Sphenoid sinus symmetry and differences between sexes

Objectives: To evaluate the anatomic variations of neurovascular structures adjacent to the sphenoid sinus and their agreement between right and left sides as well as differences between sexes. Methods: Forty-five cadavers were dissected (24 men, and differences between sexes and agreement of anatomic variations of the sphenoid sinus between sides were analyzed. Results: The mean distance from the sphenoid sinus ostium to the anterior nasal spine was greater in males than in females by an average of 3.0 mm (p = 0.001) while the mean difference of distances between the right and left side was -1.1 +/- 3.1 mm. Female cadavers had a greater frequency of optic-carotid recess (p = 0.04) and dehiscence over the maxillary nerve (p = 0.02), as well as greater relative risk of optic nerve protrusion (p < 0.001), and dehiscence over the internal carotid artery (ICA) (p = 0.002). In male cadavers the intersinus septum was inserted on the course of the ICA 3.5 times more often than in female (p = 0.02). Agreement of anatomic variations between sides ranged from moderate to almost perfect depending on the structures evaluated. Conclusions: There are anatomic differences of the sphenoid sinus between sexes and between right and left sides, and these differences should be taken into consideration during surgery.

A morphometric study on the longitudinal and lateral symmetry of the sural nerve in mature and aging female rats

Aging affects peripheral nerve function and regeneration in experimental models but few literature reports deal with animals aged more than one year. We investigated morphological and morphometric aspects of the sural nerve in aging rats. Female Wistar rats 360, 640 and 720 days old were killed, proximal and distal segments of the right and left sural nerves were prepared for light microscopy and computerized morphometry. No morphometric differences between proximal and distal segments or between right and left sides at the same levels were found in all experimental groups. No increase in fiber and axon sizes was observed from 360 to 720 days. Likewise, no difference in total myelinated fiber number was observed between groups. Myelinated fiber population distribution was bimodal, being the 720-days old animals` distribution shifted to the left, indicating a reduction of the fiber diameters. The 9 ratio distribution of the 720-days old animals` myelinated fiber was also shifted to the left, which suggests axonal atrophy. Morphological alterations due to aging were observed, mainly related to the myelin sheath, which suggests demyelination. Large fibers were more affected than the smaller ones. Axon abnormalities were not as common or as obvious as the myelin changes and Wallerian degeneration was rarely found. These alterations were observed in all experimental groups but were much less pronounced in rats 360 days old and their severity increased with aging. in conclusion, the present study indicates that the aging neuropathy present in the sural nerve of female rats is both axonal and demyelinating. (C) 2008 Elsevier B.V. All rights reserved.

Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

MapScript: A map algebra programming language incorporating neighborhood analysis

Map algebra is a data model and simple functional notation to study the distribution and patterns of spatial phenomena. It uses a uniform representation of space as discrete grids, which are organized into layers. This paper discusses extensions to map algebra to handle neighborhood operations with a new data type called a template. Templates provide general windowing operations on grids to enable spatial models for cellular automata, mathematical morphology, and local spatial statistics. A programming language for map algebra that incorporates templates and special processing constructs is described. The programming language is called MapScript. Example program scripts are presented to perform diverse and interesting neighborhood analysis for descriptive, model-based and processed-based analysis.

A(2)((2)) parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A(2)((2))/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)((2)) parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two. (C) 2002 Published by Elsevier Science B.V.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Integrable variant of the one-dimensional Hubbard model

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the eta-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. (C) 2002 American Institute of Physics.

CP properties of symmetry-constrained two-Higgs-doublet models

The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.

Constraints on leptogenesis from a symmetry viewpoint

It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.

Patterns, mathematics and culture : the search for symmetry in Azorean sidewalks and traditional crafts

In the hustle and bustle of daily life, how often do we stop to pay attention to the tiny details around us, some of them right beneath our feet? Such is the case of interesting decorative patterns that can be found in squares and sidewalks beautified by the traditional Portuguese pavement. Its most common colors are the black and the white of the basalt and the limestone used; the result is a large variety and richness in patterns. No doubt, it is worth devoting some of our time enjoying the lovely Portuguese pavement, a true worldwide attraction. The interesting patterns found on the Azorean handicrafts are as fascinating and substantial from the cultural point of view. Patterns existing in the sidewalks and crafts can be studied from the mathematical point of view, thus allowing a thorough and rigorous cataloguing of such heritage. The mathematical classification is based on the concept of symmetry, a unifying principle of geometry. Symmetry is a unique tool for helping us relate things that at first glance may appear to have no common ground at all. By interlacing different fields of endeavor, the mathematical approach to sidewalks and crafts is particularly interesting, and an excellent source of inspiration for the development of highly motivated recreational activities. This text is an invitation to visit the nine islands of the Azores and to identify a wide range of patterns, namely rosettes and friezes, by getting to know different arts and crafts and sidewalks.

Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.