Abstract: This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
Abstract: In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Abstract: This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.
Abstract: The statistical distributions are modeled in explaining
nature of various types of data sets. Although these distributions are
mostly uni-modal, it is quite common to see multiple modes in the
observed distribution of the underlying variables, which make the
precise modeling unrealistic. The observed data do not exhibit
smoothness not necessarily due to randomness, but could also be due
to non-randomness resulting in zigzag curves, oscillations, humps
etc. The present paper argues that trigonometric functions, which
have not been used in probability functions of distributions so far,
have the potential to take care of this, if incorporated in the
distribution appropriately. A simple distribution (named as, Sinoform
Distribution), involving trigonometric functions, is illustrated in the
paper with a data set. The importance of trigonometric functions is
demonstrated in the paper, which have the characteristics to make
statistical distributions exotic. It is possible to have multiple modes,
oscillations and zigzag curves in the density, which could be suitable
to explain the underlying nature of select data set.
Abstract: The purpose of this study was to present a reliable mean for human-computer interfacing based on finger gestures made in two dimensions, which could be interpreted and adequately used in controlling a remote robot's movement. The gestures were captured and interpreted using an algorithm based on trigonometric functions, in calculating the angular displacement from one point of touch to another as the user-s finger moved within a time interval; thereby allowing for pattern spotting of the captured gesture. In this paper the design and implementation of such a gesture based user interface was presented, utilizing the aforementioned algorithm. These techniques were then used to control a remote mobile robot's movement. A resistive touch screen was selected as the gesture sensor, then utilizing a programmed microcontroller to interpret them respectively.
Abstract: In the literature of fuzzy measures, there exist many
well known parametric and non-parametric measures, each with its
own merits and limitations. But our main emphasis is on
applications of these measures to a variety of disciplines. To extend
the scope of applications of these fuzzy measures to geometry, we
need some special fuzzy measures. In this communication, we have
introduced two new fuzzy measures involving trigonometric
functions and simultaneously provided their applications to obtain
the basic results already existing in the literature of geometry.
Abstract: In the traditional theory of non-uniform torsion the
axial displacement field is expressed as the product of the unit twist
angle and the warping function. The first one, variable along the
beam axis, is obtained by a global congruence condition; the second
one, instead, defined over the cross-section, is determined by solving
a Neumann problem associated to the Laplace equation, as well as for
the uniform torsion problem.
So, as in the classical theory the warping function doesn-t punctually
satisfy the first indefinite equilibrium equation, the principal aim of
this work is to develop a new theory for non-uniform torsion of
beams with axial symmetric cross-section, fully restrained on both
ends and loaded by a constant torque, that permits to punctually
satisfy the previous equation, by means of a trigonometric expansion
of the axial displacement and unit twist angle functions.
Furthermore, as the classical theory is generally applied with good
results to the global and local analysis of ship structures, two beams
having the first one an open profile, the second one a closed section,
have been analyzed, in order to compare the two theories.
Abstract: In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.