A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

On the Chern classes and the Euler characteristic for nonsingular complete intersections

It is shown that Hirzebruch's result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in PN(C), is also valid for any nonsingular complete intersection. Then rela- tions between Euler characteristic, class and Milnor number are pointed out.

Limit weierstrass points on nodal reducible curves

In the 1980s D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

O mito da inclusão produtiva: o discurso ideológico de cidadania, inclusão social e crescimento econômico do estado brasileiro de FHC à Dilma

A presente dissertação de mestrado tem por objetivo central analisar a concepção de inclusão produtiva, caracterizada por ações de qualificação da força de trabalho vigoradas com maior frequência a partir da Presidência de Lula da Silva, em 2003, e orientada pelo Ministério de Desenvolvimento Social e Combate à Fome (MDS) como tentativa contraditória de promoção do desenvolvimento econômico e enfrentamento à pobreza no Brasil. Os objetivos específicos visam identificar em que momento a inclusão produtiva passou a ser disseminada pelo Governo Federal Brasileiro; investigar os documentos oficiais do Governo Brasileiro, bem como de organismos internacionais que se referem à noção de inclusão produtiva; e analisar os documentos oficiais apreendendo as categorias que explicam a concepção de inclusão produtiva para o MDS. Para tanto, o percurso metodológico de análise do objeto de estudo, dar-se pela pesquisa qualitativa, norteada pelas pesquisas bibliográfica e documental. Assim, busca-se apreender a concepção de inclusão produtiva a partir da análise de 13 (treze) documentos e informações das paginas eletrônicas das instituições como o MTE, a CEPAL e o MDS. Os resultados da pesquisa permitem inferir que a inclusão produtiva incorporada pelo governo petista (Lula da Silva e Dilma Rousseff) é sustentada pelo discurso ideológico de cidadania, inclusão social, crescimento econômico, protagonismo, desenvolvimento de capacidades que integram a noção de qualificação/educação profissional como mediação da inserção laborativa da população pobre no mundo do trabalho. Portanto, essas categorias têm tendência em escamotear o desemprego estrutural, a exploração do trabalho, as desigualdades sociais e promover por meio do ajustamento da população às demandas do capital e, ainda, para que aceite sua posição dentro da sociedade: a de superpopulação necessária à acumulação capitalista.

The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.

Remarks on the Nagata Conjecture

2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.

Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namely
the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on
3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).

Position Document on the UN Secretary General's Report In Larger Freedom

Aquest document és el resultat de contrastar el “know-how” dels nostres projectes relacionats amb els temes tractats pel Secretari General de l’ONU, Kofi Annan.

Pressure field in a tube with a general and arbitrary time- and position-dependent gas source

In this article we present analytical and numerical results for a pressure profile along the axis of a tube with a general and arbitrary time- and position-dependent gas source. The model is able to determine the pressure values along the tube, once the pumping speed at each extremity and the gas sources are specified. The time evolution of the pressure along a tube is presented for situations commonly found in high-vacuum applications, such as particle accelerators, colliders, storage rings, and synchrotron light sources. (C) 2004 American Vacuum Society.

A letter to the Right Hon. Henry Labouchere, M.P., President of the Board of Trade, etc. etc. : on railways, their accounts and dividends, their progress, present position, and future prospects, their effects on trade and commerce : with suggestions for government assistance and the amendment of the General Railway Act of 1845 /

Mode of access: Internet.