Problème inverse de Galois : critère de rigidité

Dans ce mémoire, on étudie les extensions galoisiennes finies de C(x). On y démontre le théorème d'existence de Riemann. Les notions de rigidité faible, rigidité et rationalité y sont développées. On y obtient le critère de rigidité qui permet de réaliser certains groupes comme groupes de Galois sur Q. Plusieurs exemples de types de ramification sont construis.

Reflections of universal algebras into semilattices, their Galois theories, and related factorization systems

Estabelecemos uma condição suficiente para a preservação dos produtos finitos, pelo reflector de uma variedade de álgebras universais numa subvariedade, que é, também, condição necessária se a subvariedade for idempotente. Esta condição é estabelecida, seguidamente, num contexto mais geral e caracteriza reflexões para as quais a propriedade de ser semi-exacta à esquerda e a propriedade, mais forte, de ter unidades estáveis, coincidem. Prova-se que reflexões simples e semi-exactas à esquerda coincidem, no contexto das variedades de álgebras universais e caracterizam-se as classes do sistema de factorização derivado da reflexão. Estabelecem-se resultados que ajudam a caracterizar morfismos de cobertura e verticais-estáveis em álgebras universais e no contexto mais geral já referido. Caracterizam-se as classes de morfismos separáveis, puramente inseparáveis e normais. O estudo dos morfismos de descida de Galois conduz a condições suficientes para que o seu par kernel seja preservado pelo reflector.

Southern New England Social and Community Plan 2009 - Covering Local Government Authorities: Armidale Dumaresq, Guyra, Uralla and Walcha

The Southern New England (SNE) Social and Community Plan is a guide to collaborative, integrated planning involving the three spheres of government, the community and commercial sectors. The Plan is based on social justice principles such as: • Equity - fairness in resource distribution, particularly for those most in need • Access - fairer access for everyone to the economic resources and services essential to meeting their basic needs and improving their quality of life • Rights - recognition and promotion of civil rights • Participation - better opportunities for genuine participation and consultation about decisions affecting people's lives. The Plan is also aimed at improving the accountability of decision-makers, and should help the councils, in conjunction with their communities meet the state government's social justice commitments. Preparation of a social and community plan is required at least every five years, and as with most councils, Armidale Dumaresq Council (ADC) has produced two already, one in 1999 and one in 2004, following the amalgamation of the former Armidale City and Dumaresq Shire Councils in 2000. Those Councils formerly prepared their own Plans in 1999, based on shared consultancy work on a community profile. This is the first joint Southern New England Plan, featuring Armidale Dumaresq, Walcha, Uralla and Guyra Councils. This Social Plan has aimed to identify and address the needs of the local community by: • describing who makes up the community • summarising key priority issues • assessing the effectiveness of any previous plans • recommending strategic ways for council and other government and non-government agencies to met community needs.

Novel protective covering to enhance concrete resistance against projectile impact

A novel protective covering with a layered and staggered structure was proposed to protect concrete against projectile impact. Experimental study was conducted to investigate the ballistic behaviour of the concrete targets against 12.7 mm armour-piercing incendiary projectile at velocities ranging from 537.7 to 596.5 m/s. The results showed that the concrete targets with protective covering exhibited superior integrity with no damage on the distal surface, whereas the concrete targets without protective covering were fractured with penetrating cracks throughout the thickness of the target. Moreover, the protected concrete targets displayed significantly reduced penetration depth compared with the concrete targets without protective covering. The protective covering with epoxy adhesive interlayers had a bigger protection factor than that with silicone sealant interlayers, but the former suffered more severe damage than the latter.

Difference covering arrays and pseudo-orthogonal Latin squares

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146.

In search of Gustav: The story of the Lilienfeld (later Lynfield) family covering the last 200 years 1800-1920

This is the first of three books about the history of Geoffrey Lynfield's family. It is about four Lilienfeld brothers--Geoffrey Lynfield's grandfather and his brothers. They were born in the Jewish enclave of Marburg and ended up in South Africa when and where the first diamonds were discovered. The manuscript also includes photographs and documents.

Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

Special Frobenius Traces in Galois Representations

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues a_p of classical elliptical modular newforms f of weight 2 are never extremal, i.e., a_p is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

Calcite covering of sediment as a possible way of curbing blue-green algae

Natural calcite precipitation in lakes is a well-known control mechanism of eutrophication. In hard-water lakes, calcite deposits on the flat bottoms of shallow lakes and near the shores of deeper lakes resulted from biogenic decalcification during the millenia after the last glacial period. The objective of a new restoration technology is to intensify the natural process of precipitation by utilizing the different qualities of calcareous mud layers. In a pilot experiment in Lake Rudower See, East Germany, phosphorus-poor deeper layers of the sediments were flushed out and spread over the phosphorus-rich uppermost sediments, to promote the co- precipitation of calcite with phosphorus from the water-column.

Observation of early to full covering stages of ethylene-based CVD of graphene

Scalable growth is essential for graphene-based applications. Recent development has enabled the achievement of the scalability by use of chemical vapor deposition (CVD) at 1000°C with copper as a catalyst and methane as a precursor gas. Here we report our observation of early stage of graphene growth based on an ethylene-based CVD method, capable of reducing the growth temperature to 770°C for monolayer graphene growth on copper. We track the early stages of slow growth under low ethylene flow rate and observe the graphene domain evolution by varying the temperature and growth time. Temperature-dependence of graphene domain density gives an apparent activation energy of 1.0 eV for nucleation.

Iris recognition algorithm based on point covering of high-dimensional space and neural network

In this paper, we constructed a Iris recognition algorithm based on point covering of high-dimensional space and Multi-weighted neuron of point covering of high-dimensional space, and proposed a new method for iris recognition based on point covering theory of high-dimensional space. In this method, irises are trained as "cognition" one class by one class, and it doesn't influence the original recognition knowledge for samples of the new added class. The results of experiments show the rejection rate is 98.9%, the correct cognition rate and the error rate are 95.71% and 3.5% respectively. The experimental results demonstrate that the rejection rate of test samples excluded in the training samples class is very high. It proves the proposed method for iris recognition is effective.

Manifold covering theory in biomimetic pattern recognition

We describe a new model which is based on the concept of cognizing theory. The method identifies subsets of the data which are embedded in arbitrary oriented lower dimensional space. We definite manifold covering in biomimetic pattern recognition, and study its property. Furthermore, we propose this manifold covering algorithm based on Biomimetic Pattern Recognition. At last, the experimental results for face recognition demonstrates that the correct rejection rate of the test samples excluded in the classes of training samples is very high and effective.

incomplete exponential sums over galois rings with applications to some binary sequences derived from z(2l)

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