Isomerism as Manifestation of Intrinsic Symmetry of Molecules: Lunn–Senior’s Theory

This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 15 December, 2008.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

Effects of the condylar process fracture on facial symmetry in rats submitted to protein undernutrition

PURPOSE: To investigate the facial symmetry of rats submitted to experimental mandibular condyle fracture and with protein undernutrition (8% of protein) by means of cephalometric measurements. METHODS: Forty-five adult Wistar rats were distributed in three groups: fracture group, submitted to condylar fracture with no changes in diet; undernourished fracture group, submitted to hypoproteic diet and condylar fracture; undernourished group, kept until the end of experiment, without condylar fracture. Displaced fractures of the right condyle were induced under general anesthesia. The specimens were submitted to axial radiographic incidence, and cephalometric mensurations were made using a computer system. The values obtained were subjected to statistical analyses among the groups and between the sides in each group. RESULTS: There was significative decrease of the values of serum proteins and albumin in the undernourished fracture group. There was deviation of the median line of the mandible relative to the median line of the maxilla, significative to undernutrition fracture group, as well as asymmetry of the maxilla and mandible, in special in the final period of experiment. CONCLUSION: The mandibular condyle fracture in rats with proteic undernutrition induced an asymmetry of the mandible, also leading to consequences in the maxilla.

Spontaneous symmetry breaking in amnestically induced persistence

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

Precise measurements of direct CP violation, CPT symmetry, and other parameters in the neutral kaon system

We present precise tests of CP and CPT symmetry based on the full data set of K -> pi pi decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This data set contains 16 x 10(6) K -> pi(0)pi(0) and 69 x 10(6) K -> pi(+)pi(-) decays. We measure the direct CP violation parameter Re(epsilon'/epsilon) = (19.2 +/- 2.1) x 10(-4). We find the K(L) -> K(S) mass difference Delta m = (5270 +/- 12) x 10(6) (h) over tilde s(-1) and the K(S) lifetime tau(S) = (89.62 +/- 0.05) x 10(-12) s. We also measure several parameters that test CPT invariance. We find the difference between the phase of the indirect CP violation parameter epsilon and the superweak phase: phi(epsilon) - phi(SW) =(0.40 +/- 0.56)degrees. We measure the difference of the relative phases between the CP violating and CP conserving decay amplitudes for K -> pi(+)pi(-) (phi(+-)) and for K -> pi(0)pi(0) (phi(00)): Delta phi = (0.30 +/- 0.35)degrees. From these phase measurements, we place a limit on the mass difference between K(0) and (K) over bar (0): Delta M < 4.8 x 10(-19) GeV/c(2) at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and CPT symmetry.

Dynamical Lorentz symmetry breaking in 3D and charge fractionalization

We analyze the breaking of Lorentz invariance in a 3D model of fermion fields self-coupled through four-fermion interactions. The low-energy limit of the theory contains various submodels which are similar to those used in the study of graphene or in the description of irrational charge fractionalization.

Dynamical Lorentz and CPT symmetry breaking in a 4D four-fermion model

In a 4D chiral Thirring model we analyze the possibility that radiative corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By studying the effective potential, we verified that the chiral current (psi) over bar gamma(mu)gamma(5)psi may assume a nonzero vacuum expectation value which triggers Lorentz and CPT violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee-like model containing a Chem-Simons term.

EPR study of local symmetry sites of Ce(3+) in Pb(1-x)Ce(x)A (A=S, Se, and Te)

The local site symmetry of Ce(3+) ions in the diluted magnetic semiconductors Pb(1-x)Ce(x)A (A=S, Se, and Te) has been investigated by electron-paramagnetic resonance (EPR). The experiments were carried out on single crystals with cerium concentration x ranging from 0.001 to 0.035. The isotropic line due to Ce(3+) ions located at the substitutional Pb cation site with octahedral symmetry was observed for all the studied samples. We determined the effective Lande factors to be g=1.333, 1.364, and 1.402 for A=S, Se, and Te, respectively. The small difference with the predicted Lande factor g of 10/7 for the Gamma(7) (J=5/2) ground state was attributed to crystal-field admixture. In addition, EPR lines from Ce(3+) ions located at sites with small distortion from the original octahedral symmetry were also observed. Two distinct sites with axial distortion along the < 001 > crystallographic direction were identified and a third signal in the spectrum was attributed to sites with the cubic symmetry distorted along the < 110 > direction. The distortion at these distinct Ce sites is attributed to Pb lattice vacancies near the cerium ions that compensate for its donor activity.

f t value of the 0(+)-> 0(+) beta(+) decay of (32)Ar: A measurement of isospin symmetry breaking in a superallowed decay

We determined the absolute branch of the T=2 superallowed decay of (32)Ar by detecting the beta(+)-delayed protons and gamma decays of the daughter state. We obtain b(SA)(beta)=(22.71 +/- 0.16)%, which represents the first determination of a proton branch to better than 1%. Using this branch along with the previously determined (32)Ar half-life and energy release, we determined ft=(1552 +/- 12) s for the superallowed decay. This ft value, together with the corrected Ft value extracted from previously known T=1 superallowed decays, yields a measurement of the isospin symmetry breaking correction in (32)Ar decay delta(exp)(C)=(2.1 +/- 0.8)%. This can be compared to a theoretical calculation delta(C)=(2.0 +/- 0.4)%. As by-products of this work, we determined the gamma and proton branches for the decay of the lowest T=2 state of (32)Cl, made a precise determination of the total proton branch and relative intensities of proton groups that leave (31)S in its first excited state and deduced an improved value for the (32)Cl mass.

Dynamical breaking of gauge symmetry in supersymmetric quantum electrodynamics in three-dimensional spacetime

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term A(alpha)A(alpha) through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

Increasing the symmetry of drug crystals: a monoclinic conformational polymorph of the platelet antiaggregating agent ticlopidine hydrochloride

Ticlopidine hydrochloride (TICLID (R)) is a platelet antiaggregating agent whose use as a potent antithrombotic pharmaceutical ingredient is widespread, even though this drug has not been well characterized in the solid state. Only the crystal phase used for drug product manufacturing is known. Here, a new polymorph of ticlopidine hydrochloride was discovered and its structure was determined. While the antecedent polymorph crystallizes in the triclinic space group P (1) over bar, the new crystal phase was solved in the monoclinic space group P2(1)/c. Both polymorphs crystallize as racemic mixtures of enantiomeric (ticlopidine)(+) cations. Detailed geometrical and packing comparisons between the crystal structures of the two polymorphs have allowed us to understand how different supramolecular architectures are assembled. It was feasible to conclude that the main difference between the two polymorphs is a rotation of about 120 degrees on the bridging bond between the thienopyridine and o-chlorobenzyl moieties. The differential o-chlorobenzyl conformation is related to changeable patterns of weak intermolecular contacts involving this moiety, such as edge-to-face Cl center dot center dot center dot pi and C-H center dot center dot center dot pi interactions in the new polymorph and face-to-face pi center dot center dot center dot pi contacts in the triclinic crystal phase, leading to a symmetry increase in the ticlopidine hydrochloride solid state form described for the first time in this study. Other conformational features are slightly different between the two polymorphs, such as the thienopyridine puckerings and the o-chlorophenyl orientations. These conformational characteristics were also correlated to the crystal packing patterns.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.