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

Alkoxyallene‐Based LANCA Three‐Component Synthesis of 1,2‐Diketones, Quinoxalines, and Unique Isoindenone Dimers and a Computational Study of the Isoindenone Dimerization

A series of β‐alkoxy‐β‐ketoenamides was prepared by the well‐established LANCA three‐component reaction of lithiated 1‐(2‐trimethylsilylethoxy)‐substituted allenes, nitriles, and α,β‐unsaturated carboxylic acids. The α‐tert‐butyl‐substituted compounds were smoothly converted into the expected 1,2‐diketones by treatment with trifluoroacetic acid. A subsequent condensation of the 1,2‐diketones with o‐phenylenediamine provided the desired highly substituted quinoxalines in good overall yield. Surprisingly, the α‐phenyl‐substituted β‐alkoxy‐β‐ketoenamides investigated afford not only the expected 1,2‐diketones, but also pentacyclic compounds with an anti‐tricyclo[4.2.1.12,5]deca‐3,7‐diene‐9,10‐dione 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 regio‐ and diastereoselective ring forming steps occur. Interestingly, two neutral or two protonated isoindenones are also predicted to dimerize giving the observed pentacyclic product