Uniform stability of solutions of Boltzmann equation for soft potential with external force

The study of Cauchy problem of the Boltzmann equation is important in both theory and applications. Existence of global solutions to the equation and uniform stability of solutions in the absence of external force were introduced in the previous work on the Boltzmann equation. In this paper, we will investigate the uniform stability of solutions in L¹ for the Cauchy problem of the Boltzmann equation when there is an external force for the case of soft potentials.     

A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization

In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α$\alpha$-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)].     

Explicit secular equations of Rayleigh waves in elastic media under the influence of gravity and initial stress

The problem of Rayleigh waves in an orthotropic elastic medium under the influence of gravity and initial stress was investigated by Abd-Alla [A. M. Abd-Alla, Propagation of Rayleigh waves in an elastic half-space of orthotropic material, Appl. Math. Comput. 99 (1999) 61-69], and the secular equation of the wave in the implicit form was derived. However, due to the uncorrect representation of the solution, the secular equation is not right. The main aim of the present paper is to reconsider this problem. We find the secular equation of the wave in explicit form. By considering some special cases, we obtain the exact explicit secular equations of Rayleigh waves under the effect of gravity of some previous studies, in which only implicit secular equations were derived.     

具有偏差变元的二阶泛函微分方程周期解的存在性

该文利用k- 集压缩算子抽象连续性定理和一些分析技巧研究了一类具有偏差变元的二阶泛函微分方程周期解的存在性. 该文的结果推广和改进了文献[1-2]的主要结果.     

Bulk characterization methods for non-centrosymmetric materials: second-harmonic generation, piezoelectricity, pyroelectricity, and ferroelectricity

Characterization methods for bulk non-centrosymmetric compounds are described. These methods include second-harmonic generation, piezoelectricity, pyroelectricity, and ferroelectricity. In this tutorial review with each phenomenon, details are given of the measurement techniques along with a brief history and background. Finally, data interpretation is discussed.     

Assembly dynamics and detailed structure of 1-propanethiol monolayers on Au(111) surfaces observed real time by in situ STM

1-Propanethiol is chosen as a model alkanethiol to probe detailed mechanisms of the self-assembled monolayer (SAM) formation at aqueous/Au(111) interfaces. The assembly processes, including initial physi- and chemisorption, pit formation, and domain growth, were recorded into movies in real-time with high resolution by in situ scanning tunneling microscopy (STM) under potential control. Two major adsorption steps were disclosed in the propanethiol SAM formation. The first step involves weak interactions accompanied by the lift of the Au(111) surface reconstruction, which depends reversibly on the electrochemical potentials. The second step is chemisorption to form a dense monolayer, accompanied by formation of pits as well as structural changes in the terrace edges. Pits emerged at the stage of the reconstruction lift and increased to a maximum surface coverage of 4.0 +/- 0.4% at the completion of the SAM formation. Well-defined triangular pits in the SAM were found on the large terraces (more than 300 nm wide), whereas few and small pinholes appeared at the terrace edge areas. Smooth edges were converted into saw-like structural features during the SAM formation, primarily along the Au(111) atomic rows. These observations suggest that shrinking and rearrangement of gold atoms are responsible for both formation of the pits and the shape changes of the terrace edges. STM images disclose a (2 square root 3 x 3)R30 degrees periodic lattice within the ordered domains. Along with electrochemical measurements, each lattice unit is assigned to contain four propanethiol molecules exhibiting different electronic contrasts, which might originate in different surface orientations of the adsorbed molecules.     

Interface interaction controlled transport of CdTe nanoparticles in the microcontact printing process

High-quality CdTe nanoparticles stabilized with thioglycolic acid (TGA) are patterned on SiO2/Si surfaces using microcontact printing (microCP). Due to the weak interaction of the nanoparticles with the stamp surface, tailoring of gas flow rate during the inking process as well as the type and scale of the patterns on the stamp are used to control the distribution of the nanoparticles on the structured stamp surface. This distribution is then transferred the printed regions. Either edge printing or homogeneous printing can be achieved under optimized conditions. In addition, new structures such as nanowires form under certain conditions.     

Influence of an amide group in methyl octadecanoates on the monolayer stability

The influence of a hydrogen bond donor and acceptor in the hydrophobic part of an amphiphile on the monolayer stability at the air/water interface is investigated. For that purpose, the amide group is integrated into the alkyl chain. Eight methyl octadecanoates have been synthesized with the amide group in two orientations and in different positions of the alkyl chain, namely, CH3O2C(CH2)m NHCO(CH2)n CH3 (n + m = 14): 1 (m = 1), 3 (m = 2), 5 (m = 3), 7 (m = 14); and CH3O2C(CH2)m CONH(CH2)n CH3: 2 (m = 1), 4 (m = 2), 6 (m = 3), 8 (m = 14). The monolayers have been characterized by their pi/A isotherms, their temperature dependence and Brewster angle microscopy (BAM). Amphiphile 1 with the amide group close to the ester group (m = 1) behaves like an unsubstituted fatty acid ester, while 3, 5, and 7, with the amide group in an intermediate and terminal position, exhibit a two-phase region. The amphiphiles 2, 4, 6, and 8, with a reversed orientation of the amide group, all exhibit a two-phase region with higher plateau pressures and lower collapse pressures than those of 1, 3, 5, and 7. For 7 and 8, domains of the liquid condensed (LC) phase are visualized by BAM in the two-phase region. The liquid expanded (LE)/LC-phase transitions are all exothermic with enthalpies deltaH ranging from -31 to -12 kJ/mol. Comparison with other bipolar amphiphiles indicates that the LC phase is better stabilized by the hydroxy and dihydroxy groups than by the amide group. For model compounds of 1-4, optimized conformers in the LE and LC phases have been determined by density functional theory (DFT) calculations.     

Iridium-complex modified CdSe/ZnS quantum dots; a conceptual design for bi-functionality toward imaging and photosensitization

We report the design and synthesis of Ir-complex functionalized CdSe/ZnS quantum dots (QDs), in which the QD plays a key role in imaging, while the Ir-complex acts as a sensitizer to produce singlet oxygen; this conceptual design presents a novel scheme in both bio-imaging and photodynamic therapy.     

Preparation, characterization, resistance to protein adsorption, and specific avidin-biotin binding of poly(amidoamine) dendrimers functionalized with oligo(ethylene glycol) on gold

Protein-resistant films derived from the fifth-generation poly(amidoamine) dendrimers (PAMAM G5) functionalized with oligo(ethylene glycol) (OEG) derivatives consisting of various ethylene glycol units (EG(n), n = 3, 4, and 6) were prepared on the self-assembled monolayers (SAMs) of 11-mercaptoundecanoic acid (MUA) on gold substrates. The resulting films were characterized by ellipsometry, contact angle goniometry, and X-ray photoelectron spectroscopy (XPS). About 35% of the peripheral amines of the dendrimers were reacted with N-hydroxysuccinimide-terminated EG(n) derivatives (NHS-EG(n)). The dendrimer films showed improved stability over octadecanethiolate SAMs on gold in hot solvents, attributed to the formation of multiple amide bonds per PAMAM unit with underlying NHS-activated MUA monolayer. The EG(n)-attached PAMAM surfaces with n = 3 reduced the adsorption of fibrinogen to approximately 20% monolayer, whereas 2-3% for n = 4 or 6. The dendrimer films with various densities of EG(n) molecules on PAMAM surfaces were prepared by immersion of the NHS-terminated MUA-functionalized gold substrates in ethanolic solutions containing PAMAM and NHS-EG(n) of various mole ratios. The density (r) of the EG(n) molecules on the PAMAM surfaces is consistent with the mole ratio (r') of NHS-EG(n)/free amine of PAMAM in solutions. The resistance to protein adsorption of the resulting surfaces is correlated with the surface density and the length of the EG chains. At their respective r, the EG(n)-modified dendrimer films resisted approximately 95% adsorption of fibrinogen on gold surfaces. Finally, the specific binding of avidin to the approximately 5% and approximately 40% biotinylated EG3 dendrimers (surface density of biotin with respect to the total number of terminal amino groups on PAMAM G5) gave rise to about 50% and 100% surface coverage by avidin, respectively.