Search results for "Homogeneous"

Zeroes of real polynomials on C(K) spaces

2007

AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.

Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero

2019

Abstract We consider parametric Dirichlet problems driven by the sum of a Laplacian and a nonhomogeneous differential operator ( ( a , 2 ) -type equation) and with a reaction term which exhibits arbitrary polynomial growth and a nonlinear dependence on the parameter. We prove the existence of three distinct nontrivial smooth solutions for small values of the parameter, providing sign information for them: one is positive, one is negative and the third one is nodal.

Biomolecular characterization of wild sicilian oregano: phytochemical screening of essential oils and extracts, and evaluation of their antioxidant a…

2013

An extensive survey of wild Sicilian oregano was made. A total of 57 samples were collected from various sites, followed by taxonomic characterization from an agronomic perspective. Based on morphological and production characteristics obtained from the 57 samples, cluster analysis was used to divide the samples into homogeneous groups, to identify the best biotypes. All samples were analyzed for their phytochemical content, applying a cascade-extraction protocol and hydrodistillation, to obtain the non volatile components and the essential oils, respectively. The extracts contained thirteen polyphenol derivatives, i.e., four flavanones, seven flavones, and two organic acids. Their qualitat…

Effect of population patchiness and migration rates on the adaptation and divergence of vesicular stomatitis virus quasispecies populations

1999

The effect of migration among different isolated virus quasispecies populations on their adaptation and diversity was analysed through experimental evolution. Anin vitrocell system was employed to simulate migration of vesicular stomatitis virus between isolated homogeneous host cell populations. The results clearly demonstrated a positive correlation between the migration rate and the magnitude of the mean fitness reached by the virus quasispecies populations. The results also showed, although less clearly, that fitness differences among quasispecies decreased with the magnitude of migration. These results are in close agreement with predictions of standard population genetics theory. Thes…

Exploring the use of low-intensity ultrasonics as a tool for assessing the salt content in pork meat products

2015

Meat industry demands non-destructive techniques for the control of the salting process to achieve a homogeneous final salt content in salted meat products. The feasibility of using low-intensity ultrasound for characterizing the salting process of pork meat products was evaluated. The ultrasonic velocity (V) and time of flight (TF) were measured by through-transmission and pulse-echo methods, respectively, in salted meat products. Salting involved an increase of the V in meat muscles and a decrease of the time of flight in whole hams. Measuring the V before and after salting, the salt content could be estimated. Moreover, online monitoring of the salting process by computing the TF could b…

The algebra of symmetric analytic functions on L∞

2017

We consider the algebra of holomorphic functions on L∞ that are symmetric, i.e. that are invariant under composition of the variable with any measure-preserving bijection of [0, 1]. Its spectrum is identified with the collection of scalar sequences such that is bounded and turns to be separable. All this follows from our main result that the subalgebra of symmetric polynomials on L∞ has a natural algebraic basis.

1976

The phenomenon of “true cosolvency”, which has only recently been observed in the system acetone/diethyl ether/polystyrene (AC/DEE/PS), is investigated with regard to its pressure dependence and compared with the thermodynamic behaviour of the corresponding binary sub-systems. For the determination of the limits of complete solubility, a pressure apparatus was used which had been constructed, in order to measure the turbidity of fluids in the temperature range of −70 to +500°Cand in the pressure range of 1 to 4000 bar (105 to 4·108 Nm−2). The critical line observed for the system DEE/PS (MPS=20400) looks similar to that reported for AC/PS in the literature, i.e. the upper critical solution …

Step-along power vector method for astigmatic wavefront propagation

2013

Purpose To propose both a new algebraic solution and a graphical monitoring method for astigmatic wavefront propagation in the framework provided by power vectors. Methods The generalised propagation equation describing the propagation of astigmatic wavefronts from one plane to another is adapted to the power vectors formalism using a novel algorithm based on a step-along method. The step-along procedure is directly applied to the tuple of power vectors [M, J0, J45] representing an arbitrary astigmatic wavefront and it permits the calculation of the tuple of power vectors [M′, J′0, J′45] after a given propagation distance. This is achieved mathematically first by temporarily rotating the as…

Rutile crystals as potential trace element and isotope mineral standards for microanalysis

2009

Abstract The present paper reports trace element concentrations of 15 elements (V, Cr, Fe, Zr, Nb, Mo, Sn, Sb, Hf, Ta, W, Lu, Pb, Th and U) as well as Pb and Hf isotope data for four relatively homogeneous and large (centimeter size) rutile grains. Methods employed are SIMS, EMP, LA-ICP-MS, ID-MC-ICP-MS and TIMS. For most elements homogeneity is usually within ± 10% and occasionally variations are even narrower (± 5%), particularly in the core of two of the studied grains. The trace element concentrations of the grains span a broad compositional range (e.g., Zr concentrations are ca. 4, 100, 300 and 800 ppm). Provisional concentration values, calculated based on the homogeneity of the eleme…

Sub-Finsler Horofunction Boundaries of the Heisenberg Group

2020

We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics---that is, those that arise as asymptotic cones of word metrics---on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.