New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

Homeomorphisms of the annulus with a transitive lift

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the infinite strip (A) over tilde which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set B(-) subset of (A) over tilde such that B(-) is bounded to the right, the projection of B to A is dense, B - (1, 0) subset of B and (f) over tilde (B) subset of B. Moreover, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of B(-), lim sup (n ->infinity) p1((f) over tilde (n)((z) over tilde)) - p(1) ((z) over tilde)/n < - d. In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

HFD groups in the Solovay model

Hajnal and Juhasz proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelof. The example constructed is a topological subgroup H subset of 2(omega 1) that is an HFD with the following property (P) the projection of H onto every partial product 2(I) for I is an element of vertical bar omega(1)vertical bar(omega) is onto. Any such group has the necessary properties. We prove that if kappa is a cardinal of uncountable cofinality, then in the model obtained by forcing over a model of CH with the measure algebra on 2(kappa), there is an HFD topological group in 2(omega 1) which has property (P). Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

A stronger Dunford-Pettis property

We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both l(1) and l(infinity) It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c(0) is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Protein Assembly onto Cationic Supported Bilayers

Cationic supported bilayers on latex are useful to isolate and immobilize oppositely charged proteins as a monomolecular layer over a range of low protein concentrations and particle number densities. Cholera toxin (CT) from Vibrio cholerae, an 87 kDa AB(5) hexameric protein and bovine serum albumin (BSA) self-assembled on dioctadecyldimethylammonium bromide (DODAB) supported bilayers with high affinity yielding highly organized and monodisperse particulates at 5 x 10(9) particles/mL, over a range of low protein concentrations (0-0.025 mg/mL BSA or CT). Protein association onto the bilayer-covered polystyrene sulfate (PSS) was determined from adsorption isotherms, dynamic light scattering for size distributions and zeta-potential analysis revealing a monomolecular, thin and highly organized protein layer surrounding each particle with potential for biospecific recognition such as antigen-antibody, receptor-ligand, hybridization of oligonucleotide sequences, all of them important in immunodiagnosis, selective biomolecular chromatographic separations, microarrays design and others.

Covalent attachment of 3,4,9,10-perylenediimides onto the walls of mesoporous molecular sieves MCM-41 and SBA-15

This work describes the covalent grafting of 3,4,9,10-perylenediimides (PDI), which are fluorescent dyes with very interesting optical properties, onto the walls of mesoporous molecular sieves MCM-41 and SBA-15. The mesoporous materials were first treated with 3-aminopropyltriethoxysilane (APTES) in anhydrous toluene, generating amine-containing surfaces. The amine-containing materials were then reacted with 3,4,9,10-perylenetetracarboxylic dianhydride (PTCA), generating surface-grafted PDI. Infrared spectra of the materials showed that the reaction with amino groups took place at both anhydride ends of the PTCA molecule, resulting in surface attached diimides. No sign of unreacted anhydride groups were found. The new materials, designated as MCMN2PDI and SBAN(2)PDI, presented absorption and emission spectra corresponding to weakly coupled PDI chromophores, in contrast to the strongly coupled rings usually found in solid PDI samples. The materials showed a red fluorescence, which could be observed by the naked eye under UV irradiation or with a fluorescence microscope. The PDI-modified mesoporous materials showed electrical conductivity when pressed into a pellet. The results presented here show that the new materials are potentially useful in the design of nanowires. (C) 2007 Elsevier Inc. All rights reserved.

Protein Adsorption onto Polyelectrolyte Layers: Effects of Protein Hydrophobicity and Charge Anisotropy

Ellipsometry was used to investigate the influence of ionic strength (I) and pH on the adsorption of bovine serum albumin (BSA) or beta-lactoglobulin (BLG) onto preabsorbed layers of two polycations: poly(diallyldimethylammonium chloride) (PDADMAC) or poly(4-vinylpyridine bromide) quaternized with linear aliphatic chains of two (QPVP-C2) or five (QPVP-C5) carbons. Comparisons among results for the three polycations reveal hydrophobic interactions, while comparisons between BSA and BLG-proteins of very similar isoelectric points (pI)-indicate the importance of protein charge anisotropy. At pH close to pI, the ionic strength dependence of the adsorbed amount of protein (Gamma) displayed maxima in the range 10 < I < 25 mM corresponding to Debye lengths close to the protein radii. Visualization of protein charge by Delphi suggested that these ionic strength conditions corresponded to suppression of long-range repulsion between polycations and protein positive domains, without diminution of short-range attraction between polycation segments and locally negative protein domains, in a manner similar to the behavior of PE-protein complexes in solution.(1-4) This description was consistent with the disappearance of the maxima at pH either above or below pI. In the former case, Gamma values decrease exponentially with I(1/2), due to screening of attractions, while in the latter case adsorption of both proteins decreased at low I due to strong repulsion. Close to or below pI both proteins adsorbed more strongly onto QPVP-C5 than onto QPVP-C2 or PDADMAC due to hydrophobic interactions with the longer alkyl group. Above pI, the adsorption was more pronounced with PDADMAC because these chains may assume more loosely bound layers due to lower linear charge density.

Adsorption of anionic amphiphilic polyelectrolytes onto amino-terminated solid surfaces

The adsorption behavior of several amphiphilic polyelectrolytes of poly(maleic anhydride-alt-styrene) functionalized with naphthyl and phenyl groups, onto amino-terminated silicon wafer has been studied by means of null- ellipsometry, atomic force microscopy (AFM) and contact angle measurements. The maximum of adsorption, Gamma(plateau), varies with the ionic strength, the polyelectrolyte structure and the chain length. Values of Gamma(plateau) obtained at low and high ionic strengths indicate that the adsorption follows the ""screening-reduced adsorption"" regime. Large aggregates were detected in solution by means of dynamic light scattering and fluorescence measurements. However. AFM indicated the formation of smooth layers and the absence of aggregates. A model based on a two-step adsorption behavior was proposed. In the first one, isolated chains in equilibrium with the aggregates in solution adsorbed onto amino-terminated surface. The adsorption is driven by electrostatic interaction between protonated surface and carboxylate groups. This first layer exposes naphtyl or phenyl groups to the solution. The second layer adsorption is now driven by hydrophobic interaction between surface and chains and exposes carboxylate groups to the medium, which repel the forthcoming chain by electrostatic repulsion. Upon drying some hydrophobic naphtyl or phenyl groups might be oriented to the air, as revealed by contact angle measurements. Such amphiphilic polyelectrolyte layers worked well for the building-up of multilayers with chitosan. (C) 2010 Elsevier Ltd. All rights reserved.

Fabrication of disposable voltammetric electronic tongues by using Prussian Blue films electrodeposited onto CD-R gold surfaces and recognition of milk adulteration

A new approach to fabricate a disposable electronic tongue is reported. The fabrication of the disposable sensor aimed the integration of all electrodes necessary for measurement in the same device. The disposable device was constructed with gold CD-R and copper sheets substrates and the sensing elements were gold, copper and a gold surface modified with a layer of Prussian Blue. The relative standard deviation for signals obtained from 20 different disposable gold and 10 different disposable copper electrodes was below 3.5%. The performance, electrode materials and the capability of the device to differentiate samples were evaluated for taste substances model, milk with different pasteurization processes (homogenized/pasteurized, ultra high temperature (UHT) pasteurized and UHT pasteurized with low fat content) and adulterated with hydrogen peroxide. In all analysed cases, a good separation between different samples was noticed in the score plots obtained from the principal component analysis (PCA). Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Theoretical Characterization of Hydrogen Polyoxides: HOOH, HOOOH, HOOOOH, and HOOO

We have investigated the polyoxides HOOH, HOOOH, HOOOOH, and HOOO employing the CCSD(T) methodology, and the correlation consistent basis sets. For all molecules, we have computed fundamental vibrational frequencies, structural parameters, rotational constants, and rotation-vibration corrections. For HOOOH, we have obtained a good agreement between our results and microwave and infrared spectra measurements, although for the symmetric OO stretch some important differences were found. Heats of formation were computed using atomization energies, and our recommendation is as follows: Delta H degrees(f,298)(HOOOH) = -21.50 kcal/mol and Delta H degrees(f,298)(HOOOOH) = -10.61 kcal/mol. In the case of HOOO, to estimate the heat of formation, we have constructed three isodesmic reactions to cancel high order correlation effects. The results obtained confirmed that the latter effects are very important for HOOO. The new Delta H degrees(f,298)(HOOO) obtained is 5.5 kcal/mol. We have also calculated the zero-point energies of DO and DOOO to correct the experimental lower limit determined for the Delta H degrees(f,298)(HOOO). The Delta(Delta ZPE) decreases the binding energy of HOOO by 0.56 kcal/mol. Employing the latter value, the new experimental lower limit for Delta H degrees(f,298)(HOOO) is 3.07 kcal/mol, just 2.4 kcal/mol lower than our determination. We expect that the fundamental vibrational frequencies and rotational constants determined for HOOOOH and DOOOOD contribute to its identification in the gas phase. The vibrational spectrum of HOOOOH shows some overlapping with that of HOOOH thus indicating that one may encounter some difficulties in its characterization. We discuss the consequences of the thermochemical properties determined in this work, and suggest that the amount of HOOO present in the atmosphere is smaller than that proposed recently in this journal (J. Phys. Chem A 2007, 111, 4727).

New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are inluded as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.