Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

Paid employment and the changing system of gender relations: a cross-national comparison

Equality with men in the world of paid work has been a major feminist objective. Given that work in the `public' sphere has historically been shaped on the assumption that the `worker' will be male, then national employment systems which facilitate masculine employment patterns (i.e. full-time work and unbroken employment careers) might be expected to be more likely to generate gender equality. This paper compares women's employment in France (where `masculine' careers for women are common) and Britain (where part-time work and broken employment careers are more likely) at the macro, meso (occupational), and micro (individual) levels. The two occupations studied are finance and pharmacy. The evidence presented suggests that there are considerable similarities between women in the two countries at the occupational and individual level, despite national variations. In the light of this evidence, structural and individual explanations of women's employment behaviour are examined, and the continuing significance of structural constraint on the patterning of gender relations is emphasised.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Linear relation between deuteron matter radius and the scattering length

We explain the empirical linear relations between the triplet scattering length, or the asymptotic normalization constant, and the deuteron matter radius using the effective range expansion in a manner similar to a recent paper by Bhaduri et al. We emphasize the corrections due to the finite force range and to shape dependence. The discrepancy between the experimental values and the empirical line shows the need for a larger value of the wound extension, a parameter which we introduce here. Short-distance nonlocality of the n-p interaction is a plausible explanation for the discrepancy.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

Specificities of defense mechanisms in bipolar affective disorder: relations with symptoms and therapeutic alliance.

Defense mechanisms as a central notion of psychoanalysis have inspired various levels of interest in research in psychotherapy and psychopathology. Defense specificities have only recently been investigated systematically with regard to several clinical diagnoses, such as affective and personality disorders. For the present study, 30 inpatients diagnosed with Bipolar Affective Disorder I (BD) were interviewed. An observer-rater method, the Defense Mechanisms Rating Scales (DMRS), applied to session-transcripts, of assessment of defenses was used. A matched, nonclinical control group was introduced. Defense specificities in BD encompass a set of 5 immature defenses, of which omnipotence is linked with symptom level. The level of the therapeutic alliance is predicted by mature defenses. These results are discussed with regard to the psychological vulnerability of BD, and treatment implications for psychodynamic psychotherapy with such challenging patients are evoked.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Relations entre le programme de promotion des habiletés d’adaptation pour les enfants de 6-7 ans "Les amis de Zippy" et le climat de classe

Le programme d’enseignement des habiletés d’adaptation Les amis de Zippy vise la promotion de la santé mentale des élèves du premier cycle du primaire. La présente étude est une analyse secondaire réalisée à partir des données d’évaluation des effets du programme. L’objectif général vérifie si l’appartenance au groupe d’intervention est associée à une meilleure qualité du climat relationnel de classe à la fin de l’année scolaire, tel que perçu par les enseignants, tout en contrôlant pour la qualité du climat avant la réalisation du programme. La qualité du climat correspond aux relations entre les élèves et aux relations entre les élèves et l’enseignant. L’effet modérateur de la gestion de comportements et les pratiques pédagogiques est aussi analysé. L’échantillon est constitué de 35 enseignants auto-sélectionnés, répartis entre deux groupes non aléatoires. Les échelles suivantes du QES pour le primaire, version enseignant, sont utilisées : relations entre les élèves, relations entre les élèves et les enseignants, gestion des comportements et pratiques pédagogiques. Les résultats, obtenus grâce à des régressions linéaires multiples, montrent que généralement, l’appartenance au groupe n’explique pas significativement la qualité du climat de classe. Cependant, un effet d’interaction entre le climat de classe et la gestion de comportements est identifié. Lorsque les enseignants gèrent plus difficilement leur classe, le programme Les amis de Zippy est associé à un climat relationnel entre les élèves et l’enseignant moins favorable que dans le groupe témoin. Puisque ces résultats préliminaires peuvent être attribuables à des variables externes non contrôlées, ils devront être approfondis par des études subséquentes.

L'évolution des comportements d'agressivité physique de la petite enfance à l'âge scolaire : le rôle des relations d'amitié en début de scolarisation

Cette thèse avait pour objectif d’examiner les liens longitudinaux entre les relations d’amitié et l’évolution des comportements d’agressivité physique en début de scolarisation. Guidé par les principes énoncés par les théoriciens de l’apprentissage social, de l’attachement, du développement de la personnalité et de la théorie du jugement moral, le rôle principal et modérateur de certaines dimensions spécifiques à la qualité de la relation d’amitié, ainsi que des attributs comportementaux des amis et des caractéristiques personnelles de l’enfant a été évalué. Des données provenant de l’Étude Longitudinale du Développement des Enfants du Québec (ELDEQ), de l’Étude des Jumeaux nouveau-nés du Québec (EJNQ) et de l’évaluation des effets d’un programme d’intervention dyadique ont été analysées. Les mesures utilisées dans cette thèse ont été collectées entre la maternelle et la 2e année du primaire, soit de 5 à 8 ans, directement auprès des enfants, de leurs amis, leurs pairs, leurs parents et leurs enseignants par le biais de questionnaires, d’entrevues sociométriques et de mises en situation hypothétiques. En lien avec la perspective de l’apprentissage social, les résultats ont montré que l’association à des amis agressifs en maternelle est liée à une augmentation des comportements d’agressivité physique chez l’enfant. Cependant, en lien avec les théories du développement de la personnalité et la perspective de l’attachement, le fait d’établir une relation d’amitié de bonne qualité est reliée à une diminution des comportements agressifs à travers le temps. De plus, une interaction entre la qualité de la relation et les attributs comportementaux des amis a indiqué que le risque lié à l’association à des amis agressifs est atténué dans le contexte d’une relation d’amitié de bonne qualité. Les résultats indiquent également que chez les garçons, la présence de conflits entre amis à la maternelle est associée de façon linéaire à de plus hauts niveaux de comportements agressifs, indépendamment du risque génétique de l’enfant face à cette problématique. Une interaction triple a par ailleurs révélé que le conflit n’était pas lié à une augmentation de l’agressivité physique dans le contexte d’une relation d’amitié caractérisée par l’affect positif et une bonne capacité à régler les conflits. Enfin, les résultats ont montré un effet indirect d’une intervention dyadique sur la diminution des comportements d’agressivité physique, qui opère à travers l’amélioration de la capacité des amis à régler leurs conflits. Ces résultats appuient le rôle bénéfique de la qualité de la relation d’amitié sur l’évolution des manifestations de comportements d’agressivité physique et suggèrent que cet aspect relationnel soit pris en compte dans les programmes de prévention des conduites agressives. En somme, la mise en évidence d’associations et d’interactions significatives entre la qualité des relations d’amitié, les attributs comportementaux des amis et les manifestations de comportements d’agressivité physique en début de scolarisation suggère que certains aspects et dimensions relationnelles positives peuvent être bénéfiques au développement des enfants agressifs. La prévention du maintien et de l’aggravation des conduites agressives par l’entremise de l’amélioration de la qualité des relations d’amitié représente une avenue prometteuse.