Morfología polínica de "Lactuceae" (Asteraceae) en la Península Ibérica.: I. "Lactuca L. y géneros relacionados

Morfología polínica de Lactuceae (Asteraceae) en la Península Ibérica. 1. Lactuca L. y géneros relacionados. Se estudia la morfología del polen de los taxones incluidos en los géneros Lactuca L., Prenant hes L., Cicerbita Wallr. y Mycelis Cass. que habitan en la Península Ibérica con los microscopios óptico (MO) y electrónico de barrido (MEB). El polen, 3-zonocolporado y equinolofado (sin lagunas polares), se caracteriza por presentar una cresta ecuatorial y 15 lagunas: 3 porales, 6 abporales y 6 paraporales. Tamaño pequeño o mediano, P x E = 21-41 x 24-47 xm. Exina de 3-8 gm de grosor y ornamentación perforada y equinulado-equinada. Se han observado diferencias en cuanto al tamaño, amplitud de las apocolpias y tamaño de las espínulas-espinas. Nuestros resultados muestran de una manera bastante clara la afinidad entre los distintos géneros. En el caso de Lactuca, el género con mayor número de especies, los resultados polínicos permiten discutir sobre las relaciones evolutivas entre los representantes de la Península

On the Complexity of Solving Quadratic Boolean Systems

A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in $4\log_2 n\,2^n$ operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step. Under precise algebraic assumptions on the input system, we show that the deterministic variant of our algorithm has complexity bounded by $O(2^{0.841n})$ when $m=n$, while a probabilistic variant of the Las Vegas type has expected complexity $O(2^{0.792n})$. Experiments on random systems show that the algebraic assumptions are satisfied with probability very close to~1. We also give a rough estimate for the actual threshold between our method and exhaustive search, which is as low as~200, and thus very relevant for cryptographic applications.Comment: 25 page

Length Of Polynomial Ascending Chains And Primitive Recursiveness

In a polynomial ring K[X 1 ; : : : ; Xn ] over a field, let I 0 ae I 1 ae \Delta \Delta \Delta ae I s be a strictly ascending chain of ideals, with the condition that every I i can be generated by elements of degree not greater than f(i). A. Seidenberg showed that there is a bound on the length s of such a chain depending only on n and f , which is recursive in f for every n and primitive recursive in f for n = 2. In this paper we give a better bound, expressed in a rather simple way in terms of f , which is attained when f is an increasing function. We prove that it is primitive recursive in f for all n. We also show that, on the contrary, there is no bound which is primitive recursive in n in general

Plan de mejora y estrategia comercial para Data Recovery

Tesis (Ingeniero Civil Industrial)En la actualidad el nivel de competitividad de este servicio se ve en expansión, presentando mercado más acotado. Debido a los altos costos y baja demanda del servicio, los márgenes se ven reducidos. Esto detiene el desarrollo organizacional. En consecuencia, se deben generar alianzas estratégicas con Clientes-empresas, a fin de generar fidelización del mismo y captando una mayor segmentación del mercado, permitiendo la continuidad del servicio y la expansión del mismo

Revlex Standard Bases Of Generic Complete Intersections

In this paper we study the Hilbert-Samuel function of a generic standard graded K-algebra K[X 1 ; : : : ; Xn ]=(g 1 ; : : : ; gm ) when refined by an (`)-adic filtration, ` being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an "orderly filling up" conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases

An Ackermannian Polynomial Ideal

In this paper we answer the following question of Teo Mora ([Mora91]): Write down a monomial ideal starting with a monomial of degree d, adding a monomial of degree d + 1, another one of degree d + 2, and so on, with every new monomial added not being a multiple of the previous ones; which is the maximal degree one can reach with this construction? We also give some partial results for the opposite problem of finding the lowest bound for this degree, in the case of homogeneous ideals. The paper is organized as follows. In section 1 we state the result concerning Mora's question; sections 2 and 3 contain some preliminaries and the proof, while in section 4 an example is shown and some remarks and a generalization are made. The opposite problem is considered in section 5, where we give the results we have found and make a conjecture