Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wiri
ngs within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel grammatical truths'. We give a nogo-theorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams -- or equivalently, (free) monoidal categories.
This paper deals with a numerical method based on the simulation of a 2D tank, for
unsteady and laminar two - dimensional incompressible viscous flow. Navier-Stokes and
Continuity equations are solved in a fluid domain. These equations are discreti
zed by
Finite Differences Method. The pressure is obtained by solving a Poisson equation dealing
with a fictitious velocity field. The Poisson equation is solved by a Finite Volume Method.
The grid is refined by a new method “Adaptive Selective Mesh Refinement” called
“ASMR”.
In this work, we have been found explicit exact soliton wave solutions for Zeldovich
equation with time-dependent coefficients, by using the tanh function method with
nonlinear wave transform, in general case. The results obtained shows that these
exact
solutions are affected the nonlinear nature of the wave variable, it is also shown that this
method is effective and appropriate for solving this kind of nonlinear PDEs, which are
models of many applied problems in physics, chemistry and population evolution.
The topic of the study in this research is one of the
important topics in Number Theory, where did we get
into man techniques and systems related to Diophantus
equations.
The work includes the development of a program in an advanced – programming
language. to solve two none linear related partial differential equation that form a
mathematical model that describes the dynamic status of laser ,so that we can study the
properties of radiation density through this type the related program ,as well as the
population inversion inside the homogeneous medium of laser . We have studied the
strength f the out put power as well as the population inversion in the case of pulse –
working of the solid state laser Nd:YAG and the population inversion change as a function
of the diameter and length of the effective medium of laser .
In this paper, we study the oscillation and nonoscillation theorems
for second order nonlinear difference equations.
By using some important of definitions and main concepts in
oscillation, in addition for lemmas, we introduce examples
illustrating the relevance of the theorems discussed.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
In this research paper, we study geodesic mappings
of gravitation fields . The mapping listed are considered,
on the one hand, a generalization of aftomorfizm of
movement and harmonic mappings, and on the other
hand the practical mappings in the theory of relativity .
In this paper, we find distributional solutions of boundary value
problems in Sobolev spaces. This solution will be given as Fourier
series with respect to the Eigen functions of a positive definite
operator and its square roots.
Then, we obtain solutions of such problems of a real order.
In this article, we propose a powerful method called
homotopy perturbation method (HPM) for obtaining the
analytical solutions for an non-linear system of partial
differential equations. We begin this article by apply HPM
method for an important models of linear and non-linear
partial differential equations.
