The capability of Extended tanh–coth, sine–cosine and Exp-Function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed. In this study, the generalized nonlinear Schrödinger (GNLS) equation is solved by three different methods. To obtain the single-soliton solutions for the equation, t...

Short interspersed nuclear elements (SINEs) are retrotransposons evolutionarily derived from endogenous RNA Polymerase III RNAs. Though SINE elements have undergone exaptation into gene regulatory elements, how transcribed SINE RNA impacts transcriptional and post-transcriptional regulation is largely unknown. This is partly due to a lack of information regarding which of the loci have transcri...

Abstract This paper studies analytic functions f defined on the open unit disk of complex plane for which / g and (1 + z ) are both with positive real part some function . We determine radius constants these to belong classes strong starlike functions, order ? , parabolic as well associated lemniscate Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential a particular rationa...

The eyes absent (eya) gene is critical to eye formation in Drosophila; upon loss of eya function, eye progenitor cells die by programmed cell death. Moreover, ectopic eya expression directs eye formation, and eya functionally synergizes in vivo and physically interacts in vitro with two other genes of eye development, sine oculis and dachshund. The Eya protein sequence, while highly conserved t...

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in paper, we introduce Sumudu establish properties relations. We derive transforms power functions, sine, cosine, hyperbolic exponential function, function derivatives. also acquire a relationship between gamma function. Moreover, ...

T he foundation of seismology is the theory of wave motion, a complicated concept that is still after centuries of experiments and speculations by many of the very greatest scientists an area of active research in many disciplines. Even simple forms of wave motion are difficult to describe verbally; but, ironically, the simplest type of wave is remarkably easy to describe (and subsequently anal...

We prove that the τ-function of the integrable discrete sine-Gordon model apart from the " standard " bilinar identities obeys a number of " non-standard " ones. They can be combined into a bivector 3-dimensional difference equation which is shown to contain Hirota's difference analogue of the sine-Gordon equation and both auxiliary linear problems for it. We observe that this equation is most ...

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashi...

In this paper a new procedure to perform four parameters sine fitting is presented in a closed form, ready for standardization. This new procedure grants convergence of the algorithm, even in those cases where the traditional techniques tend to converge to local minimums of the error function. This new procedure can also be used to compute the initial values for the traditional four parameters ...