The dynamics of spatiotemporal modulations

The modulational instability of traveling waves is often thought to be a crucial point in the mechanism of transition to space-time disorder and turbulence. The aim of this paper is to study the effect of spatiotemporal modulations on some dynamics u(0)(x,t), which may occur as an instability process when a control parameter varies, for instance. We analyze the properties of the modulated dynamics of the form g(1)(x)g(2)(t)u(0)(x,t) compared to those of the reference dynamics u(0)(x,t), using operator theory. We show that, if the reference dynamics is invariant under some space-time symmetry in the sense of Ref. [J. Nonlinear Sci. 2, 183 (1992)], the modulation has the effect of either deforming this symmetry or breaking it, depending on whether the corresponding operator remains unitary or not. We also demonstrate that the smallest Euclidean space containing the modulated dynamics has a dimension smaller than or equal to the smallest Euclidean space containing u(0)(x,t). The previous results are then applied to the case of modulated uniformly traveling waves. While the spatiotemporal translation invariance of the wave never persists in the presence of a modulation, the existence of a spatiotemporal symmetry depends on the resonance of the Fourier sidebands due to the modulation. In case of nonresonance, a spatiotemporal symmetry exists and is explicitly determined. In this situation, the modulated wave and the carrier wave have the same spectrum (up to a normalization factor), the same entropy, and the spatial (resp., temporal) two-point correlation is deformed only by the spatial (resp., temporal) modulation. (c) 1995 American Institute of Physics.     

Join-continuous frames,Priestley's duality and biframes

The primary purpose of this paper is to study join-continuous frames. We present two representation theorems for them: one in terms of -subframes of complete Boolean algebras and the other in terms of certain Priestley spaces. This second representation is used to prove that the topological spaces whose frame of open sets is join-continuous are characterized by a condition which says that certain intersections of open sets are open. Finally, we show that Priestley's duality can be viewed as a partialization of the dual adjunction between the categories of, respectively, bitopological spaces and biframes, stated by B. Banaschewski, G. C. L. Brümmer and K. A. Hardie in [5].This work was partially supported by Centro de Matemáíica da Universidade de Coimbra.     

Fubini theorem for anticipating stochastic integrals in Hilbert space

Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Y_x,x X, of the anticipating integral of(x) such that the integral _x Y_x(dx) is a version of the anticipating integral of _X (x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.     

Ab initio molecular dynamics simulation of a room temperature ionic liquid

Ab initio molecular dynamics simulations have been performed for the first time on the room-temperature organic ionic liquid dimethyl imidazolium chloride [DMIM][Cl] using density functional theory. The aim is to compare the local liquid structure with both that obtained from two different classical force fields and from neutron scattering experiments. The local structure around the cation shows significant differences compared to both the classical calculations and the neutron results. In particular, and unlike in the gas-phase ion pair, chloride ions tend to be located near a ring C-H proton in a position suggesting hydrogen bonding. The results are used to suggest ways in which the classical potentials may be improved.     

Joint QTAIM and Hirshfeld study of the sigma and pi charge distribution and electron delocalization in carbonyl compounds: a comparative study with the resonance model

Atomic charges and delocalization indexes (DIs) for a series of carbonyl compounds comprising dimethyl ketone, acetaldehyde, acetic acid, methyl acetate, acetamide, methyl vinyl ketone, divinyl ketone, and benzoic acid were studied using two different atomic partitionings: the QTAIM and the Hirshfeld (stockholder) scheme. The resonance model, traditionally employed to explain the reactivity of these compounds, is not in line with the total atomic charges and DIs calculated by both methodologies. However, the resonance model is supported to some extent by the pi charges and pi DIs calculated by both schemes, but the calculated values indicate that the pi population delocalizes only to a small degree. Although the absolute values of QTAIM and stockholder atomic charges are significantly different, the pi charges and the values of the DIs show similar trends for all the atoms and molecules of this study; this is especially the case for the pi DIs. A study of the electron density on the level of a single MO performed for CO, H2CO, F2CO, and H2CS reveals that the differences in the atomic sigma charges computed with both partitionings can be traced back to their different treatment of interatomic regions.     

Use of highly efficient Draper-Lin small composite designs in the formal optimisation of both operational and chemical crucial variables affecting a FIA-chemiluminescence detection system

A new formal strategy in the multidimensional optimisation of the experimental variables affecting the chemiluminescence (CL) detection in flow injection analysis (FIA) is proposed here. The strategy implies several steps, being the most significant: selection of the variables to be studied and their experimental domain; use of a screening design to detect significant variables and interactions into the experimental region; study of the main effect of variables and second-order interactions; and finally application of a Draper-Lin small composite design (orthogonal) to obtain the optimum values of the significant variables. The methodology is applied to the determination of methylamine by FIA based on the use of the peroxyoxalate CL (PO-CL) reaction. Considering the high number of experiments required due to the different chemical and instrumental variables to be taken account and their adequate compatibility to obtain maximum sensitivity, the methodology offers a rigorous study of the main effects and interactions, achieving a reduction of experimental work.     

Electroreductive polymerization of phenylmethyldichlorosilane in a divided cell using a neutral membrane

Electrochemical formation of poly(phenylmethylsilane) in a divided cell containing a Teflon® neutral membrane was studied. The electrolysis of dichlorosilanes was carried out in a solution containing tetrahydrofuran + hexamethylphosphoramide as the solvent, tetrabutylammonium perchlorate as the support electrolyte and stainless steel as the cathode, with Pt and graphite as the resistant anodes or stainless steel as the sacrificial anode. Polysilanes with a number-average molecular weight in the range from 2,600 to 130,000 g/mol were obtained, depending on the conditions used.     

Synthesis of 2,3,8,9-tetramethoxy-11-phenyl-5,6-dihydrodibenz[2,3;7,8]indolizine

2,3,8,9-Tetramethoxy-11-phenyldibenz[2,3;7,8]indolizine was obtainedinhighyieldfrom (6,7-dimethoxyisoquinolin-1-yl)-(3,4-dimethylphenyl)phenylcarbinol by cyclization in the presence of formic acid. The behavior of (6,7-dimethoxyisoquinolin-1-yl)-(3,4-dimethoxyphenyl)methylcarbinol and (6,7-dimethoxyisoquinolin-1-yl-(3,4-dimethoxyphenyl)carbinol was studied under these same conditions. 2,3,7,8-Tetramethoxy-11-phenyl-5,6-dihydrodibenz[2,3;7,8]indolizine was obtained by hydrogenation on rhenium heptasulfide.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1233–1238, September, 1993.