Compact,convex sets in R n and a new banach lattice. II.- Application: An approximation problem.

We develop a calculus structure in the Banach lattice introduced in a preceding paper, having in mind an approximation problem appearing in non-smooth optimization. We show that the essential results depend as much on the order structure as on the analytical one.     

Dark solitons of the Biswas–Milovic equation by the first integral method

This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained.     

SL(3,3~n)和SU(3,3~n)的第一Cartan不变量

确定Cartan不变量是代数群与相关的李型有限群的模表示理论中的一个重要方面.作者利用代数群模表示理论中的一系列结果,计算了3~n个元素的有限域上特殊线性群SL(3,3~n)和特殊酉群SU(3,3~n)的第一Cartan不变量,得到如下结论:当G=SL(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n;而当G=SU(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n+2·(1+(-1)~n),其中a,b是多项式x~2-20x+48的两个根.另外,作者也得到了射影不可分解模U_n(0,0)的维数公式:dim U_n(0,0)=(12~n-6~n+∈)·3~(3n),其中,当G=SL(3,3~n)时,∈=1;而当G=SU(3,3~n)时,∈=-1.     

Exponential moments of first passage times and related quantities for Lévy processes

For a Lévy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval , the sojourn time in the interval , and the last exit time from . Moreover, whenever these quantities are finite, we derive their respective asymptotic behavior as .     

Extended Gerber–Shiu functions in a risk model with interest

We consider a compound Poisson risk model with interest. The Gerber–Shiu discounted penalty function is modified with an additional penalty for reaching a level above the initial capital. We show that the problem can be split into two independent problems; an original Gerber–Shiu function and a first passage problem. We also consider the case of negative interest. Finally, we apply the results to a model considered by Embrechts and Schmidli (1994).     

First principles calculations of oxygen reduction reaction at fuel cell cathodes

The efficiency of solid oxide fuel cells (SOFC) depends critically on materials, in particular for the cathode where the oxygen reduction reaction (ORR) occurs. Typically, mixed conducting perovskite ABO₃-type materials are used for this purpose. The dominating surface terminations are (001) AO and BO₂, with the relative fractions depending on materials composition and ambient conditions.Here, results of recent large-scale first principles (ab initio) calculations for the two alternative polar (La,Sr)O and MnO₂ (001) terminations of (La,Sr)MnO₃ cathode materials are discussed. The surface oxygen vacancy concentration for the (La,Sr)O termination is more than 5 orders of magnitude smaller compared to MnO₂, which leads to drastically decreased estimated ORR rates. Thus, it is predicted for prototypical SOFC cathode materials that the BO₂ termination largely determines the ORR kinetics, although with Sr surface segregation (long-term degradation) its fraction of the total surface area decreases, which slows down cathode kinetics.     

Remarks on the solution of extended Stokes' problems

The analytical solutions of first and second Stokes' problems are discussed, for infinite and finite-depth flows of a Newtonian fluid in planar geometries. Problems arising from the motion of the wall as a whole (one-dimensional flows) as well as of only one half of the wall (two-dimensional) are solved and the wall stresses are evaluated.The solutions are written in real form. In many cases, they improve the ones in literature, leading to simpler mathematical forms of velocities and stresses. The numerical computation of the solutions is performed by using recurrence relations and elementary integrals, in order to avoid the evaluation of integrals of rapidly oscillating functions.The main physical features of the solutions are also discussed. In particular, the steady-state solutions of the second Stokes' problems are analyzed by separating their “in phase” and “in quadrature” components, with respect to the wall motion. By using this approach, stagnation points have been found in infinite-depth flows.     

Effect of varying lanthanide local coordination sphere on luminescence properties illustrated by selected inorganic and organic rare earth complexes synthesized in sol-gel host glasses

Inorganic and organic ligands were carefully selected to illustrate the effect of modifications in the local field environment around the rare earth lanthanide (III) on its emission properties. In this article two strategies were employed to enhance emission of lanthanides encapsulated in sol-gel glass. (i) Changing the symmetry around the lanthanide, which was diagnosed by changing the local environment around the lanthanide using different inorganic counter ions (acetate, nitrate and chloride) these ligands differ in their affinity toward the lanthanide first coordination sphere. The ligand that penetrates the lanthanide more results in more asymmetric environment and thus results in higher emission. The aim of this part was to demonstrate the change of symmetry on emission in the absence of energy transfer. Our results indicate that the acetate ion has the highest affinity toward the first coordination sphere followed by the nitrate while the chloride showed the lowest affinity. Penetration by the ligands ofthe lanthanide also results in removing OH quenchers surrounding the lanthanide and this further explains the boost in emission. (ii) A bulky organic ligand that forms a complex with the lanthanide is used. The organic ligand separates the lanthanide ion from inner O-H oscillators. In this case the chelating organic chromophore with suitable photophysical properties was employed to sensitize the lanthanide and thus energy transfer occurs via the antenna effect. The organic ligand absorbs UV light, then energy is transferred to the lanthanide and finally the lanthanide emits in the visible region. The first coordination environment surrounding europium was controlled by the ligand selection and the outer sphere was modified by doping the synthesized complexes in an optically transparent sol-gel glass host. The glass network carefully prepared by sol-gel process is effective in preventing free oxygen and water from attacking lanthanide -complexes without loss of luminescence. Emission spectroscopy measurements of the doped silica specimens confirmed the variation of Eu (III) emission depending on the first coordination sphere surrounding the europium ion. The encapsulation of the europium complexes was performed for two reasons: (i) to improve the stability of red phosphor with efficient and high color-purity characteristics under ultraviolet excitation and (ii) this work provides a framework for preparing transparent composite glasses that are robust hosts to study the fundamental interactions between nano-materials and light.     

Structural, elastic and electronic properties of a new ternary-layered Ti2SiN

The structural, elastic and electronic properties of Ti₂SiN were studied by first-principle calculations. The calculated bond lengths of Ti-Si and Ti-C are 2.65 and 2.09 Å, respectively. The results show Ti₂SiN is mechanically stable, and its bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio μ and anisotropy factor A are determined to be 182 GPa, 118 GPa, 291 GPa, 0.233 and 1.57, respectively. The calculated electronic structure indicates that Ti₂SiN is anisotropic and conductive.     

First principles lattice dynamical calculation of semiboride Be2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew-Burke-Ernzehorf exchange correlation functional while local density approximations use the Perdew-Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be₂B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be₂B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be₂B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be₂B.