We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

A theoretical framework model that researches the interrelationship of organizational innovation, organizational performance and dynamic core competence of enterprise (DCCE) is proposed on the foundation of the analysis of measure dimensions which include four oriented organizational innovations and the four sub-core capabilities of DCCE and the three levels of variables of performance. By usin...

The concept of livable city was put forward naturally and began to gain more attention when people care more about human needs during the economic development. In this paper, we define a livable city as an urban area takes the residents’ demand as first priority. It has a pleasant ecological environment, a mature community with rich public resources such as culture, transportation and medical s...

and we are going to determine all the possible dynamics of this type of equation. Also, we can say that generically there are two different T-periodic solutions. In this equation we emphasize the following antecedents. First, in 1975, there appeared a paper written by N. G. Lloyd [5] about complex solutions of a real Riccati equation. This study was continued in a 1984 paper by H. S. Hassan [3]...

A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...