Linear Symmetry Research Articles

Surface ultrastructure of juvenile and adult stages of Centrocestus armatus.

Centrocestus armatus (Trematoda: Heterophyidae) develops rapidly and produces eggs at 3 days postinfection in albino rats. Excysted metacercariae are pear-shaped and concave ventrally, with 42-44 peg-like circumoral spines. The entire body surface is densely covered with scale-like serrated spines. On juveniles, serration of the tegumental spines is greatest in the middle of the ventral and dorsal surfaces, and decreases anteriorly and posteriorly. Ciliated sensory papillae are concentrated around the oral sucker. Several nonciliated sensory papillae (type II papillae) occur equidistantly on the acetabulum and are arranged in a linear symmetry on the dorsal surface. On adults, the serration of the tegumental spines decreases to 14-17 tips on the ventrolateral surface. The high density of tegumental spines on posterior half of the body and the distribution of type II papillae on dorsal surface are considered to be characteristic of C. armatus.

Intercalation route to new superconducting and insulating hybrid systems, M–X–Bi 2Sr 2Ca n−1 Cu nO y (M=Hg,Ag; X=Br,I; Py=pyridine; n=1,2)

We have systematically applied the intercalation technique to the layered superconducting oxides in order not only to develop a new high- T c superconducting nanohybrid, but also to investigate the mechanism responsible for high- T c superconductivity. In the light of the Lewis acid–base concept, we have recently synthesized new types of high- T c superconducting intercalation compounds: M–X–Bi 2Sr 2Ca n−1 Cu n O y (M=Hg,Ag; X=Br,I; n=1,2). According to X-ray absorption spectroscopic analysis, intercalated HgX 2 is stabilized in a molecular form with linear symmetry, which is the first example of molecular HgX 2 in a solid matrix, and the intercalated AgI has an α-AgI-like structure with distorted tetrahedral symmetry, which is consistent with the significant rapid ionic conductivity of AgI-intercalate in the temperature domain 25–300°C.

Linear phase and symmetries for multidimensional FIR filters over lattices

We present in this paper multidimensional FIR filters over arbitrary lattices having the linear phase property. The extended definitions of phase, group delay, and linear phase are first presented. This leads us to consider four types of filters as in the one-dimensional (1-D) case (symmetric or antisymmetric with odd or even support). The zeros in frequencies inherent to each type are presented. Hyper-octantal symmetry, in which all coefficients of a filter depend on those in one hyper-octant, is then introduced. We show conditions on lattices and filters for this kind of symmetry to be possible. We finally give equations relating dependent coefficients to independent ones.

Nonlinear filtering of magnetic resonance tomograms by geometry-driven diffusion

The paper deals with a nonuniform diffusion filtering of magnetic resonance (MR) tomograms. Alternative digital schemes for discrete implementation of the nonuniform diffusion equations are analyzed and tested. A novel locally adaptive conductance for the geometry-driven diffusion (GDD) filtering is proposed. It is based on a measure of the neighborhood unhomogeneity adopted from the optimal orientation detection of linear symmetry. The algorithm performance is evaluated on the basis of pseudoartificial 2D MR brain phantom and using the signal-to-noise ratio, as well as HC measure, developed for image discrimination characterization. Three filtering methods are applied to MR images acquired by the fast 3D FLASH sequence. The results obtained are quantitatively and visually compared and discussed.

Second Kerr effect virial coefficients of polar molecules with linear and lower symmetry

An overview is given of theoretical and experimental work undertaken on the second Kerr effect virial coefficient B K, and a new molecular tensor theory of B K for molecules of nonlinear symmetry is presented. The theory is general, and includes molecules of higher symmetry as special cases. Calculated values for the polar axially symmetric molecules fluoromethane and trifluoromethane reveal good agreement with experiment, although the large uncertainties of ±50% in the measured data do not provide a stringent test of the theory. Values of B K calculated for the nonlinear polar molecules sulphur dioxide, difluoromethane and dimethyl ether over a range of temperatures generally are within the uncertainty limits of the experimental values quoted in the literature.

Second Kerr effect virial coefficients of polar molecules with linear and lower symmetry

Second Kerr effect virial coefficients of polar molecules with linear and lower symmetry

Pattern Recognition in Images by Symmetries and Coordinate Transformations

A theory for detecting general curve families by means of symmetry measurements is presented. Symmetries are modeled by iso-gray curves of conjugate harmonic function pairs which define coordinate transformations. Harmonic function pair coordinates render the target curve patterns as parallel lines, which is defined here as linear symmetry. Detecting these lines, or generalized linear symmetry fitting, corresponds to finding invariants of Lie groups of transformations. A technique based on total least square error minimization for estimating the invariance parameters is presented. It uses the Lie infinitesimal operators to construct feature extraction methods that are efficient and simple to implement. The technique, which is shown to be an extension of the generalized Hough Transform, enables detection by voting and accumulating evidence for the searched pattern. In this approach complex valued votes are permitted, where the phase of the vote identifies the member of the family of patterns that are detectable. Experimental results illustrating the theory and its application to real as well as synthetic images are presented.

The effect of redox state on the folding free energy of azurin

The unfolding of oxidized and reduced azurin by guanidine hydrochloride has been monitored by circular dichroism. Dilution experiments showed the unfolding to be reversible, and the equilibrium data have been interpreted in terms of a two-state model. The protein is stabilized by the strong metal binding in the native state, so that the folding free energy is as high as –52.2 kJ mol–1 for the oxidized protein. The reduced protein is less stable, with a folding free energy of –40.0 kJ mol–1. A thermodynamic cycle shows, as a consequence, that unfolded azurin has a reduction potential 0.13 V above that of the folded protein. This is explained by the bipyramidal site in the native fold stabilizing Cu(II) by a rack mechanism, with the same geometry being maintained in the Cu(I) form. In the unfolded protein, on the other hand, the coordination geometries are expected to differ for the two oxidation states, Cu(I) being stabilized by the cysteine thiol group in a linear or trigonal symmetry, whereas Cu(II) prefers oxygen ligands in a tetragonal geometry.

Symmetry reduction of variational bicomplexes and the principle of symmetric criticality

Consider a system of differential equations Δ = 0 which is invariant under a Lie group G of point transformations acting on the space E of independent and dependent variables. By a method due to Lie, the G invariant solutions of these differential equations are found by solving a reduced system of differential equations [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] = 0 on the space [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] of invariants of G . In this paper we explore the relationship between the G invariant conservation laws and variational principles for the system of equations Δ = 0 and the conservation laws and variational principles for the reduced equations [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] = 0. This problem translates into one of constructing a certain cochain map [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /] between the G invariant variational bicomplex for the infinite jet space on E and the free variational bicomplex for [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="05i" /]. We prove that such a cochain map exists locally if and only if the relative Lie algebra cohomology condition H q (Γ, Γ 0 ( e 0 )) ≠ 0 is satisfied, where q is the orbit dimension of G , Γ the Lie algebra of vector fields on E which generate the infinitesimal action of G , and Γ 0 ( e 0 ) the linear isotropy subalgebra of Γ at e 0 . As a simple consequence we prove that the vanishing of H q (Γ, Γ 0 ( e 0 )) is the only local obstruction to Palais' principle of symmetric criticality.

Lie symmetries of quadratic two-dimensional difference equations

We find all systems of first-order quadratic autonomous two-dimensional difference equations which have two linear Lie symmetries. Knowledge of these symmetries permits the systems to be integrated by a reduction procedure.

An Introduction to The Lie-Santilli Isotopic Theory

Lie's theory in its current formulation is linear, local and canonical. As such, it is not applicable to a growing number of non-linear, non-local and non-canonical systems which have recently emerged in particle physics, superconductivity, astrophysics and other fields. In this paper, which is written by a physicist for mathematicians, we review and develop a generalization of Lie's theory proposed by the Italian–American physicist R. M. Santilli back in 1978 when at the Department of Mathematics of Harvard University and today called Lie–Santilli isotheory. The latter theory is based on the so-called isotopies which are non-linear, non-local and non-canonical maps of any given linear, local and canonical theory capable of reconstructing linearity, locality and canonicity in certain generalized spaces and fields. The emerging Lie–Santilli isotheory is remarkable because it preserves the abstract axioms of Lie's theory while being applicable to non-linear, non-local and non-canonical systems. After reviewing the foundations of the Lie–Santilli isoalgebras and isogroups, and introducing seemingly novel advances in their interconnections, we show that the Lie–Santilli isotheory provides the invariance of all infinitely possible (well-behaved), non-linear, non-local and non-canonical deformations of conventional Euclidean, Minkowskian or Riemannian invariants. We also show that the non-linear, non-local and non-canonical symmetry transformations of deformed invariants are easily computable from the linear, local and canonical symmetry transforms of the original invariants and the given deformation. We then briefly indicate a number of applications of the isotheory in various fields. Numerous rather fundamental and intriguing, open mathematical and physical problems are indicated during the course of our analysis.

Calculation of the third virial coefficient for water

Although the second virial coefficient has been used frequently to test intermolecular potentials, the direct calculation of third virial coefficients has only been attempted for atomic or simple (with linear symmetry) multipolar fluids. In this paper a general approach is described for the numerical evaluation of the third virial coefficient for molecular systems. Specific results for the second and third virial coefficients for several different water models are reported and compared with experimental data; critical points are also estimated. A polarizable model is found to be superior to standard effective liquid-phase potentials in reproducing the equation of state for steam.

On Face Numbers of Rational Simplicial Polytopes with Symmetry

Tight lower bounds are obtained for the h-vector-and, consequently, for all the face numbers-of a rational simplicial polytope which has a fixed-point-free linear symmetry of prime order. This extends a result of Richard Stanley for centrally symmetric polytopes.

Minimal sphere bundles in Euclidean spheres

The purpose of this paper is to pursue to work initiated by Hsiang-Lawson and study cohomogeneity 1 minimal hypersurfaces in Euclidean spheres which are equivariant under the linear isotropy representation of a rank 3 compact symmetric space.

Numerical simulation of kinetically controlled electrosorption processes under cyclic voltammetric conditions

The computations described in the paper are based on the Frumkin adsorption isotherm. Variation of the electrosorption valency with potential is taken into account. The rate-determining step can be either diffusion or interfacial kinetics. The kinetics of charge transfer associated with the formation of a chemical bond between an adsorbate and an electrode is described in terms of the Butler-Volmer equation. The effect of lateral interactions between adsorbed molecules and the activated complex is also considered. The presented dependences of the peak width and peak potential on the electrode coverage and the sweep rate allow the determination of various kinetic and thermodynamic parameters of the adsorption process. Computations were carried out for both linear and spherical symmetry of diffusion.

Momentum conserving symplectic integrators

In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL( n).

ON THE LANDAU–GINZBURG DESCRIPTION OF $(A_1^{(1)})^{\oplus N}$ INVARIANTS

We search for a Landau–Ginzburg interpretation of nondiagonal modular invariants of tensor products of minimal n = 2 superconformal models, looking in particular at automorphism invariants and at some exceptional cases. For the former we find a simple description as Landau–Ginzburg orbifolds, which reproduces the correct chiral rings as well as the spectra of various Gepner type models and orbifolds thereof. On the other hand, we are able to prove for one of the exceptional cases that this conformal field theory cannot be described by an orbifold of a Landau–Ginzburg model with respect to a manifest linear symmetry of its potential.

The stabilization of adsorbed carbon dioxide by formate on Cu(100)

The adsorption and desorption of CO 2 on copper has recently achieved much attention as it is expected to play an important role in the methanol synthesis and is known to take part in the water-gas-shift reaction as well as in the formate synthesis on copper. The CO 2 interaction with the clean surface is known to be quite weak, 25–30 kJ mol −1 and the CO 2 molecule is lying parallel to the surface. However, when formate is pre-adsorbed, the CO 2 is found to be stabilized by 14 ± 1 kJ mol −1 per monolayer formate. The bonding geometry is also heavily influenced by the formate as a new loss feature in the HREEL spectra suggests that the molecule is bent, breaking the linear symmetry.

Multipolar electrolyte solution models. II. Monte Carlo convergence and size dependence

Monte Carlo simulations of mixtures of charged and multipolar hard spheres with equivalent diameters are presented. A solution with dipolar solvent at a state point considered earlier, with greatly different results, by Chan et al. [Mol. Phys. 66, 299 (1989)] and by Caillol et al. [Mol. Phys. 69, 199 (1990)] is re-examined. Structural, thermodynamic, and dielectric properties are determined and particle number dependence in these averages is examined. The rate of convergence is shown to be satisfactory for correlation functions, other than that of repulsive ion pairs, and for thermodynamic properties. These are in good agreement with hypernetted chain theory. The reliability of the Metropolis Monte Carlo technique for the evaluation of thermodynamic properties in conveniently small systems of this solution model is established. We also consider a solution in which the solvent has both dipolar and linear quadrupolar symmetry. Two smaller systems give structural and thermodynamic properties in good agreement with hypernetted chain theory. In a larger system ionic clustering occurs to produce very different solution structure.

Nonlinear Lie symmetries in bifurcation theory

We examine the presence of general (nonlinear) time-independent Lie point symmetries in dynamical systems, and especially in bifurcation problems. A crucial result is that center manifolds are invariant under these symmetries: this fact, which may also be useful for explicitly finding the center manifold, implies that Lie point symmetries are inherited by the “reduced” bifurcation equation (a result which extends a known property of linear symmetries). An interesting situation occurs when a nonlinear symmetry of the original equation results in a linear one (e.g. a rotation — typically related to a Hopf bifurcation) of the reduced problem. We provide a class of explicit examples admitting nonlinear symmetries, which clearly illustrate all these points.