Quaterionic Construction of the W(F_4) Polytopes with Their Dual Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)

4-dimensional $F_{4}$ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary \textbf{$W(F_{4})$} orbit under the Coxeter groups $W(B_{4}$ and $W(B_{3}) \times W(A_{1})$ have been presented. The role of group theoretical technique and the use of quaternions have been emphasizedComment: 26 pages, 10 figure

Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

Comparison of three-dimensional facial morphology between upright and supine positions employing three-dimensional scanner from live subjects

Facial soft tissue thicknesses (FSTT) measurements collected from Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) imaging techniques are most commonly taken in the supine position for forensic craniofacial reconstruction. FSTT have been shown to be different in comparison to the upright position due to gravity. The variation of facial morphology between the upright and supine position of laser-scanned images taken from 44 individuals was investigated using volumetric analysis with deviation maps. Between 82.4% and 86.7% of the facial surface area were within the error range of ±2 mm between the supine and the upright position. This indicates that most anatomical landmarks taken from the MRI and CT data can be an accurate representative of the FSTT in the upright position. Seven landmarks located around the buccal region, masseteric region and the nasolabial region of the face showed the greatest FSTT deviation between the upright and supine position, thus these landmarks may affect the accuracy of facial reconstructions when using a CT or MRI database

Blood Cell Morphology and Plasma Biochemistry of Captive Mauremys caspica (Gmelin, 1774) and Mauremys rivulata (Valenciennes, 1833)

Morphological characteristics of peripheral blood cells, micronucleated erythrocyte counts and plasma biochemistry profile were examined in fourteen healthy captive Mauremys caspica and in twenty-three Mauremys rivulata. The size of erythrocyte cells were 19.07 × 11.68 μm and 19.76 × 11.44 μm for M. caspica and M. rivulata, respectively. Nucleus sizes were 6.50 × 5.30 μm for M. caspica and 6.79 × 5.45 μm for M. rivulata. The micronucleated erythrocyte (MNE) values were 0.0008 and 0.0037 for the males and females of M. caspica, respectively. The MNE values were 0.0002 for male and female M. rivulata. We found sex-dependent differences only in the Ca value in the blood biochemistry profile for healthy M. caspica. Sex-dependent differences were found only in albumin and P values in the blood biochemistry profile for healthy M. rivulata. No significant differences were found between males of both species in question with respect to plasma biochemistry values. However, only plasma total protein and Ca content levels differed significantly between the females of the two species

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

Analysis of thermal mixing in circle shaped body inserted inclined channel

In this study, thermal mixing (TM) phenomena in a rectangle channel with adiabatic circle shaped body are investigated experimentally. Two parallel jets in different temperatures are located in the channel which has a circular exit hole to supply continuity of mass. Experiments are carried out for different inclination angle of the channel. Also, effects of ratio of flow rate, jets diameters, and temperature difference between hot and cold jets were analyzed. A circle shaped passive element with low thermal conductivity is located into channel to control thermal mixing. Thermal mixing index is calculated from measured temperatures. Experimental results showed that thermal mixing of fluid is effected from geometric parameters, drastically. It is found that TM is function of the temperature difference of inlet jets

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

Blood Cell Morphology and Plasma Biochemistry of the Captive European Pond Turtle Emys orbicularis

The morphological characteristics of peripheral blood cells, micronucleated erythrocytes counts and plasma biochemistry profile were examined in ten healthy captive European pond turtles Emys orbicularis. Blood samples were obtained from the caudal vein. The Wright staining method was used for the classification of the blood cells. Mature erythrocytes of captive Emys orbicularis were nucleated ellipsoidal cells (21.7 ±1.27μm × 13.2 ±1.12 μm) with pink cytoplasm. The nucleus (6.9 ± 0.78 μm × 5.4 ± 0.65 μm) was centrally located and stained dark purple. Seven different types of blood cells were determined: erythrocytes, thrombocytes, monocytes, eosinophils, basophils, lymphocytes and heterophils. The micronucleated erythrocyte (MNE) values were 0.0016 and 0.003 for the males and females, respectively. The MNE results were presented as the mean frequency of micronucleated erythrocytes per 1000 cells per animal. The mean plasma concentrations in the total of specimens were as follows: total protein (25 g/L), albumin (7.2 g/L), globulin (17.8 g/L), glucose (2.91 mmol/L), calcium (2.32 mmol/L), phosphorus (1.55 mmol/L), creatinine (46.85 μmol/L), urea (10.93 mmol/L) , triglycerides (0.44 mmol/L), cholesterol (1.48 mmol/L), sodium (125.76 mmol/L), potassium (3.98 mmol/L), chloride (93.94 mmol/L), iron (13.34 μmol/L) and activities of aspartate aminotransferase (2.14 μkat/L), alanine aminotransferase (0.15 μkat/L), gamma glutamyl transpeptidase (2.15 U/L), amylase (8.09 μkat/L), lactate dehydrogenase (19.93 μkat/L). We found sex-dependent differences only in ALT [(0.21 μkat/L and 0.10 μkat/L for the males and females, respectively) (t = 3,107; df = 14; p Emys orbicularis. We suggest that the biochemical profile described in the present study may be used as a standard profile for healthy Emys orbicularis kept in captivity

Significance of Persistent Cytogenetic Abnormalities on Myeloablative Allogeneic Stem Cell Transplantation in First Complete Remission

AbstractRisk stratification is important to identify patients with acute myelogenous leukemia (AML) who might benefit from allogeneic hematopoietic stem cell transplantation (allo-HSCT) in first complete remission. We retrospectively studied 150 patients with AML and diagnostic cytogenetic abnormalities who underwent myeloablative allo-HSCT while in first complete remission to evaluate the prognostic impact of persistent cytogenetic abnormalities at allo-HSCT. Three risk groups were identified. Patients with favorable/intermediate cytogenetics at diagnosis (n = 49) and patients with unfavorable cytogenetics at diagnosis but without a persistent abnormal clone at allo-HSCT (n = 83) had a similar 3-year leukemia-free survival of 58%-60% despite the higher 3-year relapse incidence (RI) in the latter group (32.3%, versus 16.8% in the former group). A third group of patients with unfavorable cytogenetics at diagnosis and a persistent abnormal clone at allo-HSCT (n = 15) had the worst prognosis, with a 3-year RI of 57.5% and 3-year leukemia-free survival of only 29.2%. These data suggest that patients with AML and unfavorable cytogenetics at diagnosis and a persistent abnormal clone at allo-HSCT are at high risk for relapse after allo-HSCT. These patients should be considered for clinical trials designed to optimize conditioning regimens and/or to use preemptive strategies in the posttransplantion setting aimed at decreasing RI

Buried palaeosols of NW Sardinia (Italy) as archives of the Late Quaternary climatic fluctuations

A multi-disciplinary approach was performed to investigate two compound geosols included between wind-blown deposits at the top, and interglacial (MIS 5) beach sediments at the bottom, located along the Alghero coast (North-western Sardinia, Italy). A sedimentological and morphological study was carried out on the profile in the field, and samples collected on the main pedomembers were subjected to several laboratory analyses, consisting of physical and chemical determinations on bulk samples, mineralogy (XRD), micromorphology on undisturbed samples (thin Section, SEM), and EDAX-micro probe analyses. Dating was performed by means of Optically Stimulated Luminescence (OSL). The studied geosols show the evidence of a complex pedosedimentary evolution. Around 80 to 70. ka the lower geosol underwent weathering and clay illuviation (wet and warm conditions), followed by calcification-recalcification processes (dry-contrasted), and finally by strong bioturbation. Around 70. ka the onset of the glacial period (MIS 4) is marked by the deposition of a sand dune, capping the lower geosol. These results indicate that the coastal area of the central Mediterranean kept the relatively warm conditions typical of the interglacial climate for most of the Early Würm and reached cold conditions only at about 70. ka, possibly in relation to the rapid cooling of the Heinrich event H7. The upper geosol developed on colluvial material including abundant pedorelicts and reddish earth material, deposited around 50. ka. Before being buried by aeolian sand around 43. ka, this deposit underwent pedogenesis phases possibly associated to Middle Würm interstadial events, indicating that in the study area these events were intense enough to influence pedogenesis. © 2014 Elsevier B.V