Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

Residual-stress determination of concentric layers of cylindrically orthotropic materials

Equations have been obtained for determining residual stresses in the wall of a hollow, axially symmetric body consisting of concentric layers of elastically dissimilar materials, all having cylindrical elastic orthotropy. These equations permit residual normal stresses in the radial, circumferential, and axial directions and residual shear stresses on planes normal to the axis of the body to be calculated from measurements of the strains developed on the inner or outer cylindrical surface of the body as thin layers of stressed material are serially removed from the outer or inner surfaces, respectively. The equations are applied to a parametric study of stresses in an elastically isotropic, two-component body to determine the nature of the differences in stresses between the composite body and a homogeneous body as a function of the difference in elastic constants.     

Calibration and use of the Epprecht Rheomat

Summary This paper deals with the calibration and use of an Epprecht Rheomat with particular reference to non Newtonian liquids. A method of calculating accurate rates of shear for non-Newtonian flow is derived using theEuler-Maclaurin sum formula. Some examples are given of the calculation of shear of poly vinyl chlorideplasticiser suspensions.

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Zusammenfassung Die vorliegende Abhandlung befaßt sich mit der Eichung und dem Gebrauch eines Epprecht-Rheomats mit besonderer Hinsicht auf nicht-Newtonische Flüssigkeiten.Ein Verfahren zur exakten Berechnung von Scherwerten für nicht-Newtonische Flüssigkeiten läßt sich aus derEuler-Maclaurinschen Summenformel ableiten.Einige Beispiele zur Berechnung von Scherwerten für Weichmacher von Polyvinylchlorid sind beigefügt.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

Entanglement for the masses

Circular electron accelerators are extensively used as wide spectrum sources of photons for research in several fields of science. The basic principles and methods underlying the applications of synchrotron radiation are outlined, and its unique potential illustrated with selected examples.     

On locally spherical polytopes of type {5, 3, 5}

There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J₁×J₁×L₂(19), where J₁ is the first Janko group, of order 175560, and L₂(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective polytopes of type {5, 3, 5} must in turn cover this one.     

All Polytopes Are Quotients, and Isomorphic Polytopes Are Quotients by Conjugate Subgroups

In this paper it is shown that any (abstract) polytope is a quotient of a regular polytope by some subgroup N of the automorphism group W of , and also that isomorphic polytopes are quotients of by conjugate subgroups of W . This extends work published in 1980 by Kato, who proved these results for a restricted class of polytopes which he called ``regular'. The methods used here are more elementary, and treat the problem in a purely nongeometric manner. Received January 27, 1997, and in revised form October 1, 1997.     

More on quotient polytopes

Summary. In an earlier paper, it was shown that every abstract polytope is a quotient Q = M(W)/N {\cal Q} = {\cal M}(W)/N of some regular polytope M(W) {\cal M}(W) whose automorphism group is W, by a subgroup N of W. In this paper, attention is focussed on the quotient Q {\cal Q} , and various important structures relating to polytopes are described in terms of N ', the stabilizer of a flag of the quotient under an action of W (the 'flag action'). It is pointed out how N ' may be assumed without loss of generality to equal N. The paper also shows what properties of N ' yield polytopes which are regular, section regular, chiral, locally regular, or locally universal. The aim is to make it more practical to study non-regular polytopes in terms of group theory.     

Synthesis of a mitochondria-targeted spin trap using a novel Parham-type cyclization

A new cyclic nitrone spin trap, [4-(3′,3′-dibutyl-2′-oxy-3′H-isoindol-5′-yloxy)butyl]triphenylphosphonium bromide (MitoSpin), bearing a lipophilic cation has been prepared by a route that involves a novel Parham-type lithiation-cyclization of an isocyanate to give the isoindolinone core. MitoSpin accumulates in a membrane potential dependent way in energized mitochondria and its oxidation could potentially be used in the study of oxidative stress resulting from reactive oxygen species generated in mitochondria.     

Die Anwendung der Absorptionsspectralanalyse

Ohne Zusammenfassung