Current Issue : January - March Volume : 2021 Issue Number : 1 Articles : 7 Articles
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Interest in the construction of efficient methods for solving initial value\nproblems that have some peculiar properties with it or its solution is recently\ngaining wide popularity. Based on the assumption that the solution is representable\nby nonlinear trigonometric expressions, this work presents an explicit\nsingle-step nonlinear method for solving first order initial value problems\nwhose solution possesses singularity. The stability and convergence properties\nof the constructed scheme are also presented. Implementation of the new\nmethod on some standard test problems compared with those discussed in\nthe literature proved its accuracy and efficiency....
In order to answer a question motivated by constructing substitution\nboxes in block ciphers we will exhibit an infinite family of full-rank\nfactorizations of elementary 2-groups into two factors having equal\nsizes....
First, a Lagrangian is presented and authenticated for a Relativistic Harmonic\nOscillator in 1 + 1 dimensions. It yields a two-component set of equations of\nmotion. The time-component is the missing piece in all previous discussions\nof this system! The second result is that this Oscillator Langrangian generalizes\nto Langrangians for a class of particles in 1 + 1 dimensions subject to an\narbitrary potential V which is space dependent only....
The research considers wavelike objects that are elements of even subalgebra\nof geometric algebra in three dimensions. The used formalism particularly\neliminates long existing confusion about the reasons behind the appearance\nof the imaginary unit in quantum mechanics and introduces clear definition\nof wave functions. When a wave function acts through the Hopf fibration on\na localized geometric algebra element, that is executing a measurement, the\nresult can be named as â??collapseâ? of the wave function....
In this manuscript, we first perform a complete Lie symmetry classification\nfor a higher-dimensional shallow water wave equation and then construct the\ncorresponding reduced equations with the obtained Lie symmetries. Moreover,\nwith the extended F-expansion method, we obtain several new nonlinear\nwave solutions involving differentiable arbitrary functions, expressed by Jacobi\nelliptic function, Weierstrass elliptic function, hyperbolic function and\ntrigonometric function....
We obtain some theorems for real increasing functions showing that elementary\nfixed point theory can bring to astonishing results by assuming only a\nfew properties, some of which intrinsically possessed from these functions.\nAn application is given for a theorem of quasi-compactness and a known result\nin posets is also recalled and applied to real intervals....
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