Discrete Normal Vector Field Approximation via Time Scale Calculus

Abstract

The theory of time scales calculus have long been a subject to many researchers from different disciplines. Beside the unification and the extension aspects of the theory, it emerge as a powerful tool for mimetic discretization process. In this study, we present a framework to find normal vector fields of discrete point sets in ℝ3 by using symmetric differential on time scales. A surface parameterized by the tensor product of two time scales can be analogously expressed as the vertex set of non-regular rectangular grids. If the time scales are dense, then the discrete grid structure vanishes. If the time scales are isolated, then the further geometric analysis can be executed by using symmetric dynamic differential. Moreover, we present an algorithmic procedure to determine the symmetric dynamic differential structure on the neighborhood of points in surfaces. Our results indicate that the method we present has good approximation to unit normal vector fields of parameterized surfaces rather than the Delaunay triangulation for some points.

Regarding New Traveling Wave Solutions for the Mathematical Model Arising in Telecommunications

“…Considering some values of parameters under the strain conditions, different wave patterns can be observed from (Figures 3 and 4) for Eq. (18).…”

“…The (3 +1) Dimensional Boiti-Leon-Manna-Pempinelli equation has been deeply studied in [17]. Using time scale calculus, discrete normal vector field approximation has been presented in [18]. A Handy Technique has been handled in [19].…”

“…Classical Boussinesq equations have been immensely studied in [20]. Traveling wave solutions of nonlinear Klein Gordon equation were observed in [21] and so on [15,17,18,.…”

The global sliding mode tracking control for a class of variable order fractional differential systems

“…There exist many approaches to tackle the problem of chaos control for fractional chaotic systems, such as, back stepping methods, feedback control, adaptive control [19][20][21][22] . Sliding mode control (SMC) method [23] has been proved to be an advantageous robust approach for the tracking control of the nonlinear systems with uncertainties and external disturbances [24][25][26] , which depends on the significant characteristics of SMC approach, such as less sensitivity and acceptable transient performance [27] . In practical applications, it often requires high precision asymptotic convergence, finite time convergence, better disturbance compensation and eliminated the reaching phase.…”

Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

“…Introduction. Fractional difference equations (FDEs) have been extensively studied during the past decades because of its application in various fields of applied science (see [1,2,14,18,24]). It has been shown that these equations can accurately model challenging phenomena including mathematical biology, mathematical biology, viscoelasticity, fluid mechanics, cryptography, electrochemistry and many more (see [17,19,20,31,32]).…”