On near optimal trajectories for a game associated with the ��-Laplacian

A two-player stochastic differential game representation has recently been obtained for solutions of the equation ???_?? u?=?h in a ${{\mathcal C}^2}$ domain with Dirichlet boundary condition, where h is continuous and takes values in ${{\mathbb R}{\setminus}\{0\}}$ . Under appropriate assumptions, including smoothness of u, we identify a family of diffusion processes that may arise as the vanishing ?? limit law of the state process, when both players play ??-optimally. We also identify the limit law of the state process under a sequence of near saddle points.     

Mechanical properties of polypropylene (PP) + high‐density polyethylene (HDPE) binary blends: Non‐isothermal degradation kinetics of PP + HDPE (80/20) Blends

In this study, the mechanical properties and non‐isothermal degradation kinetics of polypropylene (PP), high‐density polyethylene (HDPE) with dilauroyl peroxide and their blends in different mixture ratios were investigated. The effects of adding dilauroyl peroxide (0–0.20 wt%) on the mechanical and thermal properties of PP + HDPE blends have been studied. On the other hand, the kinetics of the thermal degradation and thermal oxidative degradation of PP + HDPE (80/20 wt%) blends were studied in different atmospheres, to analyze their thermal stability. The kinetic and thermodynamic parameters such as the activation energy, E_a, the pre‐exponential factor, A, the reaction order, n, the entropy change, the enthalpy change, and the free energies of activated complex related to PP, HDPE, and blend systems were calculated by means of the several methods on the basis of the single heating rate. A computer program was developed for automatically processing the data to estimate the reaction parameters by using different models. Most appropriate method was determined for each decomposition step according to the least‐squares linear regression. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.     

Calorimetric study of the alpha-tocopherol solubility in reversed AOT micelles

The experimental data of heat of mixing (Q) for heterogeneous system alpha-tocopherol/AOT/n-heptane with and without water at 25 degrees C are presented. The Q dependence on AOT (sodium bis (2-ethylhexyl) sulfosuccinate) concentration, and R parameter defined as R=[H2O]/[AOT] with flow calorimetric method were investigated. Using the D'Aprano model (which is formally identical to that used earlier by Magid et al.) the binding constant (K), the distribution constant of alpha-tocopherol (K distr) between hydrocarbon and the micellar phase, and the standard enthalpy of transfer (DeltaH tr 0) of alpha-tocopherol from the hydrocarbon to AOT reversed micelles were calculated. The solubility of alpha-tocopherol in AOT reversed micelles explored with the calorimetric technique was compared to the literature data obtained respectively with UV spectrophotometry for reversed micelles and by other techniques for the phospholipid bilayer.     

Spectral, analytical, thermal, and antimicrobial studies of novel sodium 2-[4(2-hydroxy-3-izopropylaminopropoxy)phenyl]acetamide (atenolol) dithiocarbamate and its divalent transition metal complexes

Atenolol dithiocarbamate (ADTC) and its complexes with Cu(II), Co(II), Ni(II), Zn(II), and Cd(II) have been synthesized. These newly synthesized products have been characterized by elemental analyses (C, H, N, and S), thermal (thermogravimetry (TG) and differential thermal analyses (DTA)) as well as by spectral (UV, IR, and NMR (¹H)) studies. The stability constants (β) of metal complexes of ADTC have been determined by UV-Vis data in solutions in DMSO. The antimicrobial activities of the metal complexes have been screened in vitro against ten bacteria. The text was submitted by the authors in English.     

Deterministic and stochastic differential inclusions with multiple surfaces of discontinuity

We consider a class of deterministic and stochastic dynamical systems with discontinuous drift f and solutions that are constrained to live in a given closed domain G in ${\mathbb{R}}^{n}$ according to a constraint vector field D(·) specified on the boundary $\partial G$ of the domain. Specifically, we consider equations of the form $\phi = \theta + \eta + u , \quad \dot{\theta}(t) \in F(\phi(t)), \quad \mbox{a.e. } t$ for u in an appropriate class of functions, where η is the “constraining term” in the Skorokhod problem specified by (G, D) and F is the set-valued upper semicontinuous envelope of f. The case $G ={\mathbb{R}}^{n}$ (when there is no constraining mechanism) and u is absolutely continuous corresponds to the well known setting of differential inclusions (DI). We provide a general sufficient condition for uniqueness of solutions and Lipschitz continuity of the solution map, in the form of existence of a Lyapunov set. Here we assume (i) G is convex and admits the representation $G=\cup_i\overline{C_i}$ , where $\{C_i,i\in {\mathbb{I}}\}$ is a finite collection of disjoint, open, convex, polyhedral cones in ${\mathbb{R}}^{n}$ , each having its vertex at the origin; (ii) f =  b +  f ^c is a vector field defined on G such that b assumes a constant value on each of the given cones and f ^c is Lipschitz continuous on G; and (iii) D is an upper semicontinuous, cone-valued vector field that is constant on each face of ?G. We also provide existence results under much weaker conditions (where no Lyapunov set condition is imposed). For stochastic differential equations (SDE) (possibly, reflected) that have drift coefficient f and a Lipschitz continuous (possibly degenerate) diffusion coefficient, we establish strong existence and pathwise uniqueness under appropriate conditions. Our approach yields new existence and uniqueness results for both DI and SDE even in the case $G = {\mathbb{R}}^{n}.$ The work has applications in the study of scaling limits of stochastic networks.     

Invariant subspaces for Banach space operators with an annular spectral set

Consider an annulus for some , and let be a bounded invertible linear operator on a Banach space whose spectrum contains . Assume there exists a constant such that and for all polynomials . Then there exists a nontrivial common invariant subspace for and .

     

Heavy atom free singlet oxygen generation: doubly substituted configurations dominate S1 states of bis-BODIPYs

S(0), S(1), and T(1) states of various orthogonal 8,8' and 8,2'-bis-boradiaza-s-indacene (BODIPY) dyes, recently (Angew. Chem., Int. Ed.2011, 50, 11937) proposed as heavy atom free photosensitizers for O(2)((1)Δ(g)) generation, were studied by multireference quantum chemical approaches. S(0)→S(1) excitation characteristics of certain bis-BODIPYs are shown to be drastically different than the parent BODIPY chromophore. Whereas a simple HOMO→LUMO-type single substitution perfectly accounts for the BODIPY core, S(1) states of certain orthogonal bis-BODIPYs are described as linear combinations of doubly substituted (DS) configurations which overall yield four electrons in four singly occupied orbitals. Computed DS character of S(1), strongly correlated with facile (1)O(2) production, was presumed to occur via S(1)→T(1) intersystem crossing (ISC) of the sensitizer. Further confirmation of this relation was provided by newly synthesized BODIPY derivatives and comparison of spectroscopic properties of their dimers and monomers. Near-IR absorption, desired for potential photodynamic therapy applications, was not pursuable for bis-chromophores by the standard strategy of π-extension, as DS singlet states are destabilized. Decreased exchange coupling in π-extended cases appears to be responsible for this destabilization. Comparisons with iodine incorporated bis-BODIPYs suggest that the dynamics of (1)O(2) generation via DS S(1) states are qualitatively different from that via ISC originating from heavy atom spin-orbit coupling. Although red-shifting the absorption wavelength to enter the therapeutic window does not seem attainable for orthogonal bis-BODIPYs with DS S(1) states, modifications in the chromophore cores are shown to be promising in fine-tuning the excitation characteristics.     

Application of transversely isotropic materials to multi-layer shell elements undergoing finite rotations and large strains

The contribution deals with an extension of a classical Neo–Hookean model for compressible isotropic materials to transverse isotropy. With this enhancement for one preferred material direction there is a possibility to simulate large strains in volume changes of the isotropic basic continuum and supplementary in fiber direction. The integrity basis of polynomial invariants in case of transversely isotropic hyperelasticity consists of three principal invariants of the isotropic basic continuum and additionally of two principal invariants for the preferred material direction. The proposed stored energy function for transverse isotropy contains the classical theory near to the natural state and fulfills the restriction on polyconvexity and coerciveness.By numerical enforcement of the material model into shell kinematics without rotational variables a four-node isoparametric finite element is developed using special concepts to avoid locking. The capability of the algorithms proposed is demonstrated by a numerical example involving large strains as well as finite rotations.     

Molecular and Crystal Structure of 2-{(<Emphasis Type="Italic">E</Emphasis>)-[(5-Chloro-2-methoxyphenyl)imino]methyl}-4-nitrophenol

The molecular structure of the title compound, C₁₄H₁₁ClN₂O₄, was determined by single crystal X-ray diffraction. The compound crystallizes in the monoclinic sp. gr. P2₁/c with Z = 4. The title compound, C₁₄H₁₁ClN₂O₄, is a Schiff base which adopts the phenol-imine tautomeric form in the solid state.The molecule is almost planar and the dihedral angle between the planes of two aromatic ring is 2.2(1)°. The molecular structure is stabilized by intramolecular O–H···N hydrogen bond which generates a six-membered ring. In the crystal structure, the molecules are linked together by intermolecular C–H···O interactions.