Affine Wa(A4), Quaternions, and Decagonal Quasicrystals

We introduce a technique of projection onto the Coxeter plane of an arbitrary higher dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined by the simple roots of the Coxeter graph I2 (h) where h is the Coxeter number of the Coxeter group W(G) which embeds the dihedral group Dh of order 2h as a maximal subgroup. As a simple application we demonstrate projections of the root and weight lattices of A4 onto the Coxeter plane using the strip (canonical) projection method. We show that the crystal spaces of the affine Wa(A4) can be decomposed into two orthogonal spaces whose point groups is the dihedral group D5 which acts in both spaces faithfully. The strip projections of the root and weight lattices can be taken as models for the decagonal quasicrystals. The paper also revises the quaternionic descriptions of the root and weight lattices, described by the affine Coxeter group Wa(A3), which correspond to the face centered cubic (fcc) lattice and body centered cubic (bcc) lattice respectively. Extensions of these lattices to higher dimensions lead to the root and weight lattices of the group Wa(An), n>=4 . We also note that the projection of the Voronoi cell of the root lattice of Wa(A4) describes a framework of nested decagram growing with the power of the golden ratio recently discovered in the Islamic arts.Comment: 26 pages, 17 figure

Assessment of the Extracts of Centaurea tchihatcheffii Fischer for Anti-inflammatory and Analgesic Activities in Animal Models

Purpose: To evaluate the ethanol extracts of the flowers, leaves, and stems of Centaurea tchihatcheffii Fischer & C.A. Meyer (Asteraceae) for their anti-inflammatory and analgesic activities in male Swissalbino mice.Methods: For the evaluation of anti-inflammatory activity, hind paw oedema was induced in the mice with carrageenan and prostaglandin-E2 (PGE2 ) and the mice received either 100 and 200 mg/kg bodyweight doses of the flower extract or 200 mg/kg body weight dose of the leaf and stem extracts. Furthermore, ear oedema was induced in other groups of mice with 12-O-tetradecanoyl-13-acetate (TPA) and then administered with 0.5 mg/ear dose of the extract of either of the three plant parts. In order to evaluate analgesic activity, p-benzoquinone-induced abdominal constriction test was used with 100, 200 and 400 mg/kg body weight doses of the flower or 200mg/kg body weight dose of the leaf and stem extracts administered. Indomethacin and acetylsalicylic acid were the reference drugs for antiinflamatory and analgesic evaluations, respectively. Phytochemical screening of the flower extract wascarried out by thin layer chromatography (TLC).Results: The results of evaluation of the anti-inflammatory activities induced by carrageenan and PGE2 showed that the flower extract diminished cyclo-oxygenase activitiy at the 200 mg/kg dose to the samelevel as the reference drug, indomethacin. However, no anti-inflamatory activity was seen in the TPAinduced ear oedema model. The extracts from all three parts of the plant showed analgesia in pbenzoquinone-induced abdominal constriction test. TLC analysis of the flower extract indicated the presence of sesquiterpen lactones, which may have been responsible for the analgesic activity.Conclusion: Our results support the use of C. tchihatcheffii in traditional medicine in Turkey for their anti-inflammatory and analgesic properties

Evaluation of the relationship between the maxillary third molars and pterygomaxillary fissure by cephalometric radiographs

Background: The aim of this study is to evaluate the relationship between the third molars which are determined to be closely related to pterygomaxillary fissure (PTM) in cephalometric radiographs. Materials and methods: The material of this study was panoramic from 200 individuals (101 male, 99 female, mean age 19.02 ± 1.62) with three different skeletal malocclusion in the sagittal direction (class I: 109; class II: 66; class III: 25) and lateral cephalometric radiographs. It was observed that 151 of the patients included in this study had unilateral, 49 bilateral impacted maxillary third molars teeth. Angular and millimetric measurements (SNA°, SNB°, ANB°, PTM [Height-x], PTM [Width-y]) were made in accordance with the parameters determined on the lateral cephalometric radiographs of individuals. In this retrospective study, the relation of impaction with PTM evaluated on cephalometric radiographs, whether the impaction was unilateral or bilateral, was investigated in terms of skeletal anomaly. Chi-square test was used for the analysis. Results: Of the 200 individuals with impacted maxillary third molar, 99 were female and 101 were male. There is no statistical difference between them in terms of unilateral and bilateral impacted third molars (p > 0.05). Of the 200 patients, 109 patients were class I, 66 patients were class II, and 25 patients were class III. There is no statistical difference between unilateral and bilateral impacted cases in facial skeletal classification (p > 0.05). According to chi-square test results, the relationship between genders and PTM variable width and height (PTM-x and PTM-y) measurements were not statistically significant (p > 0.05). Conclusions: The fact that the third molar teeth are impacted bilaterally or unilaterally is not affected by PTM change

Family Unification in Five and Six Dimensions

In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the Standard Model gauge symmetries and a gauged family symmetry. Large orthogonal groups, and the exceptional groups $E_7$ and $E_8$ have been much studied for family unification. The main theoretical difficulty of family unification is the existence of mirror families at the weak scale. It is shown here that family unification without mirror families can be realized in simple five-dimensional and six-dimensional orbifold models similar to those recently proposed for SU(5) and SO(10) grand unification. It is noted that a family unification group that survived to near the weak scale and whose coupling extrapolated to high scales unified with those of the Standard model would be evidence accessible in principle at low energy of the existence of small (Planckian or GUT-scale) extra dimensions.Comment: 13 pages, 2 figures, minor corrections, references adde

Non-crystallographic reduction of generalized Calogero-Moser models

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero–Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic types, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models, how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group

Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Matrix metalloproteinase-9 in broncho-alveolar lavage fluid of patients with non-small cell lung cancer

Aim: To evaluate concentration of MMP-9 in blood plasma and broncho-alveolar lavage fluid (BALF) from patients with non-small cell lung cancer (NSCLC). Methods: Blood рlasma from 40 NSCLC patients and 40 healthy donors was collected and concentrations of blood plasma and BALF MMP-9 were measured using ELISA. Correlation between MMP-9 level and gender, histological type of tumor and stage of disease was analyzed. Results: Levels of blood plasma MMP-9 were significantly higher in NSCLC patients (p < 0.0001) then in control group, and were especially high in patients with stage IV of disease (stage I vs stage IV — p < 0.005, stage II vs stage IV — p < 0.01, stage III vs stage IV — p < 0.01). Also, stage IV of NSCLC was characterized by the highest level of BALF MMP-9 (stage I vs stage IV — p < 0.002, stage II vs stage IV p < 0.002, and stage III vs stage IV p < 0.007). Correlation between blood plasma and BALF MMP-9 levels and gender or histological type of tumor was insignificant. Conclusion: Our data revealed significant correlation between tumor stage and BALF and plasma MMP-9 levels in NSCLC patients.Цель: определить концентрацию матриксной металлопротеиназы 9 (ММП-9) в плазме крови и бронхо-альвеолярной жидкости (БАЖ) больных немелкоклеточным раком легкого (НМКРЛ). Методы: концентрацию ММП-9 в плазме крови и БАЖ больных НМКРЛ (n = 40) и здоровых доноров (n = 40) определяли иммуноферментным методом и анализировали корреляцию этих параметров с клиническими данными (полом больного, гистологическим типом опухоли, стадией заболевания). Результаты: содержание ММП-9 в плазме крови было значительно выше у больных НМКРЛ по сравнению с контрольной группой (p < 0,0001), особенно у больных с IV стадией заболевания. Стадия IV НМКРЛ также характеризовалась наиболее высоким уровнем ММП-9 в БАЖ. Корреляции между уровнем ММП-9 в плазме крови и БАЖ, полом больного и гистологическим типом опухоли не была выявлена. Выводы: существует статистически значимая корреляция между стадией развития НМКРЛ и содержанием ММП-9 в плазме крови и БАЖ больных

Procedural feature generation for volumetric terrains using voxel grammars

© 2018 Terrain generation is a fundamental requirement of many computer graphics simulations, including computer games, flight simulators and environments in feature films. There has been a considerable amount of research in this domain, which ranges between fully automated and semi-automated methods. Voxel representations of 3D terrains can create rich features that are not found in other forms of terrain generation techniques, such as caves and overhangs. In this article, we introduce a semi-automated method of generating features for volumetric terrains using a rule-based procedural generation system. Features are generated by selecting subsets of a voxel grid as input symbols to a grammar, composed of user-created operators. This results in overhangs and caves generated from a set of simple rules. The feature generation runs on the CPU and the GPU is utilised to extract a robust mesh from the volumetric dataset

Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory

We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions and we determine all four-dimensional gauge theories resulting from the generalized dimensional reduction a la Forgacs-Manton over coset spaces, followed by a subsequent application of the Wilson flux spontaneous symmetry breaking mechanism. Our investigation is constrained only by the requirements that (i) the dimensional reduction leads to the potentially phenomenologically interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and (ii) the Wilson flux mechanism makes use only of the freely acting discrete symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty, ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C

Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach

Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.Comment: 21 page