1,806,384 research outputs found
Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
The diameter of a disc filling a loop in the universal covering of a
Riemannian manifold may be measured extrinsically using the distance function
on the ambient space or intrinsically using the induced length metric on the
disc. Correspondingly, the diameter of a van Kampen diagram filling a word that
represents the identity in a finitely presented group can either be measured
intrinsically its 1-skeleton or extrinsically in the Cayley graph of the group.
We construct the first examples of closed manifolds and finitely presented
groups for which this choice -- intrinsic versus extrinsic -- gives rise to
qualitatively different min-diameter filling functions.Comment: 44 pages, 12 figures, to appear in the Journal of Differential
Geometr
A SPH solver for simulating paramagnetic solid fluid interaction in the presence of an external magnetic field
Acknowledgment The first two authors wish to express their sincerest thanks to Iran National Science Foundation (INSF) for supporting this work under Contract Number 92021291.Peer reviewedPostprin
Wiener Chaos and the Cox-Ingersoll-Ross model
In this we paper we recast the Cox--Ingersoll--Ross model of interest rates
into the chaotic representation recently introduced by Hughston and Rafailidis.
Beginning with the ``squared Gaussian representation'' of the CIR model, we
find a simple expression for the fundamental random variable X. By use of
techniques from the theory of infinite dimensional Gaussian integration, we
derive an explicit formula for the n-th term of the Wiener chaos expansion of
the CIR model, for n=0,1,2,.... We then derive a new expression for the price
of a zero coupon bond which reveals a connection between Gaussian measures and
Ricatti differential equations.Comment: 27 page
Metal matrix composite structural panel construction
Lightweight capped honeycomb stiffeners for use in fabricating metal or metal/matrix exterior structural panels on aerospace type vehicles and the process for fabricating same are disclosed. The stiffener stringers are formed in sheets, cut to the desired width and length and brazed in spaced relationship to a skin with the honeycomb material serving directly as the required lightweight stiffeners and not requiring separate metal encasement for the exposed honeycomb cells
Non-linear stress response of non-gap-spanning magnetic chains suspended in a Newtonian fluid under oscillatory shear test : A direct numerical simulation
The corresponding author wishes to express his sincerest thanks to the Iran National Science Foundation (INSF) for supporting this work under Contract Number 92021291.Peer reviewedPostprintPublisher PD
AlkoxyalleneâBased LANCA ThreeâComponent Synthesis of 1,2âDiketones, Quinoxalines, and Unique Isoindenone Dimers and a Computational Study of the Isoindenone Dimerization
A series of ÎČâalkoxyâÎČâketoenamides was prepared by the wellâestablished LANCA threeâcomponent reaction of lithiated 1â(2âtrimethylsilylethoxy)âsubstituted allenes, nitriles, and α,ÎČâunsaturated carboxylic acids. The αâtertâbutylâsubstituted compounds were smoothly converted into the expected 1,2âdiketones by treatment with trifluoroacetic acid. A subsequent condensation of the 1,2âdiketones with oâphenylenediamine provided the desired highly substituted quinoxalines in good overall yield. Surprisingly, the αâphenylâsubstituted ÎČâalkoxyâÎČâketoenamides investigated afford not only the expected 1,2âdiketones, but also pentacyclic compounds with an antiâtricyclo[4.2.1.12,5]decaâ3,7âdieneâ9,10âdione core. These interesting products are very likely the result of an isoindenone dimerization which was mechanistically studied with the support of DFT calculations. Under the strongly acidic reaction conditions, a stepwise reaction is likely leading to a protonated isoindenone as reactive intermediate. It may first form a van der Waals complex with a neutral isoindenone before the two regioâ and diastereoselective ring forming steps occur. Interestingly, two neutral or two protonated isoindenones are also predicted to dimerize giving the observed pentacyclic product
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