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.

This thesis presents modeling of bilinear flow in tight gas wells and its behavior on single matrix block drainage. The objectives of this research are to: simulate a tight gas well using matrix block drainage under constant production pwf and with a constant production rate; be able to predict the behavior of matrix block drainage; study the effect of natural fracture(s) near a well; examine the matrix block drainage in a natural fracture network; and to validate a matrix block drainage model with a hydraulic fracture analytical solution. Two different production scenarios, constant pwf and constant rate, are assigned to a tight gas well in matrix block drainage. Matrix block drainage has two distinct permeabilities; a low permeability matrix serves as the tight gas reservoir with a high permeability streak surrounding the matrix. A well only produces from the high permeability fracture. Models were run with different sensitivity cases toward fracture half length, xf, and fracture permeability kf,. The fracture half-length reflects on a/b aspect ratio. The analytical solution for hydraulic fracture developed by Cinco-Ley and Guppy serves as the validation of matrix block drainage. Analysis on the flow regimes which occurred for different geometries and properties are provided. The log-log diagnostic plot of pseudo-pressure drop/gas rates and the log-log plot of dimensionless pressure derivatives and dimensionless reciprocal production rates are presented. Finally, an attempt to normalize the late time and early time of all geometries and properties is presented to obtain one analytical solution.

This thesis proposes a new method to compute the lower and upper bounds of solution to the generalized Lyapunov matrix equation. Convergence of the iteratively computed bounds is illustrated by several numerical examples. Moreover, regularization of the condition required in computing the upper bound is also investigated. Finally, the method is employed to derive a less conservative bound on the magnitude of perturbation without destroying the stability of the perturbed system. All the theoretical results are verified by the numerical examples.

This thesis presents modeling of bilinear flow in tight gas wells and its behavior on single matrix block drainage. The objectives of this research are to: simulate a tight gas well using matrix block drainage under constant production pwf and with a constant production rate; be able to predict the behavior of matrix block drainage; study the effect of natural fracture(s) near a well; examine the matrix block drainage in a natural fracture network; and to validate a matrix block drainage model with a hydraulic fracture analytical solution. Two different production scenarios, constant pwf and constant rate, are assigned to a tight gas well in matrix block drainage. Matrix block drainage has two distinct permeabilities; a low permeability matrix serves as the tight gas reservoir with a high permeability streak surrounding the matrix. A well only produces from the high permeability fracture. Models were run with different sensitivity cases toward fracture half length, xf, and fracture permeability kf,. The fracture half-length reflects on a/b aspect ratio. The analytical solution for hydraulic fracture developed by Cinco-Ley and Guppy serves as the validation of matrix block drainage. Analysis on the flow regimes which occurred for different geometries and properties are provided. The log-log diagnostic plot of pseudo-pressure drop/gas rates and the log-log plot of dimensionless pressure derivatives and dimensionless reciprocal production rates are presented. Finally, an attempt to normalize the late time and early time of all geometries and properties is presented to obtain one analytical solution.

Reproduction de : Thèse doctorat : Médecine. Biomolécules et dynamique cellulaire : Reims : 2006. / Titre provenant de l'écran-titre. Bibliogr. p.110-148.

Reproduction de : Thèse doctorat : Pharmacie. Sciences du médicament : Reims : 2008. / Titre provenant de l'écran-titre. Bibliogr.

Thesis (Ph.D.)--Virginia Commonwealth University, 2009. / Prepared for: Dept. of Pharmaceutics. Title from title-page of electronic thesis. Bibliography: leaves 207-235.

abstract / Biochemistry / Doctoral / Doctor of Philosophy

The ectodomain of influenza matrix protein 2 (M2e) may be an ideal candidate in the development of influenza universal vaccine due to its highly conserved property among different subtypes/strains of influenza virus. M2e based vaccines have been extensively studied and potent cross-subtype/strain protections have been reported. However, more and more M2e mutants of influenza virus have been identified in recent years. It is still unclear whether M2e based vaccines are effective against these M2e mutants of influenza virus. This study first evaluated cross-protection of an M2e tetrameric peptide vaccine based on H5N1 virus strain A/Vietnam/1194/04 (VN/1194-M2e) against lethal challenges of M2e mutants of H5N1 virus strain A/Hong Kong/156/97 (HK/156) and a novel H7N9 virus, because there are 3 or 5 amino acid differences between VN/1194-M2e and HK/156-M2e or VN/1194-M2e and H7N9-M2e. The results showed that the vaccination of VN/1194-M2e did not induce high level of cross-reactive antibodies against HK/156-M2e and just provided poor cross-protection against lethal challenge of HK/156 virus. In contrast, VN/1194-M2e vaccination induced high level of cross-reactive antibodies against H7N9-M2e. Consistently, the vaccination provided good cross-protection against lethal challenge of H7N9 virus. These results strongly suggested that some mutations in M2e, such as mutations at positions 10, 14 and 16 which found in HK/156 M2e, might affect the M2e vaccine efficacy, but some others, such as five mutations found in H7N9-M2e, might not be critical for the M2e immunogenicity. This study then investigated the relationship between the M2e immunogenicity and amino acid mutations of the M2e. Beside VN/1194-M2e (P0), we synthesized additional 10 M2e mutant peptides which contain different single or multiple mutations. The 3D structures of these M2e peptides were predicted and analyzed. The prediction results showed that group 1 peptides (P0, P10, P14, P16, P18, P20 and P18-20) exhibited either irregular structures or loose hairpin structures which might associate with well exposure of antigenic epitope, whereas group 2 peptides (P10-14, P10-16, P14-16 and P10-14-16) formed tight hairpin structures in which antigenic epitope might bury inside their own secondary structure. Vaccination efficacies of these M2e peptides were evaluated in mice for antibody responses and cross-protection against lethal challenge of VN/1194 and HK/156 viruses. Our results showed that vaccinations of group 1 peptides induced high levels of cross-reactive antibodies against VN/1194-M2e and good cross-protection against lethal challenge of VN/1194 virus. However, vaccinations of group 2 peptides vaccinations induced significantly lower VN/1194-M2e antibody responses and poor cross-protection against lethal challenge of VN/119 virus. Furthermore, both group 1 and group 2 peptides could just induce low levels of cross-reactive antibodies against HK/156-M2e and poor protection against lethal challenge of HK/156 virus. Although H5N1-M2e tetrameric peptide has been previously shown to protect mice from lethal challenges by different subtypes/strains of influenza virus, this study has shown that certain amino acid variations in M2e could weaken M2e immunogenicity but some others might not. The different secondary structures of M2es may probably associate with their immunogenicity. Our findings have provided valuable information for the development of M2e based universal vaccines. / published_or_final_version / Microbiology / Doctoral / Doctor of Philosophy

Two influenza viruses, the virulent clone 7a (H3N2) and the attenuated A/Fiji/15899/83 (H1NI) (A/Fiji), induce different level ofapoptosis in both MDCK and HeLa cells. Apoptosis induced by these two viruses could be partially inhibited by two NA inhibitors (GGI67 and DANA), when present during virus entry, but not subsequently. GGI67, which cannot enter cells, did not affect the level of infection. These results suggest that NA plays a role in influenza virus-induced apoptosis and that it acts early in the replication cycle. However, ammonium chloride, which prevents virus entry reduced the level of apoptosis induced by both viruses. In addition, amantadine, which prevents virus uncoating, inhibited apoptosis induced by the amantadine-sensitive strain A/Udorn/307/72 (H3N2). Therefore, other viral components acting intracellularly may also be involved in influenza virus-induced apoptosis. Clone 7a, A/Fiji or A/WSN/33 (H1N1)(A/WSN) proteins were expressed in HeLa cells, fused to the Herpes simplex tegument coat protein VP22. This protein has the ability to translocate from the cell in which it is synthesised to surrounding cells. Therefore, VP22- fusion proteins are delivered to a high number of cells, regardless of the level of transfection. A/WSN PB1, PB2 and HA induced significant levels ofapoptosis as did the NA, M1, M2 and NS1 proteins from clone 7a and the M1, M2, NSI and NS2 proteins from A/Fiji. Conversely, clone 7a and A/Fiji NP and A/Fiji PB2 and NA did not induce apoptosis. Confocal microscopy revealed that apoptosis was associated with fusion protein expression and that the location of the proteins corresponded with that expected during influenza virus infection. In addition, the mechanism of clone 7a NA-induced apoptosis was investigated. GGI67 inhibited apoptosis induced by the expression of clone 7a NA. Hence, NA activity is required for the induction of apoptosis. In addition, apoptosis was completely abrogated in the presence of an anti-transforming growth factor (TGF)-B antibody suggesting the activation of TGF-B during the translocation of the fusion protein from one cell to another is involved in clone 7a NA-induced apoptosis. Furthermore, clone 7a and A/Fiji NS1 proteins induced apoptosis when expressed alone, but they inhibited double-stranded (ds) RNA-induced apoptosis. However, the level of apoptosis observed in the presence of dsRNA was not reduced to background levels suggesting a pro and anti-apoptotic action of NS1 in influenza virus-infected cells. The potential mechanisms involved in the induction of apoptosis by each protein and the relevance to infection is discussed.