Suchergebnisse
Filter
6 Ergebnisse
Sortierung:
PROPERTIES OF A DIFFERENTIAL SEQUENCE BASED UPON THE KUMMER-SCHWARZ EQUATION
In: Acta polytechnica: journal of advanced engineering, Band 60, Heft 5, S. 428-434
ISSN: 1805-2363
In this paper, we determine a recursion operator for the Kummer-Schwarz equation, which leads to a sequence with unacceptable singularity properties. A different sequence is devised based upon the relationship between the Kummer-Schwarz equation and the first-order Riccati equation for which a particular generator has been found to give interesting and excellent properties. We examine the elements of this sequence in terms of the usual properties to be investigated – symmetries, singularity properties, integrability, alternate sequence – and provide an explanation of the curious relationship between the results of the singularity analysis and a consideration of the solution of each element obtained by quadratures.
SIMILARITY SOLUTIONS AND CONSERVATION LAWS FOR THE BEAM EQUATIONS: A COMPLETE STUDY
In: Acta polytechnica: journal of advanced engineering, Band 60, Heft 2, S. 98-110
ISSN: 1805-2363
We study the similarity solutions and we determine the conservation laws of various forms of beam equations, such as Euler-Bernoulli, Rayleigh and Timoshenko-Prescott. The travelling-wave reduction leads to solvable fourth-order odes for all the forms. In addition, the reduction based on the scaling symmetry for the Euler-Bernoulli form leads to certain odes for which there exists zero symmetries. Therefore, we conduct the singularity analysis to ascertain the integrability. We study two reduced odes of second and third orders. The reduced second-order ode is a perturbed form of Painlevé-Ince equation, which is integrable and the third-order ode falls into the category of equations studied by Chazy, Bureau and Cosgrove. Moreover, we derived the symmetries and its corresponding reductions and conservation laws for the forced form of the abovementioned beam forms. The Lie Algebra is mentioned explicitly for all the cases.
Linearisation of a second-order nonlinear ordinary differential equation
In: Acta polytechnica: journal of advanced engineering, Band 63, Heft 1, S. 19-22
ISSN: 1805-2363
We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v. The eight Lie point symmetries obtained for the second-order ordinary differential equation is of maximal number and a representation of the sl(3,R) algebra. We extend this analysis to a more general nonlinear second-order differential equation and we obtain similar interesting algebraic properties.
Cuncaicha Rockshelter, a Key Site for Understanding Colonization of the High Andes: Reply to Capriles et al
In: Current anthropology, Band 57, Heft 1, S. 101-103
ISSN: 1537-5382
Reviews
In: American Indian Culture and Research Journal, Band 31, Heft 3, S. 203-254