Boundary integration of polynomials over an arbitrary linear tetrahedron in Euclidean three-dimensional space

This paper is concerned with explicit integration formulas and algorithms for computing integrals of trivariate polynomials over an arbitrary linear tetrahedron in Euclidean three-dimensional space. This basic three-dimensional integral governing the problem is transformed to surface integrals by use of the divergence theorem. The resulting two-dimensional integrals are then transformed into convenient and computationally efficient line integrals. These algorithms and explicit finite integration formulas are followed by an application - example for which we have explained the detailed computational scheme. The numerical result thus found is in complete agreement with previous works. Further, it is shown that the present algorithms are much simpler and more economical as well, in terms of arithmetic operations. The symbolic finite integration formulas presented in this paper may lead to an easy incorporation of geometric properties of solid objects, for example, the centre of mass, moment of inertia, etc. required in the engineering design process as well as several applications of numerical analysis where integration is required, for example in the finite element and boundary integral equation methods

Boundary integration of polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space

This paper is concerned with explicit integration formulas and algorithms for computing volume integrals of trivariate polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space. Three different approaches are discussed. The first algorithm is obtained by transforming a volume integral into a sum of surface integrals and then into convenient and computationally efficient line integrals. The second algorithm is obtained by transforming a volume integral into a sum of surface integrals over the boundary quadrilaterals. The third algorithm is obtained by transforming a volume integral into a sum of surface integrals over the triangulation of boundary. These algorithms and finite integration formulas are then followed by an application example, for which we have explained the detailed computational scheme. The symbolic finite integration formulas presented in this paper may lead to efficient and easy incorporation of integral properties of arbitrary linear polyhedra required in the engineering design process. © 1998 Elsevier Science S.A. All rights reserved

Symbolic integration of polynomial functions over a linear polyhedron in euclidean three-dimensional space

The paper concerns analytical integration of polynomial functions over linear polyhedra in three-dimensional space. To the authors' knowledge this is a first presentation of the analytical integration of monomials over a tetrahedral solid in 3D space. A linear polyhedron can be obtained by decomposing it into a set of solid tetrahedrons, but the division of a linear polyhedral solid in 3D space into tetrahedra sometimes presents difficulties of visualization and could easily lead to errors in nodal numbering, etc We have taken this into account and also the linearity property of integration to derive a symbolic integration formula for linear hexahedra in 3D space. We have also used yet another fact that a hexahedron could be built up in two, and only two, distinct ways from five tetrahedral shaped elements These symbolic integration formulas are then followed by an illustrative numerical example for a rectangular prism element, which clearly verifies the formulas derived for the tetrahedron and hexahedron elements

CLINICAL STUDY TO COMPARE THE EFFICACY OF NASYA KARMA WITH SHIGRU TAILA AND VIDANGADYA TAILA IN VATAJA PRATISHYAYA (ALLERGIC RHINITIS)

Background: Vataja pratishyaya is one among the Pratishyaya rogas in which there is vitiation of Vata & Kapha doshas. Currently the conventional medicine has no effective treatment for Allergic Rhinitis. In view of the facts, particularly considering the side effects in the existing methods of treatment, there is the need to develop a treatment protocol. According to Acharya Sharangadhara vairechanik Nasya is the line of treatment. Therefore Nasya has been selected as treatment modality for the present study. “Nasa hi siraso dwaram tena taddapya hanthi tana”. Nose is the gate way of head hence it acts as inlet for the Nasya Karma. It destroys the disease of the head. Objectives: To compare the efficacy of Nasya Karma with Shigru Taila & Vidangadya Taila in Vataja pratishyaya. Methods and Materials: Patients of group A were treated with Shigru Taila Nasya for 7 days & patients of group B were treated with Vidangadya Taila Nasya for 7 days. The dose of Nasya is 6 Bindu. Results: The percentage success rate of Group is A 57.5% & Group-B is 56.8%. There is no significant difference among the results of the treatment of Group-A and Group-B by paired proportion test of significance for i.e. p< 0.001. Conclusion: Patients of group A treated with Shigru Taila Nasya Karma have shown better results clinically compared to group B who were treated with Vidangadya Taila. There were no complications observed during the treatment

Evaluation of Wound Healing Activity of Angiotensin Converting Enzyme Inhibitors in Wistar Rats

Angiotensin converting enzyme (ACE) inhibitors are known to increase the level of bradykinin by preventing its breakdown and also promote prostaglandin synthesis by direct and indirect methods which in turn may promote wound healing. However there is paucity of scientific information in this regard. Therefore in the present study we have investigated the effect of ACE inhibitors like Captopril and Enalapril on different wound models in Wistar rats. Excision, resutured incision and dead space wounds were inflicted in male Wistar rats under light ether anaesthesia, taking aseptic precautions. Control animals received vehicle and other groups received Captopril (10mg/kg) and Enalapril (10mg/kg) orally for a period of 10 days in incision and dead space wound models, whereas similar treatments were continued in excision wound models till complete closure of wounds. On the 11th day, after estimating breaking strength of resutured incision wounds (under anaesthesia), granulation tissue was removed from dead space wounds to estimate breaking strength, hydroxyproline content as well as quantification of granulation tissue and histological studies were carried out in control and treated groups. Captopril and Enalapril significantly increased the rate of wound healing, reduced the number of days required for complete epithelialization and final area of scar in excision wounds. Both the ACE inhibitors significantly increased breaking strength of resutured incision wounds and granulation tissue. Also these two drugs significantly enhanced both granulation tissue formation and granulation tissue hydroxyproline content. Histological studies confirmed these findings. Captopril and Enalapril significantly promoted the healing process in all the three wound models studied. These results indicate the wound healing property of ACE inhibitors and clinical studies in this regard are worthwhile