Symmetric Eighth Algebraic Order Methods with Minimal Phase-Lag for the Numerical Solution of the Schrödinger Equation

In this paper some new eighth algebraic order symmetric eight-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Based on this formula, the calculation of free parameters is done in order the phase-lag to be minimal. The new methods have better stability properties than the classical one. Numerical illustrations on the radial Schrödinger equation indicate that the new method is more efficient than older ones.     

Synthesis of benzyl halides from aldehydes promoted by halosilanes and 1,1,3,3-tetramethyldisiloxane (TMDS).

Direct synthesis of monoalkyl halides from aldehydes by a new reductive halogenation method is briefly described.     

Nonlinear s-polarized surface plasmon polaritons

We have examined the dispersion relations for s-polarized surface plasmon polaritons, guided by (a) the interface between a semi-infinite metal and dielectric medium, and (b) a metal film bounded by semi-infinite dielectric media for situations in which one or more of the dielectric media are characterized by an intensity-dependent refractive index. We found that s-polarized waves satisfy the dispersion relations for very thin metal films bounded by nonlinear dielectric media. These waves exist only for power levels above a threshold that depends on the material parameters. We also comment on the experimental feasibility of observing these waves.     

Hyperfine spectroscopic study of the metal-insulator transition in V2O3

The metal-insulator (M-I) transition in vanadium sesquioxide V₂O₃ has been investigated by time differential perturbed angular correlation measurements of the electric fieldgradient (EFG) and the magnetic hyperfine field at dilute¹¹¹Cd impurities. The EFG undergoes a first-order change at the M-I transition at T_t=160 K, but does not reflect the high temperature resistivity anomaly. The increase of the EFG with temperature in the metallic phase can be attributed to thermal variations of the oxygen sublattice. The temperature dependence of the magnetic hyperfine field in the insulating phase follows a Brioullin function with a saturation value of H_hf(O)=15 KOe and an extrapolated Neel temperature, which, depending on the impurity concentration, varies between 188 and 230 K.     

Observation of splitting of the E2g mode and two-phonon spectrum in graphites

We have found the two-phonon mode of the disorder-induced line at 1370 cm^-1 for the single crystal and polycrystalline graphites having disorder. The degenerate E_2g mode of the D_6h symmetry for graphite is split for the disordered graphites, having frequencies at 1590 cm^-1 and 1627 cm^-1. Brewster angle measurements using lasers at 6328A and 10.6 μm yield n and k with good consistency even for surfaces with moderate roughness. Our results suggested that distortion of the crystal structure is present.     

On the conditions for a Hamiltonian matrix to have an eigen-value density with some prescribed characteristics

The following problem is considered: “Find the necessary and sufficient conditions to be fulfilled by the components of a hamiltonian operator to have an eigenvalue density with certain prescribed characteristics”. The solution when the hamiltonian operator is a Jacobi matrix and the prescribed characteristic is the unimodality, is shown. A sufficient condition for a real Jacobi matrix to have a prescribed density is also given.     

A new Co(II)-metalloviologen-based electrochromic material integrated in thin multilayer films

A metallosupramolecular coordination polyelectrolyte prepared by the reaction of cobalt(II) with a novel bisterpyridine ligand has been assembled as the active component in electrochromic films by sequential deposition using electrostatic layer-by-layer self-assembly.     

A polynomial of degree four not satisfying Rolle’s theorem in the unit ball of <Emphasis Type="Italic">l</Emphasis><Subscript>2</Subscript>

We give an example of a fourth degree polynomial which does not satisfy Rolles Theorem in the unit ball of l ₂.The author has been partially supported by MCyT and FEDER Project BFM2002-01423.     

Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity

Using a fast-motion approximation method we obtain the second-order gravitational field and equations of motion for two pointlike objects in algebraically closed form. A regularization procedure is used which is shown to guarantee the consistency of the approximation scheme. The equations of motion are then transformed within the framework of relativistic predictive mechanics into a system of ordinary differential equations.     

On a general system of orthogonal q-polynomials

A general set of orthogonal q-polynomials {P_m (x); m = 0, 1, 2, …, N} is introduced and characterized by its three-term recursion relation. This set unifies many of the different known systems of orthogonal q-polynomials, e.g. the Stieltjes-Wigert polynomials and their several generalizations, the Brenke-Chihara polynomials, the Al Salam-Carlitz polynomials, the Al Salam-Chihara polynomials, …. Compact expressions of the moments of the asymptotical density of zeros of this global set of q-polynomials are explicitly found in terms of the coefficients of the three-term recurrence relation. As an example the asymptotical density of zeros of the known, above-mentioned systems of orthogonal q-polynomials are calculated through its moments.