Braid rigidity for path algebras

Path algebras are a convenient way of describing decompositions of tensor powers of an object in a tensor category. If the category is braided, one obtains representations of the braid groups $B_n$ for all $n\in \N$. We say that such representations are rigid if they are determined by the path algebra and the representations of $B_2$. We show that besides the known classical cases also the braid representations for the path algebra for the 7-dimensional representation of $G_2$ satisfies the rigidity condition, provided $B_3$ generates \End(V^{\otimes 3}). We obtain a complete classification of ribbon tensor categories with the fusion rules of \g(G_2) if this condition is satisfied

The behavior of nanothermite reaction based on Bi2O3/Al

We studied the impact of aluminum particle size and the thickness of surrounding alumina layer on the dynamic pressure discharge of nanothermite reactions in the Bi2O3/Al system. A pressure discharge from 9 to 13 MPa was generated using as-synthesized Bi2O3 nano-particles produced by combustion synthesis and Al nanoparticles with size from 3 μm to 100 nm. The maximum reaction temperature was measured to be ∼2700 °C. The estimated activation energy of the reaction was 45 kJ/mol. A very large (several orders of magnitude) difference existed between the rate of the pressure pulse release by nanothermite reactions and by thermite reactions with large aluminum particles. The maximum observed pressurization rate was 3200 GPa/s. The time needed to reach the peak pressure was 0.01 ms and 100 ms for aluminum particles with diameter of 100 nm and 70 microns, respectively. The discharge pressure was a monotonic decreasing function of the thickness of the surrounding alumina layer

Elastic pppp and pˉp\bar pp scattering in the models of unitarized pomeron

Elastic scattering amplitudes dominated by the Pomeron singularity which obey the principal unitarity bounds at high energies are constructed and analyzed. Confronting the models of double and triple (at $t=0$) Pomeron pole (supplemented by some terms responsible for the low energy behaviour) with existing experimental data on $pp$ and $\bar pp$ total and differential cross sections at $\sqrt{s}\geq 5$ GeV and $|t|\leq 6$ GeV$^{2}$ we are able to tune the form of the Pomeron singularity. Actually the good agreement with those data is received for both models though the behaviour given by the dipole model is more preferable in some aspects. The predictions made for the LHC energy values display, however, the quite noticeable difference between the predictions of models at $t\approx -0.4$ GeV$^{2}$. Apparently the future results of TOTEM will be more conclusive to make a true choice.Comment: Revtex4, 8 pages, 5 figures. Text is improved, no changes in figures and conclusions. Version to be published in Phys. Rev.

The main features of phraseological units in the Russian and Armenian languages and their translation

The study deals with the structure of phraseological units of the Russian and Armenian languages. The researchers analyze figurative meaning of phraseological units appearing on the base of primary, nominative meaning of the words in one or another free phras

Study of dynamic features of highly energetic reactions by DSC and High-Speed Temperature Scanner (HSTS)

The dynamic features of Al2O3 - polytetrafluoroethylene (PTFE) and Al - PTFE reactions in non-isothermal conditions are presented. The Differential Scanning Calorimetry (DSC) and High-Speed Temperature Scanner (HSTS) were used to characterize the Al2O3/Al – PTFE reactions at different heating rates. The study shows that the HSTS instrument can give more information about the reaction mechanism and kinetics than the conventional DSC measurements. In this work we show that high heating rates may reveal exothermic reaction between Al2O3 and PTFE that were previously unidentified. The PTFE can potentially remove the oxide layer from aluminum in the initial period of the reaction and increase the direct contact area between oxygen and aluminum, which increases the reaction velocity and improves the energy release abilities of the system

The thickness of the ventricles and interventricular septum in males with overweight according to echocardiography

Introduction. Mortality from cardiovascular disease ranks first in the world. New and high requirements are required for the anatomical substantiation of emerging methods and methods of treatment. In modern literature, there are many publications on the issues of heart morphology, but data on the influence of gender, age, body weight on heart parameters are insufficient, fragmentary and often contradictory.Objective. To determine the thickness of the ventricles and interventricular septum in overweight men when performing echocardiography and to assess the presence or absence of the relationship of these parameters with age and body mass index (BMI) of the subjects. Patients and methods. The analysis of the protocols of ultrasound examination of the heart of 68 apparently healthy men of adolescence, the first and second periods of adulthood with a body mass index of 25.0–29.9 kg/m², with no pulmonary and cardiac pathology and the risk of cardiovascular diseases was carried out. Ultrasound examination was performed on an Aloka ProSound Alpha 6 ultrasound scanner. Results and discussion. When comparing the mean values of heart parameters in overweight men in three age groups according to the Kruskell – Wallis criterion, no statistically significant differences were found between the mean values (p > 0.05). Revealed a moderate strength relationship between the thickness of the anterior wall of the right ventricle with the age of the subject (r = 0.375; p = 0.020) and moderate strength relationship between the thickness of the posterior wall of the left ventricle and BMI (r = 0.352; p = 0.030).Conclusions. The  results of  the  study supplement the  information available in  the  scientific literature on the  thickness of  the  ventricles of  the  heart and the  interventricular septum in  healthy men with overweight in  three age groups. The data obtained will be useful to doctors of functional diagnostics when performing echocardiography in matters of differentiation between norm and pathology

Thickness of the ventricles and interventricular septum in men and women of the mesomorphic body type with normal body mass index according to echocardiography

The aim of the study was to establish the thickness of the ventricles and interventricular septum in individuals of the mesomorphic body type with a normal body mass index according to echocardiography and to assess the presence or absence of a relationship of these parameters with the gender and age of the subjects. Material and methods. The analysis of the protocols of ultrasound examination of the heart of 202 conditionally healthy persons of adolescence, the first and second periods of adulthood of the mesomorphic body type with a body mass index of 18.5–24.99 kg/m² was carried out. They have no pulmonary and cardiac pathology and risks of cardiovascular diseases. All subjects were divided into three age groups according to the age periodization of human ontogenesis (Moscow, 1965). Echocardiography was performed using a scanner Aloka ProSound Alpha 6. Results. The thicknesses of the anterior wall of the right ventricle, the posterior wall of the left ventricle, and the interventricular septum in women of the second period of adulthood is greater, than in young girl and women of the first period of adulthood (p ˂ 0.05); the thickness of the interventricular septum in men of the second period of adulthood is greater, than in young men and men of the first period of adulthood (p ˂ 0.05). It has been established that the thickness of the anterior wall of the right ventricle and interventricular septum depends on person gender: it is greater in men. In women, moderate correlation was found between the thickness of both the left ventricle (r = 0.425; p < 0.001) and the right (r = 0.411; p < 0.001) with age. A direct relationship (moderate strength) of the thickness of the interventricular septum with age (r = 0.331; p = 0.014) was found in men. Conclusion. The results of this morphological study supplement the information available in the scientific literature on the thickness of the ventricles of the heart and interventricular septum in a conditionally healthy person of the mesomorphic body type with a normal body mass index