Theory and Applications of Mathematical Science Vol. 2

Common methods found in the market such as LEAN, AGILE, SCRUM are short and insufficient to generate a high level of efficiency in discrete-continuous variables based workflows and aspects of classification, decidability and analysis remains mostly copies of successful cases. The new metric and theoretical framework proposed in this article allows qualitative classification and analysis of workflows in close proximity to qualitative theory of differential equations (QDE), raising the possibility of fulfill the gaps existent in the commercial and popular methods. These metrics are also the result of research carried out in the view of the difficulty of characterizing the solidity aspect of workflows and enabling continuous improvements as a complex adaptive system (CAS).

This paper analyses wind speed characteristics and wind power potential of Naganur site using statistical probability parameters. A measured 10-minute time series average wind speed over a period of 4 years (2006- 2009) was obtained from Site. The results of mean wind speed data is the first step of prediction of wind speed data of the site under consideration and a PROLOG program was designed and developed to calculate the Annual mean wind speed data of the site and to assess the wind power potentials, MATLAB programming is used. The Weibull two parameters (k and c) were computed in the analysis of wind speed data. The data used were real time site data and calculated by using the MATLAB programming to determine and generate the Weibull and Rayleigh distribution functions. The monthly values of k range from 2.21 to 8.64 and the values of c ranged from 2.28 to 6.80. The most probable wind speed and corresponding maximum energy are in the range of 2.45 to 6.52 and 3.10 to 6.26 respectively. The Weibull and Rayleigh distributions also revealed estimated wind power densities ranging between 7.30 W/m² to 116.51 W/m² and 9.71 W/m² to 266.00 W/m² respectively at 10 m height for the location under study. This paper is relevant to a decision-making process on significant investment in a wind power project and use of PROLOG programming to calculate the Annual mean wind speed data of the site.

The average distance  of a finite graph  is the average of the distances over all unordered pairs of vertices which can be used as a tool in analytic networks where the performance time is proportional to the distance between any two nodes. A minimum average distance spanning  tree of  is a spanning tree of   with minimum average distance. Such a tree is sometimes referred to as a minimum routing cost spanning tree and these are of interest in the design of communication networks. In this chapter, I present an efficient algorithm to compute a minimum average distance spanning tree on trapezoid graphs in  time, where  is the number of vertices of the graph.

Combining the shape derivative [1] to the maximum principle, we show that the so-called Quadrature Surfaces Free Boundary Problem  has a solution which contains strictly the support of  if and only if

where   and  is the convex hull of the support of 

We also give a necessary and sufficient condition of existence for the problem  where the term source  is a uniform density supported by a segment.

In this chapter, we establish some common fxed point theorems for a pair of self mappings in fuzzy cone metric spaces under the generalize fuzzy cone contraction conditions. we extend and improve some recent results given in the literature.

In this paper, we have considered the generalized growth ((p, q)-order and (p, q)-type) in term of coefficient of the developpement pnn given by

in the (n, n)-th Newton-pad´e approximant of meromorphic function. We use these results to study the relationship betwen the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of C (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.

It is known that the Euler and Navier-Stokes equations, which describe flows of ideal and viscid gases, are the set of equations of the conservation laws for energy, linear momentum and mass. As it will be shown, the integrability and properties of the solutions to the Euler and Navier-Stokes equations depend, firstly, on the consistency of equations of the conservation laws and, secondly, on the properties of conservation laws.

It was found that the Euler and Navier-Stokes equations have solutions of  two types, namely, the solutions that are not functions (depend not only on coordinates) and generalized solutions that are functions but realized discretely and hence, functions or their derivatives have discontinuities. A transition from the solutions of first type to generalized solutions describes the process of transition of gas-dynamic medium from non-equilibrium state to the locally-equilibrium one. Such a process is accompanied by the emergence of any observable formations (such as waves, vortices, turbulent pulsations and soon). This discloses the mechanism of such processes as emergence vorticity and turbulence.

Such results were obtained when studying the equations the conservation laws for energy and linear momentum, which turned out to be inconsistent, due to the non-commutativity of the conservation laws.

The aim of this chapter is to present the existence result for solution of nonlinear Volterra-Hammerstein- Fredholm integral equation (in short VHFIE) under some conditions. The main tools are Darbo’s fixed point theorem involving measure of noncompactness for investigating the existence of solution of nonlinear Volterra-Hammerstein-Fredholm integral equation. An application and illustrative example of Volterra-Hammerstein-Fredholm integral equation are also present in this chapter.

Domar has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later Rippon pointed out that a modification of Domar’s argument gives in fact a better result. Using our previous, rather general and flexible modifications of Domar’s original argument, we extend their results both to the subharmonic and to the quasinearly subharmonic settings.

Throughout this paper, all topological groups are assumed to be topological differential manifolds and algebraically free, our aim in this paper is to prove the open problems number (7) and (8). Which are introduced by Guran, I [1]. In many cases of spaces and under a suitable conditions. therefore, we denote by I(X) and I(Y) to be a free topological groups over a topological spaces X and Y respectively where X and Y are assumed to be a non- empty sub manifolds Which are also a closed sub sets, and P is a classes of topological spaces, as a regular, normal, Tychonoff, lindelöf, separable connected, compact and Zero- dimensional space, and we have tried to use a hereditary properties and others of these spaces, so we can prove the open problems in these cases and we have many results showed in this paper.