Bases de Gröbner e geração de exercícios matemáticos com estrutura não determinada

Definido um enredo concreto, há, frequentemente, uma grande quantidade e variedade de exercícios que sobre ele podemos escrever. Neste artigo, apresenta-se um algoritmo que permite automatizar este processo. Para gerar exercícios matemáticos, parte-se das relações entre as variáveis presentes no enredo, calcula-se os possíveis exercícios, analisa-se a complexidade do seu processo de resolução e a sua viabilidade. O algoritmo recorre a bases de Gröbner para determinar se o exercício é resolúvel e um possível caminho de resolução. Com base na análise dos resultados obtidos, torna-se possível criar uma base de exercícios ligada a esse enredo.

Sistema computacional para reconocimiento de actitudes y estilos en música culta

En esta investigación, se elaboran una serie de sistemas expertos destinados a conservatorios de música españoles. Los sistemas expertos desarrollados están basados en lógica y álgebra computacional, por ello se denominan a los sistemas presentados sistemas computacionales.. Por un lado, se diseña un primer sistema computacional para evaluar las condiciones musicales de quienes desean dedicarse profesionalmente al estudio de un instrumento. Este sistema está destinado a las pruebas de ingreso, desarrolladas en conservatorios de música españoles. Se pretende facilitar ayuda adicional para la selección del alumnado más eficiente. El sistema computacional tiene en cuenta algunos factores que los expertos pasan por alto como las actitudes personales de los candidatos, capacidades físicas, ámbito social y ámbito familiar entre otros. Se desarrollan tres sistemas, presentados en orden cronológico, para reconocer algunos de los estilos musicales más relevantes desde el siglo XVII, uno para el reconocimiento del Barroco, el Rococó y el Clásico; otro para el reconocimiento del Romanticismo, el Impresionismo y Nacionalismo; y un tercero para el reconocimiento de estilos musicales durante el siglo XX, Antiimpresionismo, Verismo y Expresionismo.. El trabajo recoge una descripción exhaustiva de la información que da lugar a las cuatro bases de conocimiento elaboradas. Se describen, de forma clara y concisa, los elementos fundamentales de la teoría de las 'Bases de Gröbner' y de la relación entre consecuencia en lógica y 'pertenencia a un ideal' en álgebra. La construcción de los programas en el lenguaje CoCoA, Computations in Commutative Álgebra, está realizada con rigor. Se incluye un interfaz para que cualquier persona sin conocimientos informáticos, pueda utilizar los sistemas. En esta tesis se combinan, de forma original y útil, música, lógica, matemáticas e informática..

Una primera lección de Geometría algebraica

En este artículo se explica cómo aparece la Geometría Algebraica, partiendo del estudio de los conjuntos de soluciones de sistemas algebraicos

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).

Free Resolutions from Involutive Bases

We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the computation of dG certain patterns appear at several positions. In particular, it is possible to compute the constants independent of the remainder of the differential. This allows us, starting from G, to determine the Betti numbers of M without computing a minimal free resolution: Thus we obtain a new algorithm to compute Betti numbers. This algorithm has been implemented in CoCoALib by Mario Albert. This way, in comparison to some other computer algebra system, Betti numbers can be computed faster in most of the examples we have considered. For Veronese subrings S(d), we have found a Pommaret basis, which yields new proofs for some known properties of these rings. Via the theoretical statements found for G, we can identify some generators of modules in G where no constants appear. As a direct consequence, some non-vanishing Betti numbers of S(d) can be given. Finally, we give a proof of the Hyperplane Restriction Theorem with the help of Pommaret bases. This part is largely independent of the other parts of this work.

Synthesis And Antitumor Activity Of Novel 1-substituted Phenyl 3-(2-oxo-1,3,4-oxadiazol-5-yl) β-carbolines And Their Mannich Bases.

A series of novel 1-(substituted phenyl)-3-(2-oxo-1,3,4-oxadiazol-5-yl) β-carbolines (4a-e) and the corresponding Mannich bases 5-9(a-c) were synthesized and evaluated for their in vitro antitumor activity against seven human cancer cell lines. Compounds of 4a-e series showed a broad spectrum of antitumor activity, with GI50 values lower than 15μM for five cell lines. The derivative 4b, having the N,N-dimethylaminophenyl group at C-1, displayed the highest activity with GI50 in the range of 0.67-3.20μM. A high selectivity and potent activity were observed for some Mannich bases, particularly towards resistant ovarian (NCI-ADR/RES) cell lines (5a, 5b, 6a, 6c and 9b), and ovarian (OVCAR-03) cell lines (5b, 6a, 6c, 9a, 9b and 9c). In addition, the interaction of compound 4b with DNA was investigated by using UV and fluorescence spectroscopic analysis. These studies indicated that 4b interact with ctDNA by intercalation binding.

Sobre a força de ácidos e bases: algumas considerações

This article intends to answer the question: what is the best way to evaluate the strength of acids and bases? The meaning of the word strength, the main acid-base theories (ionotropic and electron pair), the neutralization reactions and the thermodynamical formalism are considered. Some cases are presented and discussed. In conclusion, evaluating acid-base strength is dependent on the theory (formalism) as well as on the system and measuring techniques.

A metalinguagem como lugar da interpretação: terminologia e bases de dados informatizadas

The main objective of this work is to discuss the notion of metalanguage concerning the use of thesaurus (symbols systems, functions indicators, descriptors) utilized by indexers for article representation in computerized bibliographical databases. Our corpus comprises article abstracts and bibliographical database descriptors LILACS (Literatura Latino-Americana em Ciências da Saúde) and SOCIOFILE Sociological Abstracts. We aim at clarifying the effects of subjectivity in the functioning of indexing taking account the grounds for interpretation that allow different meanings.

Alteração dimensional linear de resinas para bases de próteses polimerizadas com microondas

This study examined the influence of three polymerization cycles (1: heat cure - long cycle; 2: heat cure - short cycle; and 3: microwave activation) on the linear dimensions of three denture base resins, immediately after deflasking, and 30 days after storage in distilled water at 37± 2ºC. The acrylic resins used were: Clássico, Lucitone 550 and Acron MC. The first two resins were submitted to all three polymerization cycles, and the Acron MC resin was cured by microwave activation only. The samples had three marks, and dimensions of 65 mm in length, 10 mm in width and 3 mm in thickness. Twenty-one test specimens were fabricated for each combination of resin and cure cycle, and they were submitted to three linear dimensional evaluations for two positions (A and B). The changes were evaluated using a microscope. The results indicated that all acrylic resins, regardless of the cure cycle, showed increased linear dimension after 30 days of storage in water. The composition of the acrylic resin affected the results more than the cure cycles, and the conventional acrylic resin (Lucitone 550 and Clássico) cured by microwave activation presented similar results when compared with the resin specific for microwave activation.

Jogos desportivos coletivos e os estimulos das inteligencias multiplas : bases para uma proposta em pedagogia do esporte

Universidade Estadual de Campinas. Faculdade de Educação Física

Stability of fruit bases and chocolate fillings

Syrups with high sugar content and dehydrated fruits in its composition can be added to chocolate fillings to reduce the need of artificial flavor and dyes attributing a natural appeal to the product. Fruit bases were produced with lyophilized strawberry, passion fruit, and sliced orange peel. Rheological dynamic oscillatory tests were applied to determine the products stability and tendency of shelf life. Values of G´< G´´ were observed for strawberry and passion fruit flavor, whereas values of G´ > G´´ were found for orange flavor during the 90 days of storage. It was observed that shear stress values did not vary significantly suggesting product stability during the studied period. For all fillings, it was found a behavior similar to the fruit base indicating that it has great influence on the filling behavior and its stability. The use of a sugar matrix in fillings provided good shelf life for the fruit base, which could be kept under room temperature conditions for a period as long as one year. The good stability and storage conditions allow the use of fruit base for handmade products as well as for industrialized products.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.