A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

On the Erdos-Szekeres n-interior point problem

The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1, every point set in the plane with sufficient number of interior points contains a convex polygon containing exactly n-interior points. This has been proved only for n-3. In this paper, we prove it for pointsets having atmost logarithmic number of convex layers. We also show that any pointset containing atleast n interior points, there exists a 2-convex polygon that contains exactly n-interior points.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

On the Erdos-Szekeres n-interior-point problem

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

High Loading of Pd Nanoparticles by Interior Functionalization of MOFs for Heterogeneous Catalysis

In this report, the issue related to nanoparticle (NP) agglomeration upon increasing their loading amount into metal-organic frameworks (MOFs) has been addressed by functionalization of MOFs with alkyne groups. The alkynophilicity of the Pd2+ (or other noble metals) ions has been utilized successfully for significant loading of Pd NPs into alkyne functionalized MOFs. It has been shown here that the size and loading amount of Pd NPs are highly dependent on the surface area and pore width of the MOFs. The loading amount of Pd NPs was increased monotonically without altering their size distribution on a particular MOF. Importantly, the distinct role of alkyne groups for Pe(2+) stabilization has also been demonstrated by performing a control experiment considering a MOF without an alkyne moiety. The preparation of NPs involved two distinct steps viz. adsorption of metal ions inside MOFs and reduction of metal ions. Both of these steps were monitored by microscopic techniques. This report also demonstrates the applicability of Pd@MOF NPs as extremely efficient heterogeneous catalysts for Heck-coupling and hydrogenation reactions of aryl bromides or iodides and alkenes, respectively.

[B_Muskiz_Muñatones] Documentación geométrica de la muralla interior del Castillo de Muñatones (Muskiz, Bizkaia)

[ES] Este proyecto corresponde a una continuación del que documenta la torre central y que se realizó en 2005. Dicho trabajo puede consultarse también es este repositorio:

Niveles de nutrientes y pigmentos fotosintéticos en el Río de la Plata interior (55°-59°W 34°-36°S)

The "Río de la Plata" River is one of the less studied systems of the basin with respect to its biological and ecological aspects. Twenty four and twenty seven surface stations were sample on September 22-23 and November 22-23, 1982, respectively. The section studied is part of the zone called inner "Río de la Plata" River. The discharge was 29.000 m3/s in September and 45.200 m3/s in November. Total phosphorus (PT), total organic nitrogen (NOT), chemical oxygen demad (COT) and total cholrophyll were measured. Dissolved oxygen (DO), turbidity (TURB), pH and electrical conductivity (K20) were also measured at the surface with a HORIBA U7 sensor on November 1982. PT was 72-208 mg/m3 and 66-205 mg/m3 in September and November repectively; the higher values were near the Argentinian coast and the outer zone. NOT was 33-106 µM and 49-117 µM and CHL was 1.4-5.8 mg/m3 and 1.3-9.4 mg/m3. TURB was between 44 and 240 NTU in November; the maximun value were obseved in the central zone. Steep K20 gradients were found near both coast. The reduced organic carbon load into the lower and external part of the "Río de la Plata" River was estimated. (Document contains 40 pages.)

Vozes saudosas, da eloquencia do espirito, do zelo, e eminente sabedoria do Padre Antonio Vieira, da Companhia de Jesus, pregador de sua magestade, e príncipe dos oradores evangélicos : acompanhadas com hum fidelissimo echo, que sonoramente resulta do interior da obra clavis prophetarum : concorda no fim a suavidade das musas em elogios raros : tudo reverente dedica ao principe nosso senhor o p. Andre de Barros Da Companhia de Jesus, Academico do numero da Academia Real da Historia portugueza

Padre Antônio Vieira nasceu em Lisboa em 6 de novembro de 1608 e morreu na Bahia em 18 de julho de 1697. Ordenado sacerdote em 1634, logo se destacou como excepcional pregador. Exerceu importante papel politico e diplomático durante o reinado de D. João IV e fez do púlpito uma tribuna a serviço da nação, em guerra com a Espanha. De 1652 a 1661 atuou como missionário no Maranhão. Em Portugal foi denunciado como herético ao Tribunal da Inquisição. Doente e encarcerado defendeu-se com extraordinário vigor, mas foi condenado a internamento numa casa jesuítica e proibido de pregar. Retirou-se em 1681 para o Brasil, onde trabalhou na edição completa dos Sermoens, iniciada em 1679. Este é o primeiro volume de Vozes saudosas, cuja edição foi executada pelo Padre Jesuíta André de Barros,após a morte do autor. Trata-se de uma compilação de texto, contendo "vários tratados sobre o Brasil escritos por Antonio Vieira, mas nenhum sermão" , como esclarece Borba de Moraes. Vozes saudosas foi o titulo atribuído à obra pelo seu compilador, como uma homenagem ao autor, que ele compara a Sêneca. O segundo tomo de Vozes saudosas foi também publicado pelo Padre André de Barros, em 1748, no livro Sermões vários e tratados ainda não impressos do grande Padre Antonio Vieira... volume 15.

Segunda viagem ao interior do Brasil : Espirito Santo

As Voyages... são estudos completos, abrangendo todos os aspectos das regiões percorridas; servem de subsídio ao estudo das condições de vida no Brasil no século passado. "Fonte primordial de informações sobre os prédios coloniais do Rio de Janeiro, Minas Gerais, São Paulo, Santa Catarina e Goiás. Poucas obras no gênero atingem o valor de Saint-Hilarire. São clássicas e indispensáveis para o estudo do sul do Brasil, antes da Independência" segundo Borba de Moraes.