahelicene-Like Molecules

The enantioselective synthesis of aza[6] and [7]helicene-like molecules have been achieved by the cationic rhodium(I)/axially chiral biaryl bisphosphine complex-catalyzed intramolecular [2+2+2] cycloaddition of cyanodiynes. This protocol was successfully applied to the diastereo- and enantioselective synthesis of an S-shaped double aza[6]helicene-like molecule with a high ee value of 89 %. Although no epimerization and racemization were observed in the double carbo[6]helicene-like molecule at 80 °C, epimerization and racemization of the double aza[6]helicene-like molecule proceeded at 80 °C. This double aza[6]helicene-like molecule showed good fluorescent quantum yields and chiroptical responses under both neutral and acidic conditions.     

Relaxation Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

This paper presents a relaxation Lax-Friedrichs sweeping scheme to approximate viscosity solutions of static Hamilton Jacobi equations in any number of spatial dimensions. It is a generalization of the scheme proposed in Kao et al. (J Comput Phys 196:367–391, 2004). Numerical examples suggest that the relaxation Lax-Friedrichs sweeping scheme has smaller number of iterations than the original Lax-Friedrichs sweeping scheme when the relaxation factor ω is slightly larger than one. And first order convergence is also demonstrated by numerical results. A theoretical analysis for our scheme in a special case is given.     

GLOBAL CONVERGENCE OF NONMONOTONIC TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION

§ 1　 IntroductionIn this paper we study the following nonlinear equality constrained optimization prob-lem:minimize f(x) ,subjectto h(x) =0 ,(P)where h(x) =(h1 (x) ,h2 (x) ,...,hm(x) ) T,f and hi(i=1 ,2 ,...,m) are Rn→R twice conti-nously differentiable(m≤n) .Many authors have studied the problem(P) with trustregion method(see,references[1～ 3 ] ) .These methods have the same property:to enforce strict monotonicity for meritfunction at every iteration.Paper[4 ] shows thatstrictmonotonic …