Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

Linear systems toolkit in Matlab :structural decompositions and their applications

This paper presents a brief description of the software toolbox, linear systems toolkit, developed in Matlab environment. The toolkit contains 66 m-functious, including structural decompositions of linear autonomous systems, unforced/uuseused systems, proper systems, and singular systems, along with their applications to system factorizations, sensor/actuator selection, H-two and H-infinity control, and disturbance decoupling problems.

Greedy Friensdhip Decompositions of Graphs

A graph that consists of t cliques sharing a vertex v is said to be a t-friendship graph with center v. A friendship graph is a graph that is t-friendship for some . We solve the problem of finding the best upper bound for the size of a greedy 2-friendship decomposition and a greedy friendship decomposition of graphs of order n.

Relative Continuity and New Decompositions of Continuity in Bitopological Spaces

The aim of this work is to introduce some weak forms of continuity in bitopological spaces. Then we use these new forms of weak continuity to give many decompositions of?i-continuity and pairwise continuity.

Friendship Decompositions of Graphs: The general problem

A friendship graph is a graph consisting of cliques sharing a common vertex. In this paper we investigate the maximum number of elements in an optimal friendship decomposition of graphs of order n. We obtain upper and lower bounds for this number. These bounds relate this problem with the classical Ramsey numbers.

ATOMIC DECOATOMIC DECOMPOSITIONS AND DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES

In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.

WEAK ATOMIC DECOMPOSITIONS OF MARTINGALE HARDY-LORENTZ SPACES AND APPLICATIONS

In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.

Generic Regular Decompositions for Parametric Polynomial Systems

This paper presents a generalization of the authors＇ earlier work. In this paper, the two concepts, generic regular decomposition （GRD） and regular-decomposition-unstable （RDU） variety introduced in the authors＇ previous work for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in the authors＇ previous work. Then the solutions of any parametric system can be represented by the solutions of finitely many regular systems and the decomposition is stable at any parameter value in the complement of the associated RDU variety of the parameter space. The related definitions and the results presented in the authors＇ previous work are also generalized and a further discussion on RDU varieties is given from an experimental point of view. The new algorithm has been implemented on the basis of DISCOVERER with Maple 16 and experimented with a number of benchmarks from the literature.

Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.

Quantum Chemical Investigations on the Structures,Stabilities and Decompositions of Trinitrobenzenes and Their Chloro Derivatives

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COMPLETE MULTIPARTITE DECOMPOSITIONS OF COMPLETE GRAPHS AND COMPLETE n-PARTITE GRAPHS

In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.

Comparison of different spectral decompositions for non-marine deep water sandstone reservoir prediction in the Xingma area

It is difficult to identify and predict non-marine deep water sandstone reservoir facies and thickness,using routine seismic analyses in the Xingma area of the western Liaohe sag,due to low dominant frequencies,low signal-to-noise ratios,rapid lateral changes and high frequencies of layered inter-bedding.Targeting this problem,four types of frequency spectral decomposition techniques were tested for reservoir prediction.Among these,the non-orthogonal Gabor-Morlet wavelet frequency decomposition method proved to be the best,was implemented directly in our frequency analysis and proved to be adaptable to non-stationary signals as well.The method can overcome the limitations of regular spectral decomposition techniques and highlights local features of reservoir signals.The results are found to be in good agreement with well data.Using this method and a 3-D visualization technology, the distribution of non-marine deep water sandstone reservoirs can be precisely predicted.

On Orthogonal Decompositions of "Pull Back" Hermitian Holomorphic Vector Bundles

Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn（Ω）. Moreover, we compute the maximal self-adjoint subalgebra of A＇（Ef） and A＇（T） respectively. Finally, we fix the masa of A＇（Ef） and .A＇ （T） which depends on the HIR decomposition of Ef or T respectively.

Discrete wavelet and modified PCA decompositions for postural stability analysis in biometric applications

The aim of this study is to compare the Discrete wavelet decomposition and the modified Principal Analysis Component (PCA) decomposition to analyze the stabilogram for the purpose to provide a new insight about human postural stability. Discrete wavelet analysis is used to decompose the stabilogram into several timescale components (i.e. detail wavelet coefficients and approximation wavelet coefficients). Whereas, the modified PCA decomposition is applied to decompose the stabilogram into three components, namely: trend, rambling and trembling. Based on the modified PCA analysis, the trace of analytic trembling and rambling in the complex plan highlights a unique rotation center. The same property is found when considering the detail wavelet coefficients. Based on this property, the area of the circle in which 95% of the trace’s data points are located, is extracted to provide important information about the postural equilibrium status of healthy subjects (average age 31 ± 11 years). Based on experimental results, this parameter seems to be a valuable parameter in order to highlight the effect of visual entries, stabilogram direction, gender and age on the postural stability. Obtained results show also that wavelets and the modified PCA decomposition can discriminate the subjects by gender which is particularly interesting in biometric applications and human stability simulation. Moreover, both techniques highlight the fact that male are less stable than female and the fact that there is no correlation between human stability and his age (under 60).

{Ck, Pk, Sk} -Decompositions of Balanced Complete Bipartite Multigraphs

Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of Hi, where . Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph has a -decomposition if and only if k is even, and .

Decompositions of Some Special Block Tridiagonal Matrices

In this paper, we present a unified approach to decomposing a special class of block tridiagonal matrices K (α ,β ) into block diagonal matrices using similarity transformations. The matrices K (α ,β )∈ Rpq× pq are of the form K (α ,β = block-tridiag[β B,A,α B] for three special pairs of (α ,β ): K (1,1), K (1,2) and K (2,2) , where the matrices A and B, A, B∈ Rp× q , are general square matrices. The decomposed block diagonal matrices (α ,β ) for the three cases are all of the form: (α ,β ) = D1 (α ,β ) ⊕ D2 (α ,β ) ⊕---⊕ Dq (α ,β ) , where Dk (α ,β ) = A+ 2cos ( θk (α ,β )) B, in which θk (α ,β ) , k = 1,2, --- q , depend on the values of α and β. Our decomposition method is closely related to the classical fast Poisson solver using Fourier analysis. Unlike the fast Poisson solver, our approach decomposes K (α ,β ) into q diagonal blocks, instead of p blocks. Furthermore, our proposed approach does not require matrices A and B to be symmetric and commute, and employs only the eigenvectors of the tridiagonal matrix T (α ,β ) = tridiag[β b, a,αb] in a block form, where a and b are scalars. The transformation matrices, their inverses, and the explicit form of the decomposed block diagonal matrices are derived in this paper. Numerical examples and experiments are also presented to demonstrate the validity and usefulness of the approach. Due to the decoupled nature of the decomposed matrices, this approach lends itself to parallel and distributed computations for solving both linear systems and eigenvalue problems using multiprocessors.

Effective Methods of QR-Decompositions of Square Complex Matrices by Fast Discrete Signal-Induced Heap Transforms

The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3(N-1), for an N × N complex matrix. Examples of the QR-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.

4-Cycle Decompositions of Graphs

In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.

ON THE ASCENDING SUBGRAPH DECOMPOSITIONS OF REGULAR GRAPHS

The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.