On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

On the existence of positive solutions for a class of singular boundary value problems

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C¹[0,1]∩C²(0,1) or C[0,1]∩C²(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.     

利用"对比法"判断气体状态参量的变化趋势

理想气体的温度、体积和压强三个状态参量之间的关系由气体状态方程pV/T=恒量决定。当气体状态发生变化时，判断某一个参量的变化趋势是一个比较复杂的问题。如图1，为p—T图中的状态变化曲线，状态由A变化到B，判断体积的变化趋势。     

Renormalization Effects in the Spectrum of a Coherently Driven Exciton–Biexciton System

Starting from the total Hamiltonian of an excited exciton–biexciton system, nonresonant renormalizations in the electronic spectrum of a coherently driven direct semiconductor are considered. Stringent group-theoretical inclusion of the particle spin in the Hamiltonian allows one to account for the dependence of different renormalization effects on polarizations of the incident laser fields. On the example of circularly polarized driving and probing pulses it is shown that the kind of observed renormalization is defined by the pump-and-probe polarization geometry. Thus, the exciton optical Stark effect must appear in the case of co-circular pump-and-probe, whereas a mixing of the polariton and biexciton spectra is possible only in the case of counter-circular pump-and-probe. The polariton--biexciton dispersion renormalization may manifest itself as synchronous splittings of the exciton--polariton and biexciton spectra under resonant pumping at a frequency of the polariton--biexciton transition, or in their shifts in opposite directions under near-resonant pumping. The mechanisms of both kinds of renormalization effects are analyzed, and the dependence of their characteristics on the pump parameters and microscopic parameters of the exciton–biexciton–photon system is established. An evaluation of the characteristics shows that the effect of polariton–biexciton dispersion renormalization dominates in the spectra of semiconductors with stable biexciton formation. Results of the theoretical study provide an adequate explanation of available experimental data.     

Synthesis and characterization of norbornene–ethylene–styrene terpolymers with a substituted ansa‐fluorenylamidodimethyltitanium‐based catalyst

This article reports a synthetic method for a norbornene–ethylene–styrene (N‐E‐S) terpolymer, which has not been well investigated so far, via incorporation of styrene (S) into vinyl‐type norbornene–ethylene (N‐E) copolymers catalyzed by a substituted ansa‐fluorenylamidodimethyltitanium [Me₂Si(3,6‐tBu₂Flu)(tBuN)]TiMe₂ catalyst ( I ) activated with a [Ph₃C][B(C₆F₅)₄]/Al(iBu)₃ cocatalyst at room temperature in toluene. The resulting terpolymerization product contained the targeted N‐E‐S terpolymer and the contaminated homopolymers, which were then able to be completely removed by solvent fractionation techniques. While homopolystyrene was easily extracted by fractionation with methylethylketone as a soluble part, homopolyethylene and a trace amount of homopolynorbornene could be perfectly separated by fractionation with chloroform as insoluble parts. The detail characterizations of a chloroform‐soluble polymer with gel permeation chromatography, nuclear magnetic resonance, and differential scanning calorimetry analyses proved that it contained a true N‐E‐S terpolymer with long N‐E sequences incorporated with isolated or short styrene sequences. The homogeneity of the morphology together with a single glass transition temperature that proportionally decreased with the increase of the styrene contents indicated that the N‐E‐S terpolymer obtained in this work is a random polymer with an amorphous structure. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2765–2773, 2007     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

断续喷洒去溶电热雾化法在电感耦合等离子体原子发射光谱方法中的应用研究

本文所讨论的电热雾化法是采用继续喷洒去溶技术,使试样在石墨炉表面逐步积累的进样方法。文章简要介绍了实验条件的选择和控制以及石墨炉装置的结构,探讨了提高电热雾化法相对检测能力的途径。实验结果表明:谱线黑度值与试样积累时间的对数值之间具有较好的线性关系。     

Metal clips induce folding of a short unstructured peptide into an alpha-helix via turn conformations in water. Kinetic versus thermodynamic products

Short peptides corresponding to two to four alpha-helical turns of proteins are not thermodynamically stable helices in water. Unstructured octapeptide Ac-His1-Ala2-Ala3-His4-His5-Glu6-Leu7-His8-NH(2) (1) reacts with two [Pd((15)NH(2)(CH(2))(2)(15)NH(2))(NO(3))(2)] in water to form a kinetically stable intermediate, [[Pden](2)[(1,4)(5,8)-peptide]](2), in which two 19-membered metallocyclic rings stabilize two peptide turns. Slow subsequent folding to a thermodynamically more stable two-turn alpha-helix drives the equilibrium to [[Pden](2)[(1,5)(4,8)-peptide]] (3), featuring two 22-membered rings. This transformation from unstructured peptide via turns to an alpha-helix suggests that metal clips might be useful probes for investigating peptide folding.     

Prediction of brand stories spreading on social networks

Advances in Data Analysis and Classification - Online social network is a major media for many types of information communication. Although the primary purpose of social networks is to connect...