In this study, some new exact travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with Kerr law of nonlinearity are retrieved by complete discrimination system for polynomial method. Under transformation, LPD is reduced an ordinary differential equation. The including rational solutions, triangle function solitary and Jacobian elliptic obtained graphically illustrated us...

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras. This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set – the set of all algebra endomorphisms of a polynomial algebra with the Jacobian 1 – the Jacobian conjecture claims ...

the helicopter-borne electromagnetic (hem) frequency-domain exploration method is an airborne electromagnetic (aem) technique that is widely used for vast and rough areas for resistivity imaging. the vast amount of digitized data flowing from the hem method requires an efficient and accurate inversion algorithm. generally, the inverse modelling of hem data in the first step requires a precise a...

‎It is shown that the knowledge of a surjective morphism $Xto Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve ‎with period lattice $(1,tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classi...

This thesis deals with linear transformations at various stages of the automatic speech recognition process. In current state-of-the-art speech recognition systems linear transformations are widely used to care for a potential mismatch of the training and testing data and thus enhance the recognition performance. A large number of approaches has been proposed in literature, though the connectio...

We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and nonlinearization spectral problem, we generate solution two different periodic backgrounds. analyze obtained for values system parameter point out certain novel features our results. also compute instability growth rate both $d...