Symmetric Criticality for Tight Knots

We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the same symmetry. We use this to construct new examples of ropelength critical configurations for knots and links which are different from the ropelength minima for these knot and link types.Comment: This version adds references, and most importantly an acknowledgements section which should have been in the original postin

Circles Minimize most Knot Energies

We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies belong to this class. This proves two conjectures of O'Hara and of Freedman, He, and Wang. We also find energies not minimized by a round circle. The proof is based on a theorem of G. Luko on average chord lengths of closed curves.Comment: 15 pages with 3 figures. See also http://www.math.sc.edu/~howard

Criticality for the Gehring link problem

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November 200

Recomendação de adubação de aveia em Latossolo vermelho-amarelo em dois sistemas de plantio.

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The Long Term Behaviour of Day-to-Day Traffic Assignment Models

The dynamical behaviour of deterministic process, day-to-day traffic assignment models is sometimes characterised by convergence to a variety of different fixed equilibrium points dependent upon the initial flow pattern, even though individual trajectories are unique for a given start point. This non-uniqueness is seemingly in sharp contrast to the evolution of stochastic process, day-to-day models; under certain assumptions these converge in law to a unique stationary distribution, irrespective of the start point. In this article, we show how models may be constructed which exhibit characteristics of both deterministic models and stochastic models, and illustrate the ideas by using a simple example network

Upland rice under no-tillage preceded by crops for soil cover and nitrogen fertilization.

The grain yield of upland rice under no-tillage has been unsatisfactory and one reason could be the nitrate/ammonium balance in the soil. Cover crops and nitrogen fertilization can be used to change the nitrate/ammonium relation in the soil and improve conditions for the development of upland rice in the no-tillage (NT) system. The aim was to study the effect of cover crops and nitrogen sources on grain yield of upland rice under no tillage. The study was carried out on the Fazenda Experimental Lageado, in Botucatu, State of São Paulo, Brazil, in an Oxisol area under no-tillage for six years. The experiment was arranged in a randomized block split-plot design with four replications. The plots consisted of six cover crop species (Brachiaria brizantha, B. decumbens, B. humidicola, B. ruziziensis, Pennisetum americanum, and Crotalaria spectabilis) and the split-plots of seven forms of N fertilizer management. Millet is the best cover crop to precede upland rice under NT. The best form of N application, as nitrate, is in split rates or total rate at topdressing or an ammonium source with or without a nitrification inhibitor, in split doses. When the cover crops C. spectabilis, B. brizantha, B. decumbens, B. humidicola, and B. ruziziensis preceded rice, they induced the highest grain yield when rice was fertilized with N as ammonium sulfate source + nitrification inhibitor in split rates or total dose at topdressing

Teor de nitrogênio inorgânico no solo em função de plantas de cobertura, fontes de nitrogênio e inibidor de nitrificação.

A utilização de plantas de cobertura pode alterar a relação NO3 -:NH4 + no solo, proporcionando maiores quantidades de NH4 + e podendo viabilizar o desenvolvimento de culturas que absorvem mais e preferem esta forma de nitrogênio (N), como o arroz. Objetivou-se avaliar a influência da interação de plantas de cobertura e fontes de N, com e sem inibidor de nitrificação (dicianodiamida), em sistema plantio direto (SPD). O experimento foi realizado em 2009/2010, em Botucatu (SP), em Latossolo Vermelho distroférrico cultivado por seis anos no SPD. O delineamento experimental foi em blocos casualizados, em esquema de parcela subdividida, com quatro repetições. As parcelas foram constituídas por seis espécies de plantas de cobertura do solo (Urochloa brizantha, U. decumbens, U. humidicola, U. ruziziensis, Pennisetum americanum e Crotalaria spectabilis) e as subparcelas por sete formas de fertilização nitrogenada, aos 0 e 30 dias após a emergência (DAE) do arroz [1 - controle, sem aplicação de nitrogênio; 2 - nitrato de cálcio (40 + 40 kg ha-1); 3 - nitrato de cálcio (0 + 80 kg ha-1); 4 - sulfato de amônio (40 + 40 kg ha-1); 5 - sulfato de amônio (0 + 80 kg ha-1); 6 - sulfato de amônio + dicianodiamida (40 + 40 kg ha-1); e 7 - sulfato de amônio + dicianodiamida (0 + 80 kg ha-1)]. O uso do inibidor de nitrificação e o cultivo de C. spectabilis proporcionaram maiores teores de amônio no solo. A aplicação da fonte amoniacal sem inibidor em dose total aos 30 DAE e com inibidor tanto parcelada quanto em dose total proporcionaram os maiores teores de nitrato no solo

Acúmulo de matéria seca e de nutrientes em forrageiras consorciadas com milho safrinha em função da adubação nitrogenada

201

Recomendação de adubação para aveia, em dois sistemas de plantio, em Latossolo Vermelho distrófico típico.

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