A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Electronic structure of axially ligated rhodium carboxylates: π back-bonding revisited

Fenske-Hall molecular orbital calculations have been applied to a new, structurally isolable analog of the intermediate involved in catalytic rhodium carboxylate carbenoid transformations. Results from the structural characterization of axially ligated rhodium acetate phenylisonitrile complexes have been utilized in approximate molecular orbital calculations. The results from the calculations suggest that a significant degree of π back-bonding exists between the metal and isonitrile fragments which, by analogy, implies that π back-bonding should also exist in the rhodium carbenoid intermediate. Sensitivity of the Fenske-Hall method to the magnitude of π back-donation in these complexes was gauged through calculations involving different phenylisonitrile groups in which the π back-bonding ability was modulated through derivativization. The reliability of the Fenske-Hall method was evaluated through a comparison to a high-level calculation. Received: 13 December 1996 / Accepted: 18 March 1997     

并行FORTRAN程序设计技术探索

简要叙述了并行程序设计语言ＣＭＦｏｒｔｒａｎ的计算模式、并行数据结构及其主要特征．并对Ｆｏｒｔｒａｎ７７和Ｆｏｒｔｒａｎ９０上的扩展部分作了概要描述．     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Global symmetry breaking in the nonconserved order parameter system during phase ordering

We study global symmetry breaking in the 2D system of scalar nonconserved order parameter following a quench to zero temperature. We show that the instant of time when the symmetry is broken and the final morphology is chosen corresponds to the saturation of the order parameter inside the domains. There are three possible final morphologies: the positive and negative order parameter final morphology, and the state of the coexisting positive and negative order parameter subsystems with a flat interface between them. We find also that each type of the final morphology constitutes about 1/3 of all cases, what agrees with the results obtained recently by Spirin et al. [Phys. Rev. E 65, 016119 (2001)]. Our results are pertinent for the two dimensional systems, but we suspect that there is also a way to apply similar arguments for the three dimensional ones.     

Phase transitions in erbium-doped silicon exposed to laser radiation

The dynamics of phase transitions induced by nanopulsed ruby laser radiation (80 nsec, 2 J/cm²) both in silicon layers doped with erbium ions and in those containing doped erbium and oxygen have been studied by an optical probing method. It is shown that the reflectivity behavior of structures under pulsed irradiation is governed by phase transitions (melting and crystallization) of implanted silicon and also by interference effects at the interfaces of the resulting phases. It is established that the profiles of erbium distribution change under nanosecond laser irradiation and that the dopant is forced out to the surface due to a segregation effect at small implantation doses. As the implanatation dose increases, diffusion deep into the sample tends to prevail over segregation. A considerable increase in the photoluminescence peak intensity at 0.81 eV is found after both the pulsed laser processing and thermal post-annealing of doped samples as opposed to spectra of samples subjected either to thermal annealing or to pulsed laser irradiation. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 2, pp. 225–231, March–April, 2009.     

Transformations in optics: Novel perspectives,approaches, applications and implementations

This paper summarizes a set of novel techniques for obtaining optical transformations, which are useful tools for signal processing. Then the paper focuses on deriving several interesting discrete transformations. The discussed transforms include continuous fractional transformations, hybrid transforms and discrete transform kernels.     

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics—I

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.     

Hamiltonian map approach to 1D Anderson model

A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization length is also obtained for the dichotomic correlated sequence in the small disorder situation.