Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Solid state structure of thorium(IV) complexes with common aminopolycarboxylate ligands

The crystal structures of the complexes formed by reaction of thorium(IV) nitrate with iminodiacetic acid (H(2)IDA), nitrilotriacetic acid (H(3)NTA), and ethylenediaminetetraacetic acid (H(4)EDTA) under hydrothermal conditions are reported. In [Th(HIDA)(2)(C(2)O(4))]·H(2)O (1), the metal atom is chelated by two carboxylate groups from two HIDA(-) anions and by two oxalate ligands formed in situ; two additional oxygen atoms from two more HIDA(-) anions complete the ten-coordinate environment of bicapped square antiprismatic geometry. The uncoordinated nitrogen atom is protonated and involved in hydrogen bonding. Two different ligands are present in [Th(NTA)(H(2)NTA)(H(2)O)]·H(2)O (2), one of them being a O(3),N-chelating trianion which acts also as a bridge toward two neighboring metal ions, and the other being a bis-monodentate bridging species with an uncoordinated carboxylic arm and a central ammonium group. An aqua ligand completes the nine-coordinated, capped square antiprismatic metal environment. The EDTA(4-) anion in [Th(EDTA)(H(2)O)]·2H(2)O (3) is chelating through one oxygen atom from each carboxylate group and the two nitrogen atoms, as in a previously reported molecular complex. Two carboxylate groups are bridging, which, with the addition of an aqua ligand, gives a capped square antiprismatic coordination polyhedron. Aminopolycarboxylate ligands have been much investigated in relation with actinide decorporation and nuclear wastes management studies, and the present results add to the structural information available on their complexes with thorium(IV), which has mainly been obtained up to now by extended X-ray absorption fine structure (EXAFS) spectroscopy. In particular, the bridging (non-chelating) coordination mode of H(2)NTA(-) is a novel feature in this context. All three complexes crystallize as two-dimensional assemblies and are thus novel examples of thorium-organic coordination polymers.     

L-Cysteine as a chiral linker in lanthanide-cucurbit[6]uril one-dimensional assemblies

The reaction of neodymium, europium, or terbium nitrate with cucurbit[6]uril (CB6) in the presence of the α-amino acid L-cysteine (L-cys) gives the complexes [Nd(L-cys)(CB6)(NO(3))(H(2)O)(4)]·2NO(3)·10H(2)O (1) and {[Ln(L-cys)(CB6)(H(2)O)(5)][Ln(L-cys)(CB6)(NO(3))(H(2)O)(4)]}·5NO(3)·22H(2)O with Ln = Eu (2) or Tb (3). 2 and 3 only differ from 1 by the presence of two independent metal ions in slightly different environments. In all cases, each metal atom is bound to the bidentate CB6 and the monodentate L-cys molecules, with the latter being in its zwitterionic form. The ammonium group of L-cys is directed away from CB6 and is involved in ion-dipole and hydrogen bonding interactions with the uncomplexed portal of the neighboring molecule, which gives rise to the formation of chiral one-dimensional assemblies of columnar shape.     

Cohen–Macaulayness of monomial ideals and symbolic powers of Stanley–Reisner ideals

We present criteria for the Cohen–Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen–Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen–Macaulayness of the second symbolic power or of all symbolic powers of a Stanley–Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen–Macaulay. In particular, all symbolic powers are Cohen–Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen–Macaulayness can pass from a symbolic power to another symbolic powers in different ways.     

Multiwavelength Raman fiber lasers with equalized peak power using a sampled chirped fiber Bragg grating

Two novel multiwavelength Raman fiber lasers using a ring cavity and a linear cavity are proposed and demonstrated experimentally. Both laser configurations include a sampled chirped fiber Bragg grating used in the reflection mode. By adjusting the polarization controller (PC) in the cavities, up to ten stable lasing wavelengths with 0.8 nm spacing and equalized peak power are achieved at room temperature. It is observed that the output spectrum depends upon which port of the grating is connected to the cavity. These two fiber ring lasers offer advantages such as, stable room temperature operation, simple structure, low loss, multiwavelength lasing lines with moderate output power. PACS 42.55.Wd; 42.55.Ye; 42.81.-i     

Nontrivial periodicity in discrete delay models of population growth

In this paper, we will study the periodicity in discrete model An+1=λAn+F(An−m) of population growth, where the delay m is large enough and the nonlinearity F is unimodal function. Actually, we prove that there is a slowly oscillated periodic solution. Our method is Browder nonextremal fixed point theorem.     

Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.     

Electrochemical properties of a polycrystalline gold electrode in propylene carbonate solutions

The adsorption of 1,6-hexanediol at the Hg—aqueous solution interface was investigated. The differential capacity, interfacial tension and the zero charge potential were measured. Analysis of the results were carried out both at constant charge and at constant potential. Good congruence with respect to the potential and noncongruence with respect to the charge was found. It was shown that the hexanediol molecules orientate flat against the surface and the adsorption could be described equally well by the Frumkin or Flory—Huggins isotherms. Adsorption parameters for the hexanediol were compared with the literature data on adsorption of ethanediol and 1,4-butanediol. It was concluded that adsorption of diols does not affect the thickness of the inner layer. Thus, this adsorption is well described by the model of two parallel capacitors.