Silylation of sodium silicate-based silica aerogel using trimethylethoxysilane as alternative surface modification agent

Trimethylethoxysilane (TMES) has been recognized as a good co-precursor to increase the degree of hydrophobicity during the synthesis of a silica aerogel because of its methyl groups. Therefore, some physical properties of silica aerogels, including the contact angle and porosity, were investigated using TMES as a co-precursor at different molar ratios with the main precursor such as tetramethoxysilane (TMOS) or tetraethoxysilane (TEOS). In contrast to TMES, most silylating agents such as hexamethyldisilazane (HMDZ) and trimethylchlorosilane (TMCS) have been used for surface modification because of their ability to enhance the hydrophobicity of the aerogel surface. This work examines the silylation effect, which includes increasing hydrophobicity by TMES to determine the possibility of using it as an alternative silylating agent during ambient pressure drying in the synthesis of sodium silicate-based silica aerogel. In addition, the physical properties of sodium silicate-based silica aerogels with silylation under different TMES/TMCS volume ratio are investigated. The physical properties of sodium silicate-based aerogels can be changed by the TMES/TMCS volume ratio during the surface modification step. Aerogels with a high specific surface area (458?m²/g), pore volume (3.215?cm³/g), porosity (92.7%), and contact angle (131.8°) can be obtained TMES/TMCS volume ratio of 40/60.

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Liquid chromatography of carbon clusters

Summary A comparison of three binary mobile phases in LC separation of C₆₀ and C₇₀ fullerences on chemically bonded 2,4-dinitroanilinopropyl (DNAP) stationary phase was carried out, n-Hexane-benzene has been found to be the best mobile phase for efficient separation of the all-carbon molecules permitting high loads in preparative LC.     

SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.     

On free semilattice-ordered semigroups satisfying x n =x

Let B(k,0,n) denote the group with k generators which is free in the group variety defined by the identity x ⁿ =1. Let B _slo (k,1,n) denote the semilattice-ordered semigroup with k generators which is free in the semilattice-ordered semigroup variety defined by the identity x ⁿ =x. We prove a generalization of the Green-Rees theorem: B _slo (k,1,n) is finite for all k≥1 if and only if B(k,0,n−1) is finite for all k≥1. We find a formula for card(B _slo (1,1,n)). We construct B _slo (k,1,n) for some concrete values of k and n.     

Exclusive and essential sets of implicates of Boolean functions

In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions.     

A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions

Given a reaction-diffusion system which exhibits Turing’s diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the classical case without unilateral obstacles. The study is based on a variational approach to a non-variational problem which even after transformation to a variational one has an unusual structure for which usual variational methods do not apply.     

An Erd?s-Ko-Rado theorem for partial permutations

Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A⊆[n], |A|=r and f:A→[n] is an injective map. A set A of r-partial permutations is intersecting if for any (A,f), (B,g)∈A, there exists x∈A∩B such that f(x)=g(x). We prove that for any intersecting family A of r-partial permutations, we have .It seems rather hard to characterize the case of equality. For 8?r?n-3, we show that equality holds if and only if there exist x₀ and ε₀ such that A consists of all (A,f) for which x₀∈A and f(x₀)=ε₀.     

A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions

We consider a simple reaction-diffusion system exhibiting Turing’s diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential operator, and a variational approach is used in a certain non-direct way.     

Analysis of space–time discontinuous Galerkin method for nonlinear convection–diffusion problems

The paper presents the theory of the discontinuous Galerkin finite element method for the space–time discretization of a nonstationary convection–diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in “L ²(L ²)”- and “DG”-norm formed by the “L ²(H ¹)”-seminorm and penalty terms. A special technique based on the use of the Gauss–Radau interpolation and numerical integration has been used for the derivation of an abstract error estimate. In the “DG”-norm the error estimates are optimal with respect to the size of the space grid. They are optimal with respect to the time step, if the Dirichlet boundary condition has behaviour in time as a polynomial of degree ≤ q.