Dissertations / Theses on the topic 'Prime polynomials'

A compact Riemann surface X is said to be a cyclic p-gonal surface if it admits an automorphism φ of prime order p such that the quotient space X/(φ) has genus 0. It is said to be normal cyclic p-gonal if in addition, the group generated by φ is normal in the full automorphism group of X. In the following notes, we determine a method to find defining polynomial equations for any cyclic p-gonal surface X. If the surface X is assumed to be normal cyclic p-gonal, then all redundancies--equations which are equations for the same surface up to conformal equivalence--are also found.

This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.

Sigui (K,v)un cos valorat discret de rang 1. En un treball pioner, S. MacLane va estudiar i caracteritzar les extensions de la valoració v al cos K(x) de les funcions racionals. M. Vaquié va generalitzar aquest treball al cas d’una valoració v arbitrària, no necessàriament de rang 1 ni discreta. En el cas discret i de rang 1, J. Fernández, J. Guàrdia, J. Montes i E. Nart, van fer una contribució constructiva a la teoria, calculant generadors de les àlgebres graduades d’aquestes valoracions, i introduint certs operadors de polinomis residuals. En aquesta memòria, estenem aquests resultats constructius al cas d’un cos valorat arbitrari, amb una valoració no necessàriament de rang 1 ni discreta. També establim una connexió entre valoracions inductives i polinomis irreductibles amb coeficients en una henselianització K^h de (K,v). Més precisament, construim una aplicació bijectiva M— Po/ =, entre l’espai de MacLane de(K,v) (identificat a un espai de “tipus forts”) i cert quocient del subconjunt Po C P format pels polinomis sense defecte amb coeficients en el cos K . Finalment, apliquem aquestes tècniques a reobtenir resultats sobre el càlcul d’invariants d’elements algebraics moderadament ramificats sobre cossos henselians.
Let (K; v) be a discrete rank-one valued eld. In a pioneering work, S. MacLane studied and characterized the extensions of the valuation v to the rational function eld K(x). M. Vaquié generalized his work for an arbitrary valued eld (K; v), not necessarily rank-one nor discrete. A more constructive contribution for the theory was given in the case where v is discrete of rank-one, where J. Fernández, J. Guàrdia, J. Montes and E. Nart provided a computation of generators of the graded algebras and introduced some residual polynomial operators. In this memoir we extend these results to a valued eld (K; v), not necessarily rank-one nor discrete. We also establish a connection between inductive valuations and irreducible polynomials with coecients in Kh, precisely, we construct a bijective mapping M — P0= between the MacLane space of (K; v) (considered as the set of strong types) and a certain quotient of the subset P0 C P of defectless polynomials with coecients in the henselian eld K. Finally, as an application of the techniques presented in this work we reobtain some results on the computation of invariants of tame algebraic elements over henselian fields

Recursion is a fundamental tool of mathematics used to define, construct, and analyze mathematical objects. This work employs induction, sieving, inversion, and other recursive methods to solve a variety of problems in the areas of algebraic number theory, topological and combinatorial graph theory, and analytic probability and statistics. A common theme of recursively defined functions, weighted sums, and cross-referencing sequences arises in all three contexts, and supplemented by sieving methods, generating functions, asymptotics, and heuristic algorithms. In the area of number theory, this work generalizes the sieve of Eratosthenes to a sequence of polynomial values called polynomial-value sieving. In the case of quadratics, the method of polynomial-value sieving may be characterized briefly as a product presentation of two binary quadratic forms. Polynomials for which the polynomial-value sieving yields all possible integer factorizations of the polynomial values are called recursively-factorable. The Euler and Legendre prime producing polynomials of the form n2+n+p and 2n2+p, respectively, and Landau's n2+1 are shown to be recursively-factorable. Integer factorizations realized by the polynomial-value sieving method, applied to quadratic functions, are in direct correspondence with the lattice point solutions (X,Y) of the conic sections aX2+bXY +cY2+X-nY=0. The factorization structure of the underlying quadratic polynomial is shown to have geometric properties in the space of the associated lattice point solutions of these conic sections. In the area of combinatorial graph theory, this work considers two topological structures that are used to model the process of homologous genetic recombination: assembly graphs and chord diagrams. The result of a homologous recombination can be recorded as a sequence of signed permutations called a micronuclear arrangement. In the assembly graph model, each micronuclear arrangement corresponds to a directed Hamiltonian polygonal path within a directed assembly graph. Starting from a given assembly graph, we construct all the associated micronuclear arrangements. Another way of modeling genetic rearrangement is to represent precursor and product genes as a sequence of blocks which form arcs of a circle. Associating matching blocks in the precursor and product gene with chords produces a chord diagram. The braid index of a chord diagram can be used to measure the scope of interaction between the crossings of the chords. We augment the brute force algorithm for computing the braid index to utilize a divide and conquer strategy. Both assembly graphs and chord diagrams are closely associated with double occurrence words, so we classify and enumerate the double occurrence words based on several notions of irreducibility. In the area of analytic probability, moments abstractly describe the shape of a probability distribution. Over the years, numerous varieties of moments such as central moments, factorial moments, and cumulants have been developed to assist in statistical analysis. We use inversion formulas to compute high order moments of various types for common probability distributions, and show how the successive ratios of moments can be used for distribution and parameter fitting. We consider examples for both simulated binomial data and the probability distribution affiliated with the braid index counting sequence. Finally we consider a sequence of multiparameter binomial sums which shares similar properties with the moment sequences generated by the binomial and beta-binomial distributions. This sequence of sums behaves asymptotically like the high order moments of the beta distribution, and has completely monotonic properties.

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Capes
Neste trabalho apresentaremos um estudo sobre polinômios centrais ordinários, Z2-graduados e com involução para algumas importantes álgebras na PI-teoria sobre corpos infinitos. Mais precisamente, descreveremos os polinômios centrais Z2-graduados para as álgebras M2(K) (matrizes 2 × 2 sobre um corpo K), M1,1(E) (subálgebra de M2(E) que consite das matrizes cujas entradas da diagonal principal estão em E0 e os da diagonal secundária estão em E1,onde E é a álgebra de Grassmann com unidade de dimensão infinita e E0 e E1 suas componentes homogêneas de graus 0 e 1, respectivamente) e E ⊗ E. Além disso descreveremos os polinômios centrais para E sobre um corpo infinito K de característica diferente de 2 e finalmente os polinômios centrais com involução para M2(K), considerando as involuções transposta e simplética.
In this work we study ordinary, Z2-graded central polinomials and central polinomials with involution for some important algebras in the theory of algebras with polinomial identities, over infinite fields.Namely, we decribe Z2-graded central polinomials for the algebras M2(K) (2 × 2 matrices over a field K), M1,1(E) (subalgebra of M2(E) whose entries on the diagonal belong to E0 and the off-diagonal entries lie in E1, E is the infinite-dimensional unitary Grassmann algebra, E0 is the center of E and E1 is the anticommutative part of E) and E ⊗ E. Also, we describe the central polinomials for e over a field K, with charK ≠ 2 and finally the central polinomial with involution for M2 (K), considering the transpose and the sympletic involutions.

In the last twenty years, algebraic techniques have been applied with great success to several areas in theoretical computer science. However, for many problems involving modular counting, there is a huge gap in our understanding depending on whether the modulus is prime or composite. A prime example is the problem of showing lower bounds for circuits with Mod gates in circuit complexity. Proof techniques that work well for primes break down over composites. Moreover, in some cases, the problem for composites turns out to be very different from the prime case. Making progress on these problems seems to require a better understanding of polynomials over composites. In this thesis, we address some such "prime vs. composite" problems from algorithms, complexity and combinatorics, and the surprising connections between them. We consider the complexity-theoretic problem of computing Boolean functions using polynomials modulo composites. We show that symmetric polynomials can viewed as simultaneous communication protocols. This equivalence allows us to use techniques from communication complexity and number theory to prove degree bounds. We use these to give the first tight degree bounds for a number of Boolean functions. We consider the combinatorial problem of explicit construction of Ramsey graphs. We present a simple construction of such graphs using polynomials modulo composites. This approach gives a unifying view of many known constructions,and explains why they all achieve the same bound.We show that certain approaches to this problem cannot give better bounds. Finally, we consider the algorithmic problem of interpolation for polynomials modulo composites. We present the first query-efficient algorithms for interpolation and learning under a distribution. These results rely on some new structural results about such polynomials.

We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.
M.S.
Department of Mathematics
Arts and Sciences
Mathematics

This thesis is a contribution to arithmetic combinatorics. We present the Green-Tao method and the Green-Tao-Ziegler theorem concerning asymptotics for linear configura- tions of primes. Then we show extensions of our own to this theorem: first to some family of quadratic configurations, and secondly to configurations with unbounded coefficients. As a result, we are able to provide an asymptotic for configurations of primes inside the set of shifted squarefree numbers. We then leave integers and move to vector spaces over finite fields. In this context, we prove a bidirectional additive smoothing result for sets of pairs P ⊂ Fnp × Fnp . This is a bilinear version of Bogolyubov’s theorem. We then equip these vector spaces with a multiplicative structure, that is, we consider polynomial rings over finite fields. Using the Croot-Lev-Pach method, we show that sets of polynomials of degree less than n that contain no nontrivial solution to a given polynomial equation (of some specific type) is exponentially small. Finally, we seek to apply the Green-Tao method on polynomial rings, with the intention of deriving asymptotics for configurations of irreducible polynomials. To this aim, we bound correlations of the M ̈obius function with linear and quadratic phases.

Ce travail de thèse porte sur l’analyse robuste et l’optimisation fiabiliste des problèmes vibro-acoustiques (ou en interaction fluide-structure) en tenant en compte des incertitudes des paramètres d’entrée. En phase de conception et de dimensionnement, il parait intéressant de modéliser les systèmes vibro-acoustiques ainsi que leurs variabilités qui peuvent être essentiellement liées à l’imperfection de la géométrie ainsi qu’aux caractéristiques des matériaux. Il est ainsi important, voire indispensable, de tenir compte de la dispersion des lois de ces paramètres incertains afin d’en assurer une conception robuste. Par conséquent, l’objectif est de déterminer les capacités et les limites, en termes de précision et de coûts de calcul, des méthodes basées sur les développements en chaos polynomiaux en comparaison avec la technique référentielle de Monte Carlo pour étudier le comportement mécanique des problèmes vibro-acoustique comportant des paramètres incertains. L’étude de la propagation de ces incertitudes permet leur intégration dans la phase de conception. Le but de l’optimisation fiabiliste Reliability-Based Design Optimization (RBDO) consiste à trouver un compromis entre un coût minimum et une fiabilité accrue. Par conséquent, plusieurs méthodes, telles que la méthode hybride (HM) et la méthode Optimum Safety Factor (OSF), ont été développées pour atteindre cet objectif. Pour remédier à la complexité des systèmes vibro-acoustiques comportant des paramètres incertains, nous avons développé des méthodologies spécifiques à cette problématique, via des méthodes de méta-modèlisation, qui nous ont permis de bâtir un modèle de substitution vibro-acoustique, qui satisfait en même temps l’efficacité et la précision du modèle. L’objectif de cette thèse, est de déterminer la meilleure méthodologie à suivre pour l’optimisation fiabiliste des systèmes vibro-acoustiques comportant des paramètres incertains
This PhD thesis deals with the robust analysis and reliability optimization of vibro-acoustic problems (or fluid-structure interaction) taking into account the uncertainties of the input parameters. In the design and dimensioning phase, it seems interesting to model the vibro-acoustic systems and their variability, which can be mainly related to the imperfection of the geometry as well as the characteristics of the materials. It is therefore important, if not essential, to take into account the dispersion of the laws of these uncertain parameters in order to ensure a robust design. Therefore, the purpose is to determine the capabilities and limitations, in terms of precision and computational costs, of methods based on polynomial chaos developments in comparison with the Monte Carlo referential technique for studying the mechanical behavior of vibro-acoustic problems with uncertain parameters. The study of the propagation of these uncertainties allows their integration into the design phase. The goal of the reliability-Based Design Optimization (RBDO) is to find a compromise between minimum cost and a target reliability. As a result, several methods, such as the hybrid method (HM) and the Optimum Safety Factor (OSF) method, have been developed to achieve this goal. To overcome the complexity of vibro-acoustic systems with uncertain parameters, we have developed methodologies specific to this problem, via meta-modeling methods, which allowed us to build a vibro-acoustic surrogate model, which at the same time satisfies the efficiency and accuracy of the model. The objective of this thesis is to determine the best methodology to follow for the reliability optimization of vibro-acoustic systems with uncertain parameters

Face à l’augmentation des exigences à la fois économiques et de santé publique, les industriels sont dans la nécessité de concevoir des systèmes mécaniques de plus en plus performants et respectant un certain niveau de confort acoustique. En mécanique ou en acoustique, le contrôle de vibrations est un champ de recherche très actif. Trois grands types de technologie sont majoritairement utilisées dans l’industrie : le contrôle passif par dissipation, le contrôle passif à l’aide d’absorbeurs linéaires accordées et le contrôle actif, chacune de ses techniques possédant ses avantages et ses inconvénients. Depuis une quinzaine d’années, l’utilisation d’absorbeurs non linéaires de type NES (« Nonlinear Energy Sink » en anglais), typiquement un système masse-ressort-amortisseur à raideur purement non linéaire, a montré son efficacité comme solution alternative de contrôle passif des vibrations en conciliant les avantages des technologies existantes. Cependant, le comportement dynamique du système couplé constitué du NES et du système primaire à protéger peut s’avérer très sensible aux paramètres qui admettent une dispersion importante. Notamment, lorsqu’il s’agit d’atténuer une instabilité dynamique (comme c’est le cas dans cette thèse) une discontinuité dans le profil de l’amplitude vibratoire du système peut s’observer, ce dernier passant brutalement d’un régime atténué (où le NES agit) à un régime non atténué (où le NES n’agit pas). Un régime non atténué étant potentiellement dangereux, il est important d’être en mesure, en prenant en compte les incertitudes paramétriques auxquelles le système primaire peut être confronté, de concevoir un NES qui soit robuste, c’est-à-dire fonctionnant au maximum dans l’espace des paramètres incertains correspondant à des régimes non atténués du système primaire.Dans la première partie, des méthodes basées sur le formalisme du chaos polynomial sont proposées pour la localisation, dans l’espace des paramètres incertains du système primaire, de la frontière entre la région correspondant aux régimes atténués et celle correspondant aux régimes non atténués, permettant ainsi le calcul de la propension du système couplé à être dans un régime atténué. Ces méthodes sont ensuite appliquées aux cas d’un système frottant à deux degrés de liberté (le modèle dit de Hultèn) couplé à deux NES identiques. Les résultats montrent d’une part que les méthodes basées sur le chaos polynomial permettent de réduire significativement le cout de calcul par rapport à la méthode de référence en conservant une bonne précision et d’autre part que la méthode basée sur le chaos polynomial multi-éléments (appelée méthode ME-gPC) est la plus efficace.Dans la deuxième partie, une méthodologie d'optimisation des NES sous incertitudes est développée. Deux approches sont proposées, à chaque fois basées sur la maximisation, sous incertitudes des paramètres du système primaire, de la propension du système couplé à être dans un régime atténué. La première approche considère que les paramètre des NES sont déterministes et sont donc les variables de conception à optimiser. La seconde méthode considère que les paramètres des NES sont également incertains mais avec une loi de probabilité connue. Ainsi, les variables de conception à optimiser ne sont plus directement les paramètres des NES mais l’une de leurs statistiques (la moyenne ou l’écart-type par exemple) appelées hyper-paramètres. Les résultats obtenus sont comparés à une optimisation déterministe de référence. L’efficacité des méthodes proposée, basées sur le chaos polynomial, à réduire significativement le cout de calcul en gardant une bonne précision est mise en évidence
Faced with increasing economic and public health requirements, industrialists are faced with the need to design increasingly efficient mechanical systems that respect a certain level of acoustic comfort. In mechanics or acoustics, vibration control is a very active field of research. Three main types of technology are mainly used in industry: passive control by dissipation, passive control using tuned linear absorbers and active control, each of these techniques having its advantages and disadvantages. Over the past 15 years, the use of NES (Nonlinear Energy Sink) non-linear absorbers, typically a purely non-linear stiffness mass-spring-damper system, has proven its effectiveness as an alternative solution for passive vibration control by combining the advantages of existing technologies. However, the dynamic behaviour of the coupled system consisting of the NES and the primary system to be protected can be very sensitive to parameters that allow for high dispersion. In particular, when attenuating dynamic instability (as is the case in this thesis) a discontinuity in the vibration amplitude profile of the system can be observed, as the system suddenly switches from an attenuated regime (where the NES acts) to an unattenuated regime (where the NES does not act). Since an unattenuated regime is potentially dangerous, it is important to be able, taking into account the parameter uncertainties that the primary system may face, to design an NES that is robust, i.e. operating at maximum within the space of the uncertain parameters corresponding to unattenuated regimes of the primary system.In the first part, methods based on the formalism of polynomial chaos are proposed for locating, in the space of the uncertain parameters of the primary system, the boundary between the region corresponding to attenuated regimes and that corresponding to non-attenuated regimes, thus allowing the calculation of the propensity of the coupled system to be in an attenuated regime. These methods are then applied to the cases of a two-degree-of-freedom friction system (the so-called Hultèn model) coupled to two identical NES. The results show, on the one hand, that the methods based on polynomial chaos allow a significant reduction of the calculation cost compared to the reference method while maintaining a good accuracy and, on the other hand, that the method based on multi-element polynomial chaos (called ME-gPC method) is the most efficient.In the second part, a methodology for optimizing NES under uncertainty is developed. Two approaches are proposed, each based on maximizing, under uncertainties of the primary system parameters, the propensity of the coupled system to be in a mitigated regime. The first approach considers that the SNF parameters are deterministic and are therefore the design variables to be optimized. The second approach considers that the SEL parameters are also uncertain but with a known probability distribution. Thus, the design variables to be optimized are no longer directly the parameters of the NES but one of their statistics (the mean or the standard deviation for example) called hyper-parameters. The results obtained are compared with a reference deterministic optimization. The effectiveness of the proposed methods, based on polynomial chaos, to significantly reduce the cost of calculation while maintaining good precision is highlighted

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A modelagem de processos industriais tem auxiliado na produ??o e minimiza??o de custos, permitindo a previs?o dos comportamentos futuros do sistema, supervis?o de processos e projeto de controladores. Ao observar os benef?cios proporcionados pela modelagem, objetiva-se primeiramente, nesta disserta??o, apresentar uma metodologia de identifica??o de modelos n?o-lineares com estrutura NARX, a partir da implementa??o de algoritmos combinados de detec??o de estrutura e estima??o de par?metros. Inicialmente, ser? ressaltada a import?ncia da identifica??o de sistemas na otimiza??o de processos industriais, especificamente a escolha do modelo para representar adequadamente as din?micas do sistema. Em seguida, ser? apresentada uma breve revis?o das etapas que comp?em a identifica??o de sistemas. Na sequ?ncia, ser?o apresentados os m?todos fundamentais para detec??o de estrutura (Modificado Gram- Schmidt) e estima??o de par?metros (M?todo dos M?nimos Quadrados e M?todo dos M?nimos Quadrados Estendido) de modelos. No trabalho ser? tamb?m realizada, atrav?s dos algoritmos implementados, a identifica??o de dois processos industriais distintos representados por uma planta de n?vel did?tica, que possibilita o controle de n?vel e vaz?o, e uma planta de processamento prim?rio de petr?leo simulada, que tem como objetivo representar um tratamento prim?rio do petr?leo que ocorre em plataformas petrol?feras. A disserta??o ? finalizada com uma avalia??o dos desempenhos dos modelos obtidos, quando comparados com o sistema. A partir desta avalia??o, ser? poss?vel observar se os modelos identificados s?o capazes de representar as caracter?sticas est?ticas e din?micas dos sistemas apresentados nesta disserta??o

碩士
國立清華大學
數學系
89
Let A be a prime ring with char(A) not 2, and with extended centroid C and Q be the maximal right quotient ring of A. Let F be a subring with 1 of the field C. Let f be a nonzero multilinear polynomial of F. Let S be a ring (or, F-algebra) and let a be an additive homomorphism of groups (or, F-modules respectively) from S to Q, and c belong to C, such that a(f(s1,s2,...,sm))=cf(a(s1),a(s2),...,a(sm)). Let R=Im(a). If R is a 2m-free subset of Q, then there exists a homomorphism or an anti-homomorphism of rings (or, F-algebras) b from S to RC+C, an additive map v from S to C, and t belong to C, such that a(s)=tb(s)+v(s), and ct^(m-1)=1 or -1. Moreover, if R is a left ideal of A and deg(R)>2m+2, then we also have the same conclusion.

This dissertation explores an analogue of the prime number theorem for polynomials over finite fields as well as its connection to the necklace factorization algorithm T-transform and the string complexity measure T-complexity. Specifically, a precise asymptotic expansion for the prime polynomial counting function is derived. The approximation given is more accurate than previous results in the literature while requiring very little computational effort. In this context asymptotic series expansions for Lerch transcendent, Eulerian polynomials, truncated polylogarithm, and polylogarithms of negative integer order are also provided. The expansion formulas developed are general and have applications in numerous areas other than the enumeration of prime polynomials. A bijection between the equivalence classes of aperiodic necklaces and monic prime polynomials is utilized to derive an asymptotic bound on the maximal T-complexity value of a string. Furthermore, the statistical behaviour of uniform random sequences that are factored via the T-transform are investigated, and an accurate probabilistic model for short necklace factors is presented. Finally, a T-complexity based conditional string complexity measure is proposed and used to define the normalized T-complexity distance that measures similarity between strings. The T-complexity distance is proven to not be a metric. However, the measure can be computed in linear time and space making it a suitable choice for large data sets.
Graduate
0544 0984 0405
nrebenich@gmail.com

碩士
國立成功大學
數學系應用數學碩博士班
97
In this thesis, we talk about polynomial identity first, where all element substitute into the fixed polynomial can vanish in the algebra R. As following process, we introduce several useful theorems to discuss the structure of prime ring, which mention that these rings have polynomial identities.

碩士
中國文化大學
資訊管理學系
100
The main factors which affect stock prices can be elaborated to two respects: one is the fundamental plane, and the other is the technical plane. Analysis in the fundamental plane can indicate financial statement of a corporation. Financial index is the spindle of fundamental-plane analysis; we can analyze financial structure, debt-paying ability, business capacity, profit ability, cash flow and so on from financial index of a corpora-tion so as to realize the factors influence stock price fluctuation further. This paper proposes methods using linear polynomial and polynomial regression. To begin with acquiring weighting coefficient of financial index, and then it is combined with the financial index resulted from a polynomial regression forecasting. As a result, the prediction of stock price rise and fall is obtained. In conclusion, there are two results indicated from this paper. First, the methods of the research that use the relationship between financial index and stock price can obtain the credibility of the financial factor weight. Investors giving priority to the fundamental plane could see the degree of correlation as a reference, to know whether the stock investing is able to meet the expectation via estimating by financial index. Second, selecting 39 listed companies, when the financial index weight of the credibility is higher than 83%, the accuracy rate of the 39 listed companies of forecasting stock price rise and fall was 58.57% ~ 64.71%. This result provides a valuable reference of forecasting stock price variation to a certain degree.

In a preceding paper [9] we reported on some experience with a new version of the well known Gröbner algorithm with factorization and constraint inequalities. Here we discuss, how this approach may be refined to produce triangular systems in the sense of [12] and [13]. Such a refinement guarantees, different to the usual Gröbner factorizer, to produce a quasi prime decomposition, i.e. the resulting components are at least pure dimensional radical ideals. As in [9] our method weakens the usual restriction to lexicographic term orders. Triangular systems are a very helpful tool between factorization at a heuristical level and full decomposition into prime components. Our approach grew up from a consequent interpretation of the algorithmic ideas in [5] as a delayed quotient computation in favour of early use of (multivariate) factorization. It is implemented in version 2.2 of the REDUCE package CALI [8].

This work presents a fracture mechanics analysis of the cathodic delamination problem for the polyurethane/titanium and polyurea/steel interfaces. The nonlinear behavior of both polymers was investigated. The recent Marlow model was used to define the strain energy function of the polymers. Viscoelastic effects of the polyurea were also studied. The Marlow model was associated with a nine-term Prony series. This model was seen to represent experimental data relatively well for a wide range of strain rates both in tension and compression. The driving force for delamination, the strain energy release rate G, is presented for both interfaces. Cathodic delamination data for several temperatures are presented as crack growth rate as a function of crack driving force. The approach recognizes that both temperature and stress can be used as accelerated life testing parameters.
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