Use of Micelles in the TLC Separation of Polynuclear Aromatic Compounds and Amino Acids

Abstract

The polynuclear aromatic compounds (PNA): anthracene, napthalene, phenanthrene, pyrene, pyrenecarboxaldehyde, benzo (a) pyrene, benzo (e) pyrene, perylene and fluorene can be chromatographed on polyamide TLC sheets using an aqueous micellar solution cf sodium dodecylsulfate (SDS) as the mobile phase. Reversed micellar solutions (of sodium dioctylsulfosuccinate) were used in a reverse phase chromatographic separation of amino acids. Some amino acids tended to streak slightly rather than move as discrete spots. Conditions could be adjusted, however, so that most of the amino acids and all PNA's would move as spots.     

Normal operators and inequalities in norm ideals

In this work we characterize normal invertible operators via inequalities with unitarily invariant norm of elementary operators.     

THE (U K)-ORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

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Normal forms for fuzzy logics: a proof-theoretic approach

A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for ?ukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.     

Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.     

函数与其导数具有公共值的全纯函数族的正规性

设F为区域G上的全纯函数族, a,b(≠0)为两有穷复数,n为正整数,本文推广了Miranda定则,证明了:若对任意的f∈F,(a,b)为f与f(n)在G上的IM分担数组,且当f=a时, f'=f(n+1)=b,则F在G中正规.     

Decision problems in the space of Dehn fillings

Normal surface theory is used to study Dehn fillings of a knot-manifold. We use that any triangulation of a knot-manifold may be modified to a triangulation having just one vertex in the boundary. In this situation, it is shown that there is a finite computable set of slopes on the boundary of the knot-manifold, which come from boundary slopes of normal or almost normal surfaces. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely those manifolds obtained by Dehn filling of a given knot-manifold that: (1) are reducible, (2) contain two-sided incompressible surfaces, (3) are Haken, (4) fiber over S¹, (5) are the 3-sphere, and (6) are a lens space. Each of these algorithms is a finite computation.Moreover, in the case of essential surfaces, we show that the topology of each filled manifold is strongly reflected in the combinatorial properties of a triangulation of the knot-manifold with just one vertex in the boundary. If a filled manifold contains an essential surface then the knot-manifold contains an essential normal vertex solution which caps off to an essential surface of the same type in the filled manifold. (Normal vertex solutions are the premier class of normal surface and are computable.)     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence:

A generalized Duffing equation with the Coulomb’s friction law and Signorini–type contact conditions

This work provides mathematical and numerical analyses for a spring–mass system, in which Signorini–type contact conditions and Coulomb’s friction law with thermal effects are taken into consideration. The motion of a mass attached to a viscoelastic (Kelvin–Voigt type) nonlinear spring is described by a generalized Duffing equation. Signorini contact conditions are understood as extended complementarity conditions (CCs), where convolution is incorporated, allowing to consider thermal aspects of an obstacle. We prove the existence of global weak solutions for the highly nonlinear differential equation system with all the conditions, based on the regularized differential equation and the normal compliance condition with the standard mollifier. In addition, we investigate what side effects produce higher singularities of contact forces in dynamic contact problems, which is also supported by numerical evidences. Numerical schemes are proposed and then several groups of data are selected for the display of our numerical simulations.