H-removable sequences, for arbitrary H, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected H and H complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs H with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of H in H_{pn} ^ &Lambda^* is also presented via examples.

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International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / According to the advantages of chaotic analog sequences and chaotic binary sequences, this paper proposes a method generating chaotic binary spread-spectrum sequence by multilevel quantifying. This paper proved that even correlation and odd correlation between such sequences of length N are all Gaussian distributed with mean 0 and variance N, the even of mean-square cross-correlation is N, and the variance of mean-square cross-correlation is 2N. The method can increase the number of chaotic sequences, made the spread-spectrum system more secure. The theoretical analyses and the results of simulation show that the performance of such sequence general is as same as traditional spread-spectrum sequence, its number is very large, and can be used in CDMA in future.

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A large number of distillation sequences can be generated to separate a multicomponent azeotropic mixture. However, there is no systematic and efficient method for synthesising promising sequences, which also consider recycle connections and flowrates. In this work, a systematic procedure is developed for synthesising economically promising distillation sequences separating multicomponent homogeneous azeotropic mixtures. The procedure uses spherically approximated distillation boundaries, a shortcut column design method, and allows recycle and sequence alternatives to be screened. Both feasibility and design are addressed. Approximation of a distillation boundary as a spherical surface is a simple nonlinear, yet more accurate representation of the actual boundary than a linear approximation. For shortcut column design, azeotropes are treated as pseudocomponents and the relative volatilities of all singular points of the system are characterised, based on the transformation of vapour-liquid equilibrium behaviour in terms of pure components into that in terms of singular points. Once the relative volatilities of singular points are obtained, the classical Fenske-Underwood-Gilliland method can be used to design columns separating azeotropic mixtures. This method is extremely computationally efficient and can be applied to homogeneous azeotropic mixtures with any number of components; the results are useful for initialising rigorous simulations using commercial software and for assessing feasibility of proposed splits. Together with the spherical approximation of distillation boundaries, this shortcut method provides a basis for evaluating distillation sequences with recycles. Analysis of feasibility requirements of splits, component recovery requirements and the effects of recycles on the performance of proposed splits allows rules and procedures for selecting recycles to be proposed. Recycles with compositions of either singular points or mixtures of singular points are identified that are beneficial to the feasibility of sequences and the recovery of components. The principles are applicable to azeotropic mixtures with any number of components; using these procedures, recycle structures can be generated and are much simpler than the superstructures of recycle alternatives. The sequence synthesis procedure of Thong and Jobson (2001c) allows all potentially feasible sequences to be generated. To screen among these sequences, a split feasibility test and a two-step screening procedure are proposed. In the first step, feasibility of splits is tested efficiently and sequences containing either infeasible or sloppy splits are eliminated. In the second step, sequences containing sloppy splits are generated, based on the evaluation of sequences containing only feasible sharp splits. Using this procedure, the number of distillation sequences identified using the procedure of Thong and Jobson (2001c) can be significantly reduced. A systematic methodology is proposed for the synthesis and evaluation of multicomponent homogeneous azeotropic distillation sequences. The methodology is computationally efficient. It is demonstrated through a case study, the synthesis of distillation sequences separating a five-component mixture, in which two homogeneous azeotropes are formed, and for which over 5000 sequences producing pure component products can be generated. Using this methodology, only ten sequences are evaluated to identify three promising sequences. The evaluation of each sequence using the shortcut column design method is extremely efficient compared with that using the boundary value method.

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The goal of this thesis is to explore the properties of a certain class of sequences, rigid divisibility sequences, generated by the iteration of certain polynomials whose coefficients are algebraic integers. The main goal is to provide, as far as is possible, a classification and description of those polynomials which generate rigid divisibility sequences.

This thesis deals with the behaviour modulo n of linear recurring sequences of integers with characteristic polynomial ƒ ( x ) where n is a positive integer and ƒ ( x ) is a monic polynomial of degree k. Let α [subscript 1], α [subscript 2],...,α [subscript k] be the zeros of ƒ ( x ) and D ( ƒ ) ≠ 0 its discriminant. We focus on the v-sequence ( v [subscript j] ), defined by v [subscript j] = α[superscript j] over [subscript 1] + α [superscript j] over [subscript 2] + ... + α [superscript j] over [subscript k] for j ≥ 0. Our main interest is in algebraic congruences modulo n which hold when n is a prime and which involve only terms of the sequence and rational integers. For k = 1,2 such results have been used extensively in primality testing and have led to the study of various types of pseudoprimes. For k = 3, such results have been studied by Adams and Shanks ( 1 ) under the further assumption ƒ ( 0 ) = - 1. For general k, quite different approaches have been taken by Gurak ( 2 ) and Szekeres ( 3 ). The infinite test matrix modulo n is the infinite matrix M with rows and columns numbered 0,1,2 ... whose ( i, j ) entry is m [subscript ij], the least residue modulo n of v [subscript in + j] - v [subscript i + j] for i ≥ 0 and j ≥ 0. We study the congruence properties of M and especially of the k x k submatrix M ( [superscript k] ) determined by rows and columns 0 to k - 1. Chapters 1 and 2 introduce the thesis and summarise auxiliary results. Chapter 3 presents background on linear recurring sequences with an emphasis on the matrix approach, including the v - sequence and the k " u - sequences " ( whose initial vectors are the rows of Ik ). Chapter 4 comprises theoretical study of the properties of M for a general k, both when n is a prime and for general n, together with investigation of the condition of Gurak ( 2 ). For ( n, k!D ( ƒ ) ) = 1, we show that the condition of Szekeres is equivalent to the condition that m [subscript i0] = 0 for 1 ≤ i ≤ k and also to certain permutation conditions. Gurak ' s condition is then described using these conditions. Chapter 5 assumes k = 3. For this case we study congruences modulo n satisfied by the m [subscript ij] when n is a prime, and hence develop a combination of tests on M ( [superscript 3] ) which are passed by all primes. We report on extensive computer investigation of composites passing these tests. Such composites are found to be rare. Investigation of the relevant work of Adams and Shanks and colleagues, together with use of the permutation condition of Chapter 4, leads to a modification of the earlier tests on M ( [superscript 3] ). Under suitable assumptions we show that the new modified condition is equivalent to the basic condition of Adams and Shanks and also to that of Gurak but has significant advantages over both. References ( 1 ) Adams, W. and Shanks, D. Strong primality tests that are not sufficient, Math. Comp., 39, 1982, 255-300. ( 2 ) Gurak, S. Pseudoprimes for higher - order linear recurrence sequences, Math. Comp., 55, 1990, 783-813. ( 3 ) Szekeres, G., Higher order pseudoprimes in primality testing, pp 451-458, in Combinatorics, Paul Erdos is eighty, Vol. 2 ( Jesztgektm 1993 ), Bolyai Soc. Math. Stud., 2, Jnos Bolyai Math. Soc. Budapest, 1996. / Thesis (M.Sc.)--School of Mathematical Sciences, 2006.

Abstract Analyzing the eight genomic protein segments of influenza A virus could provide a better understanding of this specific virus. Along with the progress of computer technology, numerous influenza A virus protein sequences were available in various internet data banks. However, analyzing a large number of protein sequences is a cumbersome work. Thus it is necessary to develop new tools with algorithmic method. This study used distributed method to develop a protein sequence clustering analysis software by JAVA programming language. The software could split a large number of protein sequences downloaded from NCBI into several files. Because of these individual files were calculated at the same time, therefore it could reduce the time in process of comparison and analysis. Finally, we used PRIMER 5 program to analyze these individual files and produce similarity analysis chart diagrams of MDS and UPGMA. In The similarity analysis chart diagrams indicated high homology in genomic protein segments of influenza A virus from year 1997 to 2006. The analysis also showed the genomic protein segments of influenza A virus are similar in Asia countries. However, the similarity between Asian countries and China is not significant. From analyzing the hosts, the genomic protein segments of influenza A virus are highly similar in species such like birds, chickens, ducks and pigs. Therefore, our data strongly support that the possibility of influenza A viruses can cross species to infect humans.