The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obt...

We present here an overview of the hypermatrix spectral decomposition deduced from the Bhattacharya-Mesner hypermatrix algebra [BM1, BM2]. We describe necessary and sufficient conditions for the existence of a spectral decomposition. We further extend to hypermatrices the notion of resolution of identity and use them to derive hypermatrix analog of matrix spectral bounds. Finally we describe an...

Spectral decomposition has been rarely used to investigate complex networks. In this work we apply this concept in order to define two types of linkdirected attacks while quantifying their respective effects on the topology. Several other types of more traditional attacks are also adopted and compared. These attacks had substantially diverse effects, depending on each specific network (models a...

For a nite system A of bounded linear operators whose real linear combinations have real spectrum, the monogenic functional calculus is used to associate a function f(A) of the operators with any analytic function f in n real variables deened in a neighbourhood of the monogenic spectrum (A). Here, the existence of projection operators that decompose the functional calculus onto invariant subspa...

[2] Apparently Fourier did not possess the inner-product expression for (concrete) Fourier coefficients when he first proposed that functions are expressible in Fourier series. This understandably weakened his claim. Worse, at the time, notions of convergence and even the notion of function were amorphous, so that the sense(s) in which a function might be represented by a Fourier series could n...

In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if A generates a polynomially bounded n-times integrated group whose spectrum set σ(A) = {iλk; k ∈ Z} is discrete and satisfies ∑ 1 |λk|δ k < ∞ (n and l nonnegative integers), then there exists projectors (Pk)k∈Z∗ such that ∑ Pkx = x (x ∈ D(A)), where δk = min ( |λk+1−λk| 2 , ...

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative CayleyHamilton’s theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it h...

Interpretation of subsurface geology is greatly enhanced by 3-D seismic data, and this accounts for its ubiquity in today’s search for hydrocarbons. Seismic interpretation has two fundamental disciplines at its core: seismic geomorphology and seismic stratigraphy. Plan views allow the explorationist to apply principles of geomorphology, based on analogies with modern sedimentary systems, to int...

In the Mari field, 3D seismic, conventional attribute methodologies on the full stack, broadband data set showed an ambiguous fault definition. Frequency Spectral Decomposition has been applied on Mari 3D seismic data and generated attribute maps, which exhibited substantially more fidelity than full-bandwidth, conventional attributes. It has been found that fault definition is superior to conv...