AAU Institutional Repository

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This work deals with Central Delannoy numbers, enumerated as Dn;n = (Dn)n_0 = 1, 3, 13, 63, 321, 1683, 8989, 48639, . . ., which counts the number of lattice paths running from (0; 0) to (n; n) by using the steps (1; 0), ...
This project paper is aimed to explain observability of linear time invariant dynamical system. We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems. ...
Hankel transforms are among the well-known transforms. In this paper integer Hankel transforms, Riordan Matrices and generating functions are defined. We also examine a set of special Riordan arrays, their inverses and ...
In this thesis, we study the application of FBI transforms to the C1; analytic and Gevrey wave front sets of functions. We characterize the C1 wave front set of a function by providing a simpler proof of a result by ...
This thesis provides an overview of harmonic functions of the following topic a) Some basic results like, Maximum principle, uniqueness Theorem and Green’s Formula. b) The fundamental properties of harmonic functions, ...
In this paper we study Bessel differential equation of the form ���������� + ������ + (���� − ����)�� = 0, and the modified Bessel equation of the form ���������� + ������ − (���� + ����)�� = 0 Along with the corresponding ...
Combinatorics on words has imposed itself as a powerful tool for the study of large number of discrete, linear, non-commutative objects. This report is intended to discuss words, in particular,Christoffel words
This Project is about the study of rst order necessary and su cient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone.These conditions are ...
In this paper, we will observe how to find the spanning trees of a graph and the methods that we use to calculate. The methods that we use for calculating the spanning tree of the graph are deletion and contraction, matrix ...
. This thesis discusses the relationship between Bernstein-Sato ideals of = xy(a3x + y):::(amx + y); ai 2 C; ai 6= aj ;m _ 3 and the decomposition of the D2-module M_ Chx; y; @x; @yi___ over the Weyl algebra Chx; y; ...
This project contains two parts; theory of distribution and Sobolev spaces. In this project, we discussed theory of distribution and also the differentiations of distribution, multiplication by smooth function of distribution, ...
In this thesis, we investigate entire solutions of the quasilinear equation (y) __u = h(x; u) where __u := div(_(jruj)ru): Under suitable assumptions on the right-hand side we will show the existence of in_nitely many ...
The complete set of this project is about feed – forward networks. The realization of Boolean function for linearly separable problem by a single perceptron is possible. The problem is that how the non-linearly separable ...
The focus of this thesis is on the property and the use of Fourier analysis in different fields containing differential equations. The Fourier transform of an integrable function f, is    F( )  f (x)eixdx We ...
Finding the Number of n-permutations avoiding a pattern q and also _nding the Stanley-Wilf limit of this pattern are some of the most di_cult questions in the theory of pattern avoidance. Very few a_rmative answers are ...
In This Project We Study The Existence Of Some Positive, Periodic Solutions Of Systems Of Functional Differential Equations. In The First Topic We Introduce The Delay Differential Equations From The Simple Ordinary ...
In a certain sense, closed orbits are the only types of orbits that we can ever hope to understand completely throughout their evolution from the distant past (i.e. as t ! −1) to the distant future (i.e., as t ! 1) since ...
Let be a field and given a polynomials inK(x1,x2,...Xn)2 K(X1X2......NK)], we can define an affine varieties in and ideals in a polynomials ring1 ,2 ,. . .]. This project considers the polynomial functions on a variety. ...