Ontheproof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.

On the proof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.

A unified approach to known and unknown cases of Berge's conjecture

Berge's elegant dipath partition conjecture from 1982 states that in a dipath partition P of the vertex set of a digraph minimizing , there exists a collection Ck of k disjoint independent sets, where each dipath P?P meets exactly min{|P|, k} of the independent sets in C. This conjecture extends Linial's conjecture, the GreeneKleitman Theorem and Dilworth's Theorem for all digraphs. The conjecture is known to be true for acyclic digraphs. For general digraphs, it is known for k=1 by the GallaiMilgram Theorem, for k?? (where ?is the number of vertices in the longest dipath in the graph), by the GallaiRoy Theorem, and when the optimal path partition P contains only dipaths P with |P|?k. Recently, it was proved (Eur J Combin (2007)) for k=2. There was no proof that covers all the known cases of Berge's conjecture. In this article, we give an algorithmic proof of a stronger version of the conjecture for acyclic digraphs, using network flows, which covers all the known cases, except the case k=2, and the new, unknown case, of k=?-1 for all digraphs. So far, there has been no proof that unified all these cases. This proof gives hope for finding a proof for all k.

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.

Beyond Schur's Conjecture

Schur 4] conjectured that the maximum length N of consecutive quadratic nonresidues modulo a prime p is less than root p if p is large enough. This was proved by Hummel in 2003. In this note, we outline a clear improvement over Hummel's bound for p > 23.

Beyond Schur's Conjecture

Schur 4] conjectured that the maximum length N of consecutive quadratic nonresidues modulo a prime p is less than root p if p is large enough. This was proved by Hummel in 2003. In this note, we outline a clear improvement over Hummel's bound for p > 23.

Efectividad de cuatro insecticidas en el control de larvas de Plutella maculipennis (Curtis) y Leptophobia aripa (Boisd) en el cultivo del repollo (Brassica oleracea var. superette)

Las plagas de foliadores como plutella y leptophobia constituyen uno de los principales problemas fitosanitarios en el cultivo del repollo en Nicaragua. Fundamentalmente contra plutella se han aplicado de forma irracional diversos insecticidas; solos y en combinaciones, lo que posiblemente ha hecho que esta plaga desarrolle resistencia a algunos productos plaguicidas, En este estudio se evaluo la efectividad de cuatro insecticidas: Dipel Decis, Lannate y Tamaron , contra las larvas de estos dos lepidópteros; encontrándose que estos tienen buen control sobre Leptophobia: sin embargo, contra Plutella el único efectivo fue Dipel, resultando los productos químicos en efectivo contra ella, esa diferencia de efectividad podría estar asociada al factos resistencia que plutella podría tener hacia dichos productos; a pesar de estos resultados los productores continúan utilizando estos insecticidas debido al bajo costo de los mismos. Producto de la política de subsidio del estado para los agroquímicos y al alto precio que reciben por el repollo debido a la inflación; lo que genera un desequilibrio entre el valor económico del repollo y los costos de aplicación de los insecticidas lo que les permite tener siempre ganancias aunque realicen numerosas aplicaciones teniendo esto como resultado una alteración en el ecosistema, por tanto , se debe discutir ampliamente el impacto que tiene la policía de subsidio de los agroquímicos en la agricultura nacional. El ingreso económico en repollo es una función del número de cabezas formadas y el precio /cabeza; leptophobia influye el rendimiento, afectando el número de cabezas formadas; el precio/cabezas esata afectado por las poblaciones de plutella y leptophobia por lo que la efectividad de los insecticidas se evalúa en base al ingreso económico que combina el rendimiento y la calidad del repollo en relación con la población de plagas que permaneces en el cultivo.

Studies of the effects of industrial pollution in the lower Patapsco river area: 1. Curtis Bay Region 1941

Industrial effluents in the lower Patapsco area, which constitutes the navigable portion of the river and includes Baltimore Harbor, are many and include waste acid, distillery waters, tannery wastes and copper as (ferrous sulphate) from pigment and steel industries. (PDF contains 22 pages (2 on 1)

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

On the local Tamagawa number conjecture for Tate motives

There is a wonderful conjecture of Bloch and Kato that generalizes both the analytic Class Number Formula and the Birch and Swinnerton-Dyer conjecture. The conjecture itself was generalized by Fukaya and Kato to an equivariant formulation. In this thesis, I provide a new proof for the equivariant local Tamagawa number conjecture in the case of Tate motives for unramified fields, using Iwasawa theory and (φ,Γ)-modules, and provide some work towards extending the proof to tamely ramified fields.

Combinatorial properties of finite geometric lattices

Let L be a finite geometric lattice of dimension n, and let w(k) denote the number of elements in L of rank k. Two theorems about the numbers w(k) are proved: first, w(k) ≥ w(1) for k = 2, 3, ..., n-1. Second, w(k) = w(1) if and only if k = n-1 and L is modular. Several corollaries concerning the "matching" of points and dual points are derived from these theorems.

Both theorems can be regarded as a generalization of a theorem of de Bruijn and Erdös concerning ʎ= 1 designs. The second can also be considered as the converse to a special case of Dilworth's theorem on finite modular lattices.

These results are related to two conjectures due to G. -C. Rota. The "unimodality" conjecture states that the w(k)'s form a unimodal sequence. The "Sperner" conjecture states that a set of non-comparable elements in L has cardinality at most max/k {w(k)}. In this thesis, a counterexample to the Sperner conjecture is exhibited.

Cultura de tecidos e análise do potencial antioxidante de Passiflora alata Curtis

Passiflora alata Curtis, comumente conhecida como maracujá-doce, é uma das espécies do gênero Passiflora cultivadas comercialmente, sendo consumida in natura devido ao seu gosto adocicado. Ela também é utilizada em todo o mundo como ornamental e na medicina popular. O objetivo deste trabalho foi o estabelecimento de diferentes estratégias para a cultura in vitro de P. alata e a análise da produção de substâncias antioxidantes nos materiais obtidos in vitro, em comparação com as plantas in vivo. Diferentes tratamentos visando à quebra da dormência das sementes foram avaliados para a germinação in vitro ou in vivo, além da incubação das sementes sob tipos distintos de luz. Para o estabelecimento das culturas primárias, apices caulinares e segmentos nodais das plântulas derivadas da germinação in vitro foram cultivados em meio MSM . A taxa de alongamento dos brotos e o número de nós por brotos das culturas primárias foram aumentados pela adição de água de coco ao meio. Plantas derivadas dessas culturas foram utilizadas como fontes de explantes nodais, internodais e foliares. O potencial morfogênico de sementes sem tegumento foi também avaliado. Calos friáveis foram induzidos a partir de segmentos nodais e foliares na presença de PIC, e aqueles obtidos a partir de folhas em meio suplementado com PIC a 28,9 μM foram selecionados para o estabelecimento de culturas de células em suspensão. Após o desenvolvimento de diferentes estratégias in vitro para P. alata, folhas de plantas in vivo foram utilizadas para a avaliação de parâmetros que afetam a extração de substâncias antioxidante. O potencial antioxidante foi determinado pelo ensaio DPPH e o conteúdo de fenóis totais foi determinado utilizando o método Folin-Ciocalteau. Após o desenvolvimento do protocolo de extração, a atividade antioxidante dos diferentes materiais in vitro foi também avaliada. A eficiência antirradicalar variou entre os sistemas de cultura estudados, sendo diretamente proporcional ao conteúdo de fenóis totais dos extratos. Esses resultados indicam que as estratégias para cultura in vitro de P. alata desenvolvidas neste trabalho representam alternativas para a multiplicação de plantas e produção de substâncias fenólicas com ação antioxidante.

Regional context of the climate of H.J. Andrews Experimental Forest, Oregon

H.J. Andrews Experimental Forest is a 6400 ha forest of Douglas fir, western hemlock, and Pacific silver fir located in, and typical of, the central portion of the western slope of the Cascade mountain range of Oregon. The forest is one of 19 sites in the Long-Term Ecological Research (LTER) program sponsored by the National Science Foundation. ... Because of the scientific significance of Andrews Forest, it is important to investigate the temporal variability of annual and seasonal temperature and precipitation values at the site and identify past times of anomalous climatic conditions. It is also important to establish quantitatively the relationships between the climate of Andrews Forest and that of its surrounding area and, hence, place the climate of Andrews Forest into its regional context.