A Modified SQP Method and Its Global Convergence

The sequential quadratic programming method developed by Wilson, Han andPowell may fail if the quadratic programming subproblems become infeasibleor if the associated sequence of search directions is unbounded. In [1], Hanand Burke give a modification to this method wherein the QP subproblem isaltered in a way which guarantees that the associated constraint region isnonempty and for which a robust convergence theory is established. In thispaper, we give a modification to the QP subproblem and provide a modifiedSQP method. Under some conditions, we prove that the algorithm eitherterminates at a Kuhn–Tucker point within finite steps or generates aninfinite sequence whose every cluster is a Kuhn–Tucker point.Finally, we give some numerical examples.     

Generation of Broadband High Harmonics through Linear Mode Conversion in Inhomogeneous Plasmas

The generation of high order harmonics from an inhomogeneous ovderdense plasma target irradiated by an ultrashort intense laser pulse is studied by numerical simulation. During such interaction, ultrafast electron bunches are generated and excite electron plasma oscillations as they pass through the overdense target. These plasma oscillations will emit high-frequency electromagnetic emission by linear mode conversion. Instead of the integer harmonies generation, the emission appears with a broadband and even continuous spectrum corresponding to the electron plasma frequency range of the inhomogeneous plasma density.     

Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nth-order singular nonlocal boundary value problem

     

Critical points theorems concerning strongly indefinite functionals and infinite many periodic solutions for a class of Hamiltonian systems

Based on new deformation theorems concerning strongly indefinite functionals, we give some new min-max theorems which are useful in looking for critical points of functionals which are strongly indefinite and satisfy Cerami condition instead of Palais-Smale condition. As one application of abstract results, we study existence of multiple periodic solutions for a class of non-autonomous first order Hamiltonian system

     

Oscillation criteria for second order linear matrix differential systems with damping

Using a generalization of Sturm’s comparison theorem, some new oscillation criteria are established for the matrix differential system with damping

(P(t)Y^′)^′+R(t)Y^′+Q(t)Y=0${\left(P\left(t\right)Y^{\prime }\right)}^{\prime }+R\left(t\right)Y^{\prime }+Q\left(t\right)Y=0$

Elastic beam problem with higher order derivatives

We apply a fixed point theorem to obtain sufficient conditions for existence of triple positive solutions of the symmetric nonlinear fourth-order boundary value problem$u^{(4)}(t)=a(t)f(t,u(t),|u^{\prime }(t)|,u^{″}(t),|u^{‴}(t)|),t\in (-1,1)\text{,}$$u(-1)=u^{\prime }(-1)=0\text{,}$$u(-t)=u(t),t\in [-1,1]\text{,}$where f satisfies certain growth conditions. In the process, we obtain nontrivial a priori bounds on the derivatives of the solution.     

Amphiphilic block copolymer-stabilized PtRu nanoparticles highly dispersed on multi-walled carbon nanotube for methanol oxidation

We report a one-pot synthesis of amphiphilic block copolymer-stabilized PtRu nanoparticle modified multi-walled carbon nanotubes (MWCNTs) using RuCl(3)·xH(2)O and H(2)PtCl(6)·6H(2)O as ruthenium and platinum sources, and block copolymer poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) as stabilizer agent. PtRu alloyed nanoparticles with an average diameter of 4.6nm are well decorated homogeneously on the exterior surfaces of the MWCNTs. The electrochemical catalytic activity for methanol oxidation of PtRu/MWCNTs and commercial PtRu/C (E-TEK) is comparatively investigated using cyclic voltammetry and chronoamperometry. It is revealed that the PtRu nanoparticle modified MWCNT samples display an enhanced electrochemical catalytic activity than commercial PtRu/C electrode. These results show that PtRu nanoparticles may find applications to fuel cells.     

Volumetric and surface properties of pure ionic liquid n-octyl-pyridinium nitrate and its binary mixture with alcohol

The density and surface tension for pure ionic liquid N-octyl-pyridinium nitrate were measured from (293.15 to 328.15) K. The coefficient of thermal expansion, molecular volume, standard entropies, and lattice energy were calculated from the experimental density values. The critical temperature, surface entropy, surface enthalpy, and enthalpy of vaporization were also studied from the experimental surface tension results. Density and surface tension were also determined for binary mixtures of (N-octyl-pyridinium nitrate + alcohol) (methanol, ethanol, and 1-butanol) systems over the whole composition range at 298.15 K and atmospheric pressure. Excess molar volumes and surface tension deviations for the binary systems have been calculated and were fitted to a Redlich–Kister equation to determine the fitting parameters and the root mean square deviations. The partial molar volume, excess partial molar volume, and apparent molar volume of the component IL and alcohol in the binary mixtures were also discussed.