Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

A theoretical investigation of a-Fe2O3–Cr2O3 solid solutions

We have examined the thermodynamic stability of a-Fe2O3–Cr2O3 solid solutions as a function of temperature and composition, using a combination of statistical mechanics with atomistic simulation techniques based on classical interatomic potentials, and the addition of a model magnetic interaction Hamiltonian. Our calculations show that the segregation of the Fe and Cr cations is marginally favourable in energy compared to any other cation distribution, and in fact the energy of any cation configuration of the mixed system is always slightly higher than the combined energies of equivalent amounts of the pure oxides separately. However, the positive enthalpy of mixing is small enough to allow the stabilisation of highly disordered solid solutions at temperatures of B400 K or higher. We have investigated the degree of cation disorder and the effective cell parameters of the mixed oxide as functions of temperature and composition, and we discuss the effect of magnetic interactions and lattice vibrations on the stability of the solid solution.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Phase separation and surface segregation in ceria-zirconia solid solutions

Using a combination of density functional theory calculations and statistical mechanics, we show that a wide range of intermediate compositions of ceria – zirconia solid solutions are thermodynamically metastable with respect to phase separation into Ce-rich and Zr-rich oxides. We estimate that the maximum equilibrium concentration of Zr in CeO2 at 1373 K is ~2%, and therefore equilibrated samples with higher Zr content are expected to exhibit heterogeneity at the atomic scale. We also demonstrate that in the vicinity of the (111) surface, cation redistribution at high temperatures will occur with significant Ce enrichment of the surface, which we attribute to the more covalent character of Zr-O bonds compared to Ce-O bonds. Although the kinetic barriers for cation diffusion normally prevent the decomposition/segregation of ceria-zirconia solid solutions in typical catalytic applications, the separation behaviour described here can be expected to occur in modern three-way catalytic converters, where very high temperatures are reached.

Effects of the brief viewing of emotional stimuli on understanding of insight solutions

In the present study, we examined whether and how brief viewing of positive and negative images influences subsequent understanding of solutions to insight problems. For each trial, participants were first presented with an insight problem and then briefly viewed a task-irrelevant positive, negative, or neutral image (660 ms), which was followed by the solution to the problem. In our behavioral study (Study 1), participants were faster to report that they understood the solutions following positive images, and were slower to report it following negative images. A subsequent fMRI study (Study 2) revealed enhanced activity in the angular gyrus and medial prefrontal cortex (MPFC) while viewing solutions following positive, as compared with negative, images. In addition, greater activation of the angular gyrus was associated with more rapid understanding of the solutions. These results suggest that brief viewing of positive images enhances activity in the angular gyrus and MPFC, which results in facilitation of understanding solutions to insight problems.

Internal nanoparticle structure of temperature-responsive self-assembled PNIPAM-b-PEG-b-PNIPAM triblock copolymers in aqueous solutions: NMR, SANS and light scattering studies

In this study we report detailed information on the internal structure of PNIPAM-b-PEG-b-PNIPAM nanoparticles formed from self-assembly in aqueous solutions upon increase in temperature. NMR spectroscopy, light scattering and small-angle neutron scattering (SANS) were used to monitor different stages of nanoparticle formation as a function of temperature, providing insight into the fundamental processes involved. The presence of PEG in a copolymer structure significantly affects the formation of nanoparticles, making their transition to occur over a broader temperature range. The crucial parameter that controls the transition is the ratio of PEG/PNIPAM. For pure PNIPAM, the transition is sharp; the higher the PEG/PNIPAM ratio results in a broader transition. This behavior is explained by different mechanisms of PNIPAM block incorporation during nanoparticle formation at different PEG/PNIPAM ratios. Contrast variation experiments using SANS show that the structure of nanoparticles above cloud point temperatures for PNIPAM-b-PEG-b-PNIPAM copolymers is drastically different from the structure of PNIPAM mesoglobules. In contrast with pure PNIPAM mesoglobules, where solid-like particles and chain network with a mesh size of 1-3 nm are present; nanoparticles formed from PNIPAM-b-PEG-b-PNIPAM copolymers have non-uniform structure with “frozen” areas interconnected by single chains in Gaussian conformation. SANS data with deuterated “invisible” PEG blocks imply that PEG is uniformly distributed inside of a nanoparticle. It is kinetically flexible PEG blocks which affect the nanoparticle formation by prevention of PNIPAM microphase separation.

Adsorption Isotherms for Removal of Linoleic Acid from Ethanolic Solutions Using the Strong Anion Exchange Resin Amberlyst A26 OH

Adsorption isotherms for the removal of linoleic acid from aqueous ethanol were measured using a strong anion exchange resin (Amberlyst A26 OH). The data for linoleic acid were compared with previously published results for oleic acid. The equilibrium data were correlated using the Langmuir and Freundlich isotherms. Lower average deviations between experimental and calculated results were obtained with the Langmuir model. The capacity of the resin for adsorbing linoleic acid was evaluated at different water contents in ethanol, 100 w = 0.50 to 15.27, and at 298.15 K. The water content in ethanol does not influence significantly the equilibrium behavior, and the strong anion exchange resin has a good performance in the removal of linoleic acid from the liquid phase.

Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Influência dos íons K+ e Mg2+ na obtenção de apatitas biomiméticas

O crescimento da hidroxiapatita - HA, tanto no meio biológico quanto em soluções aquosas como a Synthetic Body Fluid - SBF, ocorre em meio contendo, além dos elementos Ca e P, elementos-traços essenciais tais como: Mg2+, HCO3-, K+ e Na+. Alguns destes elementos são conhecidos como inibidores do crescimento da HA, como Mg2+ e HCO3-. Neste trabalho, estudou-se a influência dos íons K+ e Mg2+ na formação de apatitas sobre substratos metálicos de Ti c.p. previamente tratados com NaOH 5M. Os efeitos destes íons no recobrimento obtidos, antes e após o tratamento térmico a 800ºC, foram analisados por microscopia eletrônica de varredura - MEV, espectroscopia de energia dispersiva de raios-X - EDX, difratometria de raios-X - DRX e espectroscopia no infravermelho - IV e mostraram que o efeito inibitório do Mg2+ na formação da HA se manifesta após o tratamento térmico. Diferentemente, o crescimento cristalino da HA não foi afetado pela presença do íon K+. Além disso, a formação de apatita carbonatada se deu também em soluções que não continham o íon CO3(2-) em sua composição.

Alocação de biomassa e nutrientes em Heteranthera reniformis sob o efeito de N, P e K

Este trabalho objetivou estudar a distribuição de biomassa e nutrientes entre os componentes vegetativos de Heteranthera reniformis sob o efeito de diferentes concentrações de N, P e K. As plantas foram cultivadas em vasos plásticos preenchidos com pedra rolada, em soluções nutritivas a 80% da concentração original de Sarruge, sendo esta a solução-base. O delineamento experimental utilizado foi o inteiramente casualizado, com quatro níveis (0, 25, 50 e 75% da solução-base) avaliados individualmente em N, P e K, além da testemunha (100% da solução-base), com quatro repetições no período de 35 dias. As maiores áreas foliares ocorreram em soluções com 75% de P e 50% de N e K. A solução com 50% de N proporcionou a maior biomassa seca de plantas. A contribuição do caule na alocação de recursos apresentou resultados que variaram entre 55,5 e 74,5% em relação à matéria seca total referente ao nível 0 e 75% de N; a contribuição de raízes reduziu com o aumento da concentração de N, bem como de P e K. As maiores contribuições de raízes ocorreram nas ausências de N (26,8%) e P (19,2%), os quais foram maiores em relação aos seus respectivos níveis mais concentrados. Os teores de N, P e K corresponderam a uma ordem crescente em folha, caule e raízes, em que os maiores teores foram obtidos nos níveis de 50 a 125 mg L-1 de N, 5 a 15 mg L-1 de P e 100 a 150 mg L- 1 de K.

Magnetic properties of Cu1+xMn2-xO4 and Ni1+xMn2-xO4 solid solutions

Magnetic properties of two spinel oxides solid solutions, Cul+xMn2-xO4 and Ni1+xMn2-xO4 are reported. These series are characterized by two magnetic transitions: the upper one, of ferrimagnetic type, occurs at about 85 K (for copper-based) and at 105-110 K (for nickel-based spinels), independently of the x-content: the lower transition may be related to a Neel-type collinear ordering and takes place at 30 and 45 K, respectively. Application of moderate fields (H > 250 Oe) make both transitions to merge into one broad maximum in the magnetization, which takes place at lower temperature when applying larger fields. Magnetization cycles with temperature (ZFC/FC) or field (loops) allowed us to well characterize the ordered state. The effective moment follows the expected behavior when manganese ions are being substituted by ions of lower magnetic moment (Ni(2+)andCU(2+)). (c) 2007 Elsevier Ltd. All rights reserved.