In vivo Evaluation and in silico Prediction of the Toxicity of Drepanoalpha Hard capsules

This study was carried out in order to investigate the safety of Drepanoalpha hard hard capsules, a phytomedicine used for the management of sickle cell disease in the Democratic Republic of Congo by the acute and sub-acute administration in Guinea pigs. The hard capsules were dissolved in saline normal solution (NaCl 0.9 %). The animals were randomly selected, marked and divided into 2 groups of 5 animals each (3 males and 2 females) for acute toxicity and 4 groups of 3 animals each for sub-acute toxicity. Those received by gavage a single dose of 5000 mg/kg body weight (B.W.) of Drepanoalpha hard capsules for acute toxicity followed by 125 mg/Kg, 250 mg/Kg and 500 mg/Kg B.W. twice daily for 28 days for sub-acute toxicity and saline normal solution (NaCl 0.9 % solution as vehicle). Hematological, biochemical and histopathological analyses were performed and the behavior of the animals was observed after treatment. The results showed that 50 % of the lethal dose (LD50) is greater than 5000 mg/Kg B.W., and the relative weights of vital organs (kidney, liver, lungs, and heart) collected from Guinea pigs at the end of treatment on D14 (acute toxicity) and D28 (sub-acute toxicity) did not undergone significant changes (p>0.05). The results of haematological (Red Blood Cells, White Blood Cells, Haemoglobin, Haematocrit) and biochemical (ALT, AST, Albumin, Total Protein) tests did not show significant differences between the control and test groups at significance level (0.05 for acute toxicity), while the histopathological study revealed none damage to the various organs excised. In conclusion, the results confirm the safety of Drepanoalpha, as shown in previous studies with lyophilisate and decocate in rats and Guinea pigs. Keywords: Acute Toxicity, Sub-acute Toxicity, Hard Capsule, Drepanoalpha

Grad's Second Problem and Its Solution Within the Framework of Burnett Hydrodynamics

In his seminal work, Grad not only derived 13 moment equations but also suggested two problems to check his derived equations. These problems are highly instructive as they bring out the character of the equations by examining their solutions to these problems. In this work, we propose Grad's second problem as the potential benchmark problem for checking the accuracy of different sets of higher-order transport equations. The problem definition can be stated as: examination of steady-state solution for a gas at rest in infinite domain upon application of a one-dimensional heat flux. With gas at rest (no bulk velocity), the interest lies in obtaining the solution for pressure and temperature. The problem is particularly interesting with respect to the solution for pressure when Maxwell and hard-sphere molecules are considered. For Maxwell molecules, it is well known that the exact normal solution of Boltzmann equation gives uniform pressure with no stresses in the flow domain. In the case of hard-sphere molecules, direct simulation Monte Carlo (DSMC) results predict nonuniform pressure field giving rise to stresses in the flow domain. The simplistic nature of the problem and interesting results for pressure for different interaction potentials makes it an ideal test problem for examining the accuracy of higher-order transport equations. The proposed problem is solved within the framework of Burnett hydrodynamics for hard-sphere and Maxwell molecules. For hard-sphere molecules, it is observed that the Burnett order stresses do not become zero; they rather give rise to a pressure gradient in a direction opposite to that of temperature gradient, consistent with the DSMC results. For Maxwell molecules, the numerical solution of Burnett equations predicts uniform pressure field and one-dimensional temperature field, consistent with the exact normal solution of the Boltzmann equation.

Simulation of Quasistationary Electromagnetic Fields in Regions Containing Disconnected Conducting Subregions

Methods for a numerical solution of Maxwell's equations in the quasistationary aproximation in a region with multiply connected conducting subregions were discussed. The case of nontrivial operator kernel was explored. The methods for finding the solution of the linear algebraic equations system were analyzed. The method of introducing a "fictional armature" was offered as alternative method for searching [retrieving] a normal solution of linear algebraic equations. Results of computational experiments were presented. The study was carried out on the example of calculation for electrodynamic acceleration process in the railgun channel

Divorce as the Crisis in the Family and the Impact on Children’s Behaviour

Divorces are becoming available and completely normal solution of a crisis in the family. Although all participants suffer from the divorce, the most affected becomes the child and his future life, no matter a, what age he has to go through this perio. In the study we reflect on marriage and the family, currently going through a crisis. We analyse the divorce as one of the traumatic moments in people's lives and its impact on the child from different points of view. Divorce, however, represents in many cases a redemption from traumatic life situation, therefore the contribution remains open to further professional discussion.

NORMAL BGG SOLUTIONS AND POLYNOMIALS

First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries and many other widely studied PDE of geometric origin. The machinery of BGG sequences also singles out a subclass of solutions called normal solutions. These correspond to parallel tractor fields and hence to (certain) holonomy reductions of the canonical normal Cartan connection. Using the normal Cartan connection, we define a special class of local frames for any natural vector bundle associated to a parabolic geometry. We then prove that the coefficient functions of any normal solution of a first BGG operator with respect to such a frame are polynomials in the normal coordinates of the parabolic geometry. A bound on the degree of these polynomials in terms of representation theory data is derived. For geometries locally isomorphic to the homogeneous model of the geometry we explicitly compute the local frames mentioned above. Together with the fact that on such structures all solutions are normal, we obtain a complete description of all first BGG solutions in this case. Finally, we prove that in the general case the polynomial system coming from a normal solution is the pull-back of a polynomial system that solves the corresponding problem on the homogeneous model. Thus we can derive a complete list of potential normal solutions on curved geometries. Moreover, questions concerning the zero locus of solutions, as well as related finer geometric and smooth data, are reduced to a study of polynomial systems and real algebraic sets.