1,720,989 research outputs found
Invariant solutions and conservation laws for soil water redistribution and extraction flow models
No full text(M.Sc.) North-West University, Mafikeng Campus, 2003In this dissertation we use Lie symmetry analysis to obtain invariant solutions for
certain soil water equations. These solutions are invariant under two-parameter
symmetry groups obtained by the group classification of the governing equation. We
also obtain all nontrivial conservation laws for a class of (2+1) nonlinear evolution
partial differential equations which are related to the soil water equations. It is shown
that nontrivial conservation laws exist for certain classes of equations which admit
point symmetries. We note that one cannot invoke Noether's theorem here as there
is no Lagrangian for these partial differential equations.Master
A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach
Get PDFIn this communication, we utilize some basic symmetry
reductions to transform the governing nonlinear partial differential
equations arising in the study of third-grade fluid flows into ordinary
differential equations. We obtain some simple closed-form steady-state
solutions of these reduced equations. Our solutions are valid for the whole
domain [0,∞) and also satisfy the physical boundary conditions. We
also present the numerical solutions for some of the underlying equations.
The graphs corresponding to the essential physical parameters of the flow
are presented and discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On The Lane-emden System In Dimension One
No full textWe carry out a complete group classification of the nonlinear Lane-Emden systems in dimension one. © 2012 Elsevier Inc. All rights reserved.218211076210766Bluman, G.W., Anco, S., (2002) Symmetry and Integration Methods for Differential Equations, , Springer New YorkBluman, G.W., Kumei, S., (1989) Symmetries and Differential Equations, 81. , Applied Mathematical Sciences Springer New YorkBokhari, A.H., Mahomed, F.M., Zaman, F.D., Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation (2010) J. Math. Phys., 51, p. 053517Bozhkov, Y., Gilli Martins, A.C., Lie point symmetries of the Lane-Emden systems (2004) Journal of Mathematical Analysis and Applications, 294 (1), pp. 334-344. , DOI 10.1016/j.jmaa.2004.02.022, PII S0022247X04001532Bozhkov, Y., Freire, I.L., Symmetry analysis of the bidimensional Lane-Emden systems (2012) J. Math. Anal. Appl., 388, pp. 1279-1284. , 10.1016/j.jmaa.2011.11.024Bozhkov, Y., Freire, I.L., (2012) The Complete Group Classification of Lane-Emden Systems, , in preparationDai, Q., Tisdell, C., Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications (2009) Acta Math. Sci. Ser., 29, pp. 435-446Freire, I.L., Silva, P.L., Torrisi, M., Symmetry and Integrability of A Fourth-order Emden-Fowler Equation, , 2012 submitted for publicationIbragimov, N.H., (1985) Transformation Groups Applied to Mathematical Physics, , Translated from the Russian Mathematics and its Applications (Soviet Series) D. Reidel Publishing Co. DordrechtIbragimov, N.H., Integrating factors, adjoint equations and Lagrangians (2006) Journal of Mathematical Analysis and Applications, 318 (2), pp. 742-757. , DOI 10.1016/j.jmaa.2005.11.012, PII S0022247X05011546Ibragimov, N.H., A new conservation theorem (2007) J. Math. Anal. Appl., 333, pp. 311-328Muatjetjeja, B., Khalique, C.M., Lagrangian approach to a generalized coupled Lane-Emden system: Symmetries and first integrals (2010) Commun. Nonlinear Sci. Numer. Simulat., 15, pp. 1166-1171Muatjetjeja, B., Khalique, C.M., Noether partial Noether operators and first integrals for the coupled Lane-Emden system (2010) Math. Comput. Appl., 15, pp. 325-333Muatjetjeja, B., Khalique, C.M., First integrals for a generalized coupled Lane-Emden system (2011) Nonlinear Anal. Real World Appl., 12, pp. 1202-1212Olver, P.J., (1986) Applications of Lie Groups to Differential Equations, , Springer New Yor
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Group Classification of a General Bond-Option Pricing Equation
Get PDFThesis (M.Sc. (Applied Mathematics) North-West University, Mafikeng Campus, 2013The main purpose of this work is to perform the Lie group classification of a general bond-option
pricing equation. The procedure involves finding the Lie symmetries of the said
partial differential equation and employing direct method to classify the equation. The
optimal systems are then obtained for some cases encountered and group-invariant solutions
are found for the optimal systems of one-dimensional subalgebras obtained.Master
Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)-dimensional zakharov-kuznetsov equation
Get PDFThesis (M. Sci in Applied Mathematics) North-West University, Mafikeng Campus, 2011This research studies two nonlinear problems arising in mathematical physics. Firstly
the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is
used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also
conservation laws are obtained for this equation using the new conservation theorem.
Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK)
equation of time dependent variable coefficients from the Lie group-theoretic point
of view. We classify the Lie point symmetry generators to obtain the optimal system
of one-dimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc
then used to construct a number of symmetry reductions and exact group-invariant
solutions of the ZK equation. We utilize the new conservation theorem to construct
the conservation laws of t he ZK equation.Master
Lie group analysis of the new extended KP and three-dimensional KP-BBM equations
Get PDFMSc (Applied Mathematics), North-West University, Mahikeng CampusIn this dissertation, we examine three partial deferential equations that are nonlin- ear. Namely, nonlinear filtration equation, the new extended Kadomtsev-Petviashvili equation (eKP) and the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation (KP-BBM). Nonlinear filtration equation is used as an illustrative example. The main equations of this dissertation are then examined. These equation's exact solutions are generated by Lie group analysis. The underlying equation's conservation laws are also determined using the multiplier method, Ibragimov's method and Noether theorem.Master
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