Two dimensional dynamical systems which admit Lie and Noether symmetries

We prove two theorems which relate the Lie point symmetries and the Noether symmetries of a dynamical system moving in a Riemannian space with the special projective group and the homothetic group of the space respectively. The theorems are applied to classify the two dimensional Newtonian dynamical systems, which admit a Lie point/Noether symmetry. Two cases are considered, the non-conservative and the conservative forces. The use of the results is demonstrated for the Kepler - Ermakov system, which in general is non-conservative and for potentials similar to the H\`enon Heiles potential. Finally it is shown that in a FRW background with no matter present, the only scalar cosmological model which is integrable is the one for which 3-space is flat and the potential function of the scalar field is exponential. It is important to note that in all applications the generators of the symmetry vectors are found by reading the appropriate entry in the relevant tables.Comment: 25 pages, 17 table

Calculation of the structure and nuclear magnetic shielding constants of some H-bonded carbon acid complexes

Electronic and spatial structure of some H-bonded complexes ((HCOOH)(n) (n = 1-4), formic, acrylic acids and their complexes with water and dimethylsulfoxide) were studied by ab initio methods using MP2/RHF//6-31G*, RHF/6-31G* basis sets, and also by using density functional theory (DFT)within the B3LYP approximation. The possibility of formation of chain and cyclic complexes of formic and acrylic acids with dimethylsulfoxide is shown. In a cyclic complex two hydrogen bonds are formed. One is as usually with the O-H bond (S=O···H-O), the other is between the acid carbonyl group and one hydrogen atom of DMSO methyl groups (C-H···O=C). The calculations of nuclear magnetic shielding were carried out within a framework of the coupled Hartree-Fock method using gauge invariant atomic orbitals. Analysis of the results for various basis sets and comparison of the calculated and experimentally obtained chemical shifts show that the calculations predict a significant downfield shift for 1H and 13C nuclei for H-bonded systems. The results of calculations of 17O magnetic shielding constants strongly depend on the used basis set and theoretical approach. (C) 2000 Elsevier Science B. V

Problems of ethnocultural identity and cross-language communication

© Journal of Language and Literature. The article deals with the problem of relationship between language and culture, identifies factors affecting understanding of information in the process of intercultural communication, and points out a positive role of the artistic bilingualism. The emphasis is put to the fact that formation of national identity in the modern multicultural environment grows into a dialogue that promotes coexistence of different nations in common land

Nonempirical calculations of the effect of molecular fragments on proton chemical shifts in heterocycles

We have calculated the relative changes in the proton chemical shifts for a number of six-membered heterocycles (1,3-dioxan, 1,3-oxazine, 1,3-dithiane, trimethylene sulfite, and also their derivatives). A procedure is proposed for estimating the chemical shifts due to the effect of model molecular fragments. In calculating the chemical shifts expected allowance is made for the way in which the given molecule differs in structure from a similar molecule for which the chemical shift is known. The chemical shifts were calculated in the approximation of gradient-invariant atomic orbitals in a Gaussian basis. The calculations reproduce correctly the effect of alkyl substituents and the trends in the chemical shifts as a function of the orientation of the substituents and of the heterocyclic component of the molecule. © 1990, Plenum Publishing Corporation. All rights reserved

Using the Noether symmetry approach to probe the nature of dark energy

We propose to use a model-independent criterion based on first integrals of motion, due to Noether symmetries of the equations of motion, in order to classify the dark energy models in the context of scalar field (quintessence or phantom) FLRW cosmologies. In general, the Noether symmetries play an important role in physics because they can be used to simplify a given system of differential equations as well as to determine the integrability of the system. The Noether symmetries are computed for nine distinct accelerating cosmological scenarios that contain a homogeneous scalar field associated with different types of potentials. We verify that all the scalar field potentials, presented here, admit the trivial first integral namely energy conservation, as they should. We also find that the exponential potential inspired from scalar field cosmology, as well as some types of hyperbolic potentials, include extra Noether symmetries. This feature suggests that these potentials should be preferred along the hierarchy of scalar field potentials. Finally, using the latter potentials, in the framework of either quintessence or phantom scalar field cosmologies that contain also a non-relativistic matter(dark matter) component, we find that the main cosmological functions, such as the scale factor of the universe, the scalar field, the Hubble expansion rate and the metric of the FRLW space-time, are computed analytically. Interestingly, under specific circumstances the predictions of the exponential and hyperbolic scalar field models are equivalent to those of the $\Lambda$CDM model, as far as the global dynamics and the evolution of the scalar field are concerned. The present analysis suggests that our technique appears to be very competitive to other independent tests used to probe the functional form of a given potential and thus the associated nature of dark energy.Comment: Accepted for publication in Physical Review D (13 pages

Proton chemical shifts and three-dimensional structure of seven-membered ring 1,3,2-dioxaheterocycles and their six-membered ring heteroanalogs

1. A theoretical basis has been provided for the demonstrated experimental principles in series of seven-membered ring, partially fixed, 1,3,2-dioxaheterocycles and their six-membered ring heteroanalogs, the theoretical foundation makes it possible to correlate proton chemical shifts and conformational structures of the heterocycles in question. 2. An approach has been used here for the first time, based on simultaneous analysis of experimental data for related compounds and theoretical calculations of expected changes in magnetic shielding arising from the influence of fragments with random symmetry. © 1988 Plenum Publishing Corporation

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

Deformation quantization of linear dissipative systems

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding Poisson tensor is allowed to explicitly depend on time. Starting from this pseudo-Hamiltonian formulation we develop a consistent deformation quantization procedure involving a non-stationary star-product $*_t$ and an ``extended'' operator of time derivative $D_t=\partial_t+...$, differentiating the $\ast_t$-product. As in the usual case, the $\ast_t$-algebra of physical observables is shown to admit an essentially unique (time dependent) trace functional $\mathrm{Tr}_t$. Using these ingredients we construct a complete and fully consistent quantum-mechanical description for any linear dynamical system with or without dissipation. The general quantization method is exemplified by the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Protease Activated Receptor Signaling Is Required for African Trypanosome Traversal of Human Brain Microvascular Endothelial Cells

Human African trypanosomiasis, or sleeping sickness, occurs when single-cell trypanosome protozoan parasites spread from the blood to brain over the blood-brain barrier (BBB). This barrier is composed of brain microvascular endothelial cells (BMECs) especially designed to keep pathogens out. Safe drugs for treating sleeping sickness are lacking and alternative treatments are urgently required. Using our human BMEC BBB model, we previously found that a parasite protease, brucipain, induced calcium activation signals that allowed this barrier to open up to parasite crossing. Because human BMECs express protease-activated receptors (PARs) that trigger calcium signals in BMECs, we hypothesized a functional link between parasite brucipain and BMEC PARs. Utilizing RNA interference to block the production of one type of PAR called PAR-2, we hindered the ability of trypanosomes to both open up and cross human BMECs. Using gene-profiling methods to interrogate candidate BMEC pathways specifically triggered by brucipain, several pathways that potentially link brain inflammatory processes were identified, a finding congruent with the known role of PAR-2 as a mediator of inflammation. Overall, our data support a role for brucipain and BMEC PARs in trypanosome BBB transmigration, and as potential triggers for brain inflammation associated with the disease