On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

A New Family of Distance Functions for Perceptual Similarity Retrieval of Medical Images

A long-standing challenge of content-based image retrieval (CBIR) systems is the definition of a suitable distance function to measure the similarity between images in an application context which complies with the human perception of similarity. In this paper, we present a new family of distance functions, called attribute concurrence influence distances (AID), which serve to retrieve images by similarity. These distances address an important aspect of the psychophysical notion of similarity in comparisons of images: the effect of concurrent variations in the values of different image attributes. The AID functions allow for comparisons of feature vectors by choosing one of two parameterized expressions: one targeting weak attribute concurrence influence and the other for strong concurrence influence. This paper presents the mathematical definition and implementation of the AID family for a two-dimensional feature space and its extension to any dimension. The composition of the AID family with L (p) distance family is considered to propose a procedure to determine the best distance for a specific application. Experimental results involving several sets of medical images demonstrate that, taking as reference the perception of the specialist in the field (radiologist), the AID functions perform better than the general distance functions commonly used in CBIR.

Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

Structural properties of lipid reconstructs and lipid composition of normotensive and hypertensive rat vascular smooth muscle cell membranes

Multiple cell membrane alterations have been reported to be the cause of various forms of hypertension. The present study focuses on the lipid portion of the membranes, characterizing the microviscosity of membranes reconstituted with lipids extracted from the aorta and mesenteric arteries of spontaneously hypertensive (SHR) and normotensive control rat strains (WKY and NWR). Membrane-incorporated phospholipid spin labels were used to monitor the bilayer structure at different depths. The packing of lipids extracted from both aorta and mesenteric arteries of normotensive and hypertensive rats was similar. Lipid extract analysis showed similar phospholipid composition for all membranes. However, cholesterol content was lower in SHR arteries than in normotensive animal arteries. These findings contrast with the fact that the SHR aorta is hyporeactive while the SHR mesenteric artery is hyperreactive to vasopressor agents when compared to the vessels of normotensive animal strains. Hence, factors other than microviscosity of bulk lipids contribute to the vascular smooth muscle reactivity and hypertension of SHR. The excess cholesterol in the arteries of normotensive animal strains apparently is not dissolved in bulk lipids and is not directly related to vascular reactivity since it is present in both the aorta and mesenteric arteries. The lower cholesterol concentrations in SHR arteries may in fact result from metabolic differences due to the hypertensive state or to genes that co-segregate with those that determine hypertension during the process of strain selection.

Productive performance and milk protein fraction composition of dairy cows supplemented with sodium monensin

The objective of this work was to evaluate the levels of sodium monensin on lactating cows and their effects on productive performance and milk protein fraction composition. It was used 12 Holstein cows, distributed in four balanced 3 × 3 Latin squares, and fed three diets: one control without monensin, and two diets with monensin at the levels of 24 or 48 mg/kg DM added to the concentrate. Milk production was daily measured throughout the entire experimental period. The samples used for analysis of milk composition were collected on two alternated days from the two daily milking. Non-protein nitrogen, total nitrogen and non-casein nitrogen contents were directly evaluated in the milk, and casein, whey protein and true protein contents were indirectly determined. The use of monensin in the rations reduced dry matter and nutrient intake, especially when diet with 48 mg/kg of dry matter was given. The ration with 24 mg/kg of DM increased milk production, with or without correction, and also fat and lactose yield, and it improved productive efficiency. The levels of monensin in the ratios did not influence contents of milk crude protein, non-protein nitrogen, non-casein nitrogen, true protein, casein, casein/true protein ratio, whey protein, and of all those fractions expressed as percentage of crude protein. The utilization of monensin in the ratio at the dose of 24 mg/kg of DM influences positively the productive performance of lactating cows, and it does not influence the composition of milk protein fractions.

Productive performance and composition of milk protein fraction in dairy cows supplemented with fat sources

The objective of this study was to evaluate the use of fat sources in rations for lactating cows on the productive performance and composition of milk protein fraction. Twelve Holstein cows were used, grouped in three balanced 4 × 4 Latin squares, fed with the following rations: control; refined soybean oil; whole raw soybean; and calcium salts of unsaturated fatty acid (Megalac-E). Dry matter and nutrient intake, and daily milk production were evaluated. The samples used to analyze milk composition were collected in two alternate days and were obtained from two daily milking. Milk composition and total nitrogen, non-protein nitrogen and non-casein nitrogen ratios were analyzed. The casein, serum protein and true protein ratios were obtained by difference. Dry matter and nutrient intakes were lower when cows received the diet containing calcium salts of fatty acids, in relation to the control diet. Among the diets with fat sources, the one with whole raw soybean and calcium salts decreased milk production. There was no effect of fat sources added to the diet on crude protein, non-protein nitrogen, non-casein nitrogen, true protein, casein, casein/milk true protein ratio and serum protein. Similarly, the experimental diets did not influence the protein fractions when expressed in percentage of milk crude protein. The utilization of fat sources in diets changes milk production and composition of lactating cows, but does not influence the composition of milk protein fractions.

Carbon Stocks and Isotopic Composition of the Organic Matter in Soils Covered by Native Vegetation and Pasture in Sorocaba, SP, Brazil

Land cover change constitutes one of main way of alteration of soil organic matter in both quantitative and qualitative terms. The goal of this study was to compare the carbon stock and the isotopic signature of the organic matter in the soil of areas with different land use,covered with forest and grass (pasture). The study area is located at Sorocaba, SP, Brazil. Using un-deformed soil samples, we measured the carbon content and bulk density. The isotopic signature of soil carbon was determined through the analysis of isotopic ratio (12)C/(13)C. The pasture soil stocks 48% less carbon than the soil covered by natural forest. The isotopic signature indicated that 42.2% of organic matter of the soil covered by pasture is originated from grasses. This characterizes a highly degradation of organic matter in the environment, both quantitatively and qualitatively. Hence, some guidelines of recuperation are described in order to restore the soil organic matter, structure and porosity.

Antioxidant activity and phenolic composition of herbal infusions consumed in Brazil

Processed tea and herbal infusions were Studied for their phenol content, antioxidant activity and main flavonoids. Total phenolics were determined by Folin-Ciocalteu method and ranged from N.D. to 46.46 +/- 0.44 mg/g GAE. Flavonoids were investigated by HPLC, and myricetin, quercetin, kaempferol were identified in black, green, and chamomile tea. Antioxidant activity was evaluated using two methods: DPPH and beta-carotene bleaching test (BCB). Using the BCB, the highest activities were found for infusions of black tea, mate, lemongrass, chamomile, and fennel; whereas fresh herbal infusions presented the lowest activities. Using the DPPH method, fresh herbal infusions presented the highest activities. Processed leaves with the lowest IC50 values were green and black tea (147.63 and 288.60 mu g/mL, respectively). The results of this research show that the infusions studied are good Source of compounds presenting antioxidant activity in vitro.

Modification of composition of a nanoemulsion with different cholesteryl ester molecular species: Effects on stability, peroxidation, and cell uptake

Purpose: Use of lipid nanoemulsions as carriers of drugs for therapeutic or diagnostic purposes has been increasingly studied. Here, it was tested whether modifications of core particle constitution could affect the characteristics and biologic properties of lipid nanoemulsions. Methods: Three nanoemulsions were prepared using cholesteryl oleate, cholesteryl stearate, or cholesteryl linoleate as main core constituents. Particle size, stability, pH, peroxidation of the nanoemulsions, and cell survival and uptake by different cell lines were evaluated. Results: It was shown that cholesteryl stearate nanoemulsions had the greatest particle size and all three nanoemulsions were stable during the 237-day observation period. The pH of the three nanoemulsion preparations tended to decrease over time, but the decrease in pH of cholesteryl stearate was smaller than that of cholesteryl oleate and cholesteryl linoleate. Lipoperoxidation was greater in cholesteryl linoleate than in cholesteryl oleate and cholesteryl stearate. After four hours' incubation of human umbilical vein endothelial cells (HUVEC) with nanoemulsions, peroxidation was minimal in the presence of cholesteryl oleate and more pronounced with cholesteryl linoleate and cholesteryl stearate. In contrast, macrophage incubates showed the highest peroxidation rates with cholesteryl oleate. Cholesteryl linoleate induced the highest cell peroxidation rates, except in macrophages. Uptake of cholesteryl oleate nanoemulsion by HUVEC and fibroblasts was greater than that of cholesteryl linoleate and cholesteryl stearate. Uptake of the three nanoemulsions by monocytes was equal. Uptake of cholesteryl oleate and cholesteryl linoleate by macrophages was negligible, but macrophage uptake of cholesteryl stearate was higher. In H292 tumor cells, cholesteryl oleate showed the highest uptakes. HUVEC showed higher survival rates when incubated with cholesteryl stearate and smaller survival with cholesteryl linoleate. H292 survival was greater with cholesteryl stearate. Conclusion: Although all three nanoemulsion types were stable for a long period, considerable differences were observed in size, oxidation status, and cell survival and nanoemulsion uptake in all tested cell lines. Those differences may be helpful in protocol planning and interpretation of data from experiments with lipid nanoemulsions.

First stars XI. Chemical composition of the extremely metal-poor dwarfs in the binary CS 22876-032

Context. Unevolved metal-poor stars constitute a fossil record of the early Galaxy, and can provide invaluable information on the properties of the first generations of stars. Binary systems also provide direct information on the stellar masses of their member stars. Aims. The purpose of this investigation is a detailed abundance study of the double-lined spectroscopic binary CS 22876-032, which comprises the two most metal-poor dwarfs known. Methods. We used high-resolution, high-S/N ratio spectra from the UVES spectrograph at the ESO VLT telescope. Long-term radial-velocity measurements and broad-band photometry allowed us to determine improved orbital elements and stellar parameters for both components. We used OSMARCS 1D models and the TURBOSPECTRUM spectral synthesis code to determine the abundances of Li, O, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Fe, Co and Ni. We also used the (COBOLD)-B-5 model atmosphere code to compute the 3D abundance corrections, notably for Li and O. Results. We find a metallicity of [Fe/H] similar to -3.6 for both stars, using 1D models with 3D corrections of similar to -0.1 dex from averaged 3D models. We determine the oxygen abundance from the near-UV OH bands; the 3D corrections are large, -1 and -1.5 dex for the secondary and primary respectively, and yield [O/Fe] similar to 0.8, close to the high-quality results obtained from the [OI] 630 nm line in metal-poor giants. Other [alpha/Fe] ratios are consistent with those measured in other dwarfs and giants with similar [Fe/H], although Ca and Si are somewhat low ([X/Fe] less than or similar to 0). Other element ratios follow those of other halo stars. The Li abundance of the primary star is consistent with the Spite plateau, but the secondary shows a lower abundance; 3D corrections are small. Conclusions. The Li abundance in the primary star supports the extension of the Spite Plateau value at the lowest metallicities, without any decrease. The low abundance in the secondary star could be explained by endogenic Li depletion, due to its cooler temperature. If this is not the case, another, yet unknown mechanism may be causing increased scatter in A( Li) at the lowest metallicities.