Surface and capillary transitions in an associating binary mixture model

We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere the physical mechanism involved in the appearance of these phase diagrams, leading to an enhanced tendency to phase separate below the lower critical solution point. Three different cases are considered: a planar solid surface in contact with a bulk fluid, while the other two represent two models of porous systems, namely a slit and an array on infinitely long parallel cylinders. We confirm that surface transitions, as well as capillary transitions for a large area/volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.Comment: 12 two-column pages, 12 figures, accepted for publication in Physical Review E; corrected versio

Aportación al estudio micosociológico de la provincia de León

Se muestran los resultados de algunas excursiones y el catálogo de las especies de macromicetes recolectadas en cada localidad.We show the results of some excursions with the catalogue of species rellected in each place

Some local properties defining T0T_0-groups and related classes of groups

We call G a Hall_X -group if there exists a normal nilpotent subgroup N of G for which G/N' is an X -group. We call G a T_0-group provided G/Φ(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define HallX -groups and T0 -groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relation

Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products

This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G = AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y -groups (groups satisfying the converse of Lagrange's theorem) and SC-groups (groups whose chief factors are simple) are SC -groups. Next, we show that a product of pairwise mutually permutable Y -groups is supersoluble. Finally, we give a local version of the result stating that if a mutually permutable product of two groups is a PST - group (that is, a group in which every subnormal subgroup permutes with all Sylow subgroups), then both factors are PST -group

Some Classes of finite supersoluble Groups

In this survey we study the relation between the class of groups in which Sylow permutability is a transitive relation (the PST-groups) and the class of groups in which every subgroup possesses supergroups of all possible indices, the so-called Y -groups. The parellelism between these classes in the soluble universe and the interest of the local study of PST-groups motivates a local study of Y-groups. A group G factorised as a product of two subgroups A and B is said to be a mutually permutable product whenever A permutes with every subgroup of B and B permutes with every subgroup of A . We present some results concerning mutually permutable products of groups in the orbit of the above classes

Solving random homogeneous linear second-order differential equations: a full probabilistic description

[EN] In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Second, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on random variable transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.This work has been partially supported by the Spanish M. C. Y. T. Grant MTM2013-41765-P.Casabán, M.; Cortés, J.; Romero, J.; Roselló, M. (2016). Solving random homogeneous linear second-order differential equations: a full probabilistic description. Mediterranean Journal of Mathematics. 13(6):3817-3836. https://doi.org/10.1007/s00009-016-0716-6S38173836136Øksendal B.: Stochastic Differential Equations: An Introduction with Applications, 6th edn. Springer, Berlin (2007)Soong T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)Neckel, T., Rupp, F.: Random Differential Equations in Scientific Computing. Versita, London (2013)Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterr. J. Math. 1–18 (2014). doi: 10.1007/s00009-014-0452-8Villafuerte, L., Chen-Charpentier, B.M.: A random differential transform method: theory and applications. Appl. Math. Lett. 25(10), 1490–1494 (2012). doi: 10.1016/j.aml.2011.12.033Licea, J.A., Villafuerte, L., Chen-Charpentier, B.M.: Analytic and numerical solutions of a Riccati differential equation with random coefficients. J. Comput. Appl. Math. 239, 208–219 (2013). doi: 10.1016/j.cam.2012.09.040Casabán, M.C., Cortés, J.C., Romero, J.V., Roselló, M.D.: Probabilistic solution of random homogeneous linear second-order difference equations. Appl. Math. Lett. 34, 27–32 (2014). doi: 10.1016/j.aml.2014.03.010Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216 (5), 1524–1530 (2010). doi: 10.16/j.amc.2010.03.001El-Tawil, M., El-Tahan, W., Hussein, A.: Using FEM-RVT technique for solving a randomly excited ordinary differential equation with a random operator. Appl. Math. Comput. 187(2), 856–867 (2007). doi: 10.1016/j.amc.2006.08.164Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012). doi: 10.1016/j.amc.2011.12.088Casabán, M.C., Cortés, J.C., Romero, J.V., Roselló, M.D.: Probabilistic solution of random SI-type epidemiological models using the random variable transformation technique. Commun. Nonlinear Sci. Numer. Simul. 24(1–3), 86–97 (2015). doi: 10.1016/j.cnsns.2014.12.016Casabán, M.C., Cortés, J.C., Romero, J.V., Roselló, M.D.: Determining the first probability density function of linear random initial value problems by the random variable transformation (RVT) technique: a comprehensive study. In: Abstract and Applied Analysis 2014-ID248512, pp. 1–25 (2014). doi: 10.1155/2013/248512Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Commun. Nonlinear Sci. Numer. Simul. 32, 199–210 (2016). doi: 10.1016/j.cnsns.2015.08.009El-Wakil, S.A., Sallah, M., El-Hanbaly, A.M.: Random variable transformation for generalized stochastic radiative transfer in finite participating slab media. Phys. A 435 66–79 (2015). doi: 10.1016/j.physa.2015.04.033Dorini, F.A., Cunha, M.C.C.: On the linear advection equation subject to random fields velocity. Math. Comput. Simul. 82, 679–690 (2011). doi: 10.16/j.matcom.2011.10.008Dhople, S.V., Domínguez-García, D.: A parametric uncertainty analysis method for Markov reliability and reward models. IEEE Trans. Reliab. 61(3), 634–648 (2012). doi: 10.1109/TR.2012.2208299Williams, M.M.R.: Polynomial chaos functions and stochastic differential equations. Ann. Nucl. Energy 33(9), 774–785 (2006). doi: 10.1016/j.anucene.2006.04.005Chen-Charpentier, B.M., Stanescu, D.: Epidemic models with random coefficients. Math. Comput. Model. 52(7/8), 1004–1010 (2009). doi: 10.1016/j.mcm.2010.01.014Papoulis A.: Probability, Random Variables and Stochastic Processes. McGraw-Hill, New York (1991

On the formulation of a BEM in the Bézier–Bernstein space for the solution of Helmholtz equation

This paper proposes a novel boundary element approach formulated on the Bézier-Bernstein basis to yield a geometry-independent field approximation. The proposed method is geometrically based on both computer aid design (CAD) and isogeometric analysis (IGA), but field variables are independently approximated from the geometry. This approach allows the appropriate approximation functions for the geometry and variable field to be chosen. We use the Bézier–Bernstein form of a polynomial as an approximation basis to represent both geometry and field variables. The solution of the element interpolation problem in the Bézier–Bernstein space defines generalised Lagrange interpolation functions that are used as element shape functions. The resulting Bernstein–Vandermonde matrix related to the Bézier–Bernstein interpolation problem is inverted using the Newton-Bernstein algorithm. The applicability of the proposed method is demonstrated solving the Helmholtz equation over an unbounded region in a two-and-a-half dimensional (2.5D) domainMinisterio de Economía y Competitividad BIA2016-75042-C2-1-RFondos FEDER POCI-01-0247-FEDER-01775

Permutable subnormal subgroups of finite groups

The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called PT -groups. In particular, it is shown that the finite solvable PT -groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is permutable sensitive. However, there exist finite insolvable groups which are not PT -groups but all subnormal subgroups of defect two are permutable