The sources of moral motivation : studies on empathy, guilt, shame and values

The goals of this study were to analyze the forms of emotional tendencies that are likely to motivate moral behaviors, and to find correlates for these tendencies. In study 1, students narratives of their own guilt or shame experiences were analyzed. The results showed that pure shame was more likely to motivate avoidance than reparation, whereas guilt and combination of guilt and shame were likely to motivate reparation. However, all types of emotion could lead to chronic rumination if the person was not clearly responsible for the situation. In study 2, the relations of empathy with two measures of guilt were examined in a sample of 13- to 16-year-olds (N=113). Empathy was measured using Davis s IRI and guilt by Tangney s TOSCA and Hoffman s semi-projective story completion method that includes two different scenarios, guilt over cheating and guilt over inaction. Empathy correlated more strongly with both measures of guilt than the two measures correlated with each other. Hoffman s guilt over inaction was more strongly associated with empathy measures in girls than in boys, whereas for guilt over cheating the pattern was the opposite. Girls and boys who describe themselves as empathetic may emphasize different aspect of morality and feel guilty in different contexts. In study 3, cultural and gender differences in guilt and shame (TOSCA) and value priorities (the Schwartz Value Survey) were studied in samples of Finnish (N=156) and Peruvian (N=159) adolescents. Gender differences were found to be larger and more stereotypical among the Finns than among the Peruvians. Finnish girls were more prone to guilt and shame than boys were, whereas among the Peruvians there was no gender difference in guilt, and boys were more shame-prone than girls. The results support the view that psychological gender differences are largest individualistic societies. In study 4, the relations of value priorities to guilt, shame and empathy were examined in two samples, one of 15 19-year-old high school students (N = 207), and the other of military conscripts (N = 503). Guilt was, in both samples, positively related to valuing universalism, benevolence, tradition, and conformity, and negatively related to valuing power, hedonism, stimulation, and self-direction. The results for empathy were similar, but the relation to the openness conservation value dimension was weaker. Shame and personal distress were weakly related to values. In sum, shame without guilt and the TOSCA shame scale are tendencies that are unlikely to motivate moral behavior in Finnish cultural context. Guilt is likely to be connected to positive social behaviors, but excessive guilt can cause psychological problems. Moral emotional tendencies are related to culture, cultural conceptions of gender and to individual value priorities.

The Herzog-Vasconcelos conjecture for affine semigroup rings

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

A Triangulation of CP3 as Symmetric Cube of S-2

The symmetric group acts on the Cartesian product (S (2)) (d) by coordinate permutation, and the quotient space is homeomorphic to the complex projective space a'',P (d) . We used the case d=2 of this fact to construct a 10-vertex triangulation of a'',P (2) earlier. In this paper, we have constructed a 124-vertex simplicial subdivision of the 64-vertex standard cellulation of (S (2))(3), such that the -action on this cellulation naturally extends to an action on . Further, the -action on is ``good'', so that the quotient simplicial complex is a 30-vertex triangulation of a'',P (3). In other words, we have constructed a simplicial realization of the branched covering (S (2))(3)-> a'',P (3).

EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

On linear series and a conjecture of D. C. Butler

Let C be a smooth irreducible projective curve of genus g and L a line bundle of degree d generated by a linear subspace V of H-0 (L) of dimension n+1. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map V circle times O-C -> L and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.

Equilibrium and equivariant triangulations of some small covers with minimum number of vertices

Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal 4-equivariant triangulations of 2-dimensional small covers. We discuss vertex minimal equilibrium triangulations of RP3#RP3, S-1 x RP2 and a nontrivial S-1 bundle over RP2. We construct some nice equilibrium triangulations of the real projective space RPn with 2(n) + n 1 vertices. The main tool is the theory of small covers.

Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

An evolutionary formalism for weak quantum measurements

Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs, which is consistent with the well-established framework of quantum mechanics. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of the Born rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Relative mirror symmetry and ramifications of a formula for Gromov-Witten invariants

For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

Modelando evolução por endossimbiose

Nesta dissertação é apresentada uma modelagem analítica para o processo evolucionário formulado pela Teoria da Evolução por Endossimbiose representado através de uma sucessão de estágios envolvendo diferentes interações ecológicas e metábolicas entre populações de bactérias considerando tanto a dinâmica populacional como os processos produtivos dessas populações. Para tal abordagem é feito uso do sistema de equações diferenciais conhecido como sistema de Volterra-Hamilton bem como de determinados conceitos geométricos envolvendo a Teoria KCC e a Geometria Projetiva. Os principais cálculos foram realizados pelo pacote de programação algébrica FINSLER, aplicado sobre o MAPLE.

Cálculo de área de poligonais geodésicas ou loxodrômicas sobre o elipsóide do Sistema Geodésico WGS-84.

O cálculo da área de poligonais geodésicas é um desafio matemático instigante. Como calcular a área de uma poligonal sobre o elipsóide, se seus lados não possuem parametrização conhecida? Alguns trabalhos já foram desenvolvidos no intuito de solucionar este problema, empregando, em sua maioria, sistemas projetivos equivalentes ou aproximações sobre esferas autálicas. Tais métodos aproximam a superfície de referência elipsoidal por outras de mais fácil tratamento matemático, porém apresentam limitação de emprego, pois uma única superfície não poderia ser empregada para todo o planeta, sem comprometer os cálculos realizados sobre ela. No Código de Processo Civil, Livro IV, Título I, Capítulo VIII, Seção III artigo 971 diz, em seu parágrafo único, que não havendo impugnação, o juiz determinará a divisão geodésica do imóvel. Além deste, existe ainda a Lei 10.267/2001, que regula a obrigatoriedade, para efetivação de registro, dos vértices definidores dos limites dos imóveis rurais terem suas coordenadas georreferenciadas ao Sistema Geodésico Brasileiro (SGB), sendo que áreas de imóveis menores que quatro módulos fiscais terão garantida isenção de custos financeiros.Este trabalho visa fornecer uma metodologia de cálculo de áreas para poligonais geodésicas, ou loxodrômicas, diretamente sobre o elipsóide, bem como fornecer um programa que execute as rotinas elaboradas nesta dissertação. Como a maioria dos levantamentos geodésicos é realizada usando rastreadores GPS, a carga dos dados é pautada em coordenadas (X, Y, Z), empregando o Sistema Geodésico WGS-84, fornecendo a área geodésica sem a necessidade de um produto tipo SIG. Para alcançar o objetivo deste trabalho, foi desenvolvida parametrização diferente da abordagem clássica da Geodésia geométrica, para transformar as coordenadas (X, Y, Z) em geodésicas.

Ditos populares em músicas do cancioneiro popular: uma abordagem cognitiva

Nesta dissertação, analisam-se alguns ditos populares retomados em músicas do cancioneiro popular, com base na teoria da metáfora conceptual (Lakoff e Jonhson, 1980; Kövecses, 2002), e na teoria da integração conceptual (Fauconnier e Turner, 2002). Busca se investigar se a projeção metafórica presente no dito empregado em situações cotidianas se sustenta, quando o mesmo é retomado em uma letra de música. Este estudo encontra sua justificativa em uma das assunções basilares da linguística cognitiva de que as metáforas conceptuais estão presentes tanto nas conversas cotidianas quanto nas manifestações literárias e artísticas. Pretende se, assim, observar a multidirecionalidade dos processos de significação desse tipo de construção linguística, a fim de postular seu poder projetivo e metafórico na mente dos falantes. Dentro do repertório de construções proverbiais em português, é perceptível a construção proverbial condicional com a configuração sintático semântica [x P Q], entre as quais foi escolhida como objeto de estudo a configuração [Quem P Q]. A escolha das músicas foi aleatória, já que não se buscou um gênero ou estilo específico, mas canções que possuíssem ditos populares em suas letras. Na análise, de cunho interpretativo, procedeu-se a identificação do papel da metáfora conceptual presente no dito empregado em situações cotidianas e nas 10 músicas selecionadas para este estudo. Em seguida, postularam-se redes de integração conceptual subjacente ao sentido dos ditos nas interações em geral e nas músicas, de modo a explicar que as diferenças de sentido observadas ou não nos ditos transpostos para letras de músicas estão relacionadas ao tipo de rede de integração conceptual ativado durante o processo de mesclagem. As redes de integração postuladas para explicar a construção de sentido dos ditos e destes nas músicas analisadas, revelam compressões das relações de CAUSA EFEITO, MUDANÇA, IDENTIDADE, ANALOGIA DESANALOGIA e TEMPO, devido, sobretudo, ao papel que os ditos desempenham ao ilustrar cenas da vida das pessoas. Entre as metáforas que estruturam os ditos, nas interações e nas músicas, encontram-se A VIDA É UMA VIAGEM / A VIDA É UM TRAJETO QUE DEVE SER PERCORRIDO COM CAUTELA / VIDA É UM JOGO DE AZAR; TEMPO É LOCAL PARA ONDE ALGO SE DESLOCA; DIFICULDADES SÃO IMPEDIMENTOS (IN) TRANSPONÍVEIS; RELIGIÃO É UMA TRANSAÇÃO COMERCIAL; MORAL É UM OBJETO PRECIOSO (MAS FRÁGIL COMO O VIDRO); EXAGEROS SÃO GOLPES INCERTOS. Espera-se que a hipótese aventada com este estudo motive outras pesquisas sob o escopo teórico da Linguística Cognitiva; em especial, as teorias da metáfora e da mesclagem conceptual, as quais revelaram um potencial descritivo promissor para análise de fenômenos semântico-pragmáticos da língua portuguesa, como os ditos populares, construções situadas no topo da escala de idiomaticidade