Riesz Means on Graphs and Discrete Groups

Suppose that Γ is a weighted graph or a discrete group. Let $m_{\alpha,R}(\lambda )=\big(1-\big|\frac{\lambda}{R}\big|\big)_{+}^{\alpha}$ be the Riesz means and let Δ be the discrete Laplacian on Γ. We prove that if D is the homogeneous dimension of Γ then the operator m _α,R (Δ) is bounded on L ^p , provided that $\alpha>D|\frac{1}{p}-\frac{1}{2}|$ .     

Effect of off-frequency sampling in magnetic resonance elastography

In magnetic resonance elastography (MRE), shear waves at a certain frequency are encoded through bipolar gradients that switch polarity at a controlled encoding frequency and are offset in time to capture wave propagation using a controlled sampling frequency. In brain MRE, there is a possibility that the mechanical actuation frequency is different from the vibration frequency, leading to a mismatch with encoding and sampling frequencies. This mismatch can occur in brain MRE from causes both extrinsic and intrinsic to the brain, such as scanner bed vibrations or active damping in the head. The purpose of this work was to investigate how frequency mismatch can affect MRE shear stiffness measurements. Experiments were performed on a dual-medium agarose gel phantom, and the results were compared with numerical simulations to quantify these effects. It is known that off-frequency encoding alone results in a scaling of wave amplitude, and it is shown here that off-frequency sampling can result in two main effects: (1) errors in the overall shear stiffness estimate of the material on the global scale and (2) local variations appearing as stiffer and softer structures in the material. For small differences in frequency, it was found that measured global stiffness of the brain could theoretically vary by up to 12.5% relative to actual stiffness with local variations of up to 3.7% of the mean stiffness. It was demonstrated that performing MRE experiments at a frequency other than that of tissue vibration can lead to artifacts in the MRE stiffness images, and this mismatch could explain some of the large-scale scatter of stiffness data or lack of repeatability reported in the brain MRE literature.     

Any work-conserving policy stabilizes the ring with spatial re-use

We consider the ring network with spatial reuse. Traffic streams may enter and exit the network at any node. We adopt an arrival traffic model with deterministic constraints on its sample paths, which conforms to the output traffic of a leaky bucket rate control mechanism. A transmission policy specifies each time at which the traffic stream will be transmitted at the outgoing link by each node. We provide an upper bound on the asymptotic backlog of the ring that holds for all work-conserving policies and is independent of the initial conditions. This bound remains finite as long as the maximum load of every link is less than one. The latter condition is also necessary for the existence of an asymptotic bound that is independent of the initial conditions     

Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows

A hydrodynamic boundary condition is developed for lattice Boltzmann hydrodynamics using a square, orthogonal grid. A constraint based on energy considerations is developed to provide closure for the equations which govern the particle distribution at the boundaries. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid behind a grid, known as Kovasznay flow. The results are compared to those using alternate boundary conditions using the known exact solution. The hydrodynamic boundary condition produces quadratic spatial convergence, while alternate techniques fail to maintain this second-order accuracy.     

Synthesis and comparative study on the reactivity of peptidyl-type phosphinic esters: intramolecular effects in the alkaline and acidic cleavage of methyl beta-carboxyphosphinates

Using the phosphinic analogue of Cbz-Phe-Gly-OEt 1a as a template for this study, several phosphinic esters (2a-g) were prepared, employing an efficient method for each case. The reactivity of these derivatives under conventional deprotection conditions was studied, and the results are listed comparatively. The effect of steric hindrance as well as the contribution of neighboring groups in the rate of hydrolysis of suitably selected beta-carboxyphosphinates under acidic and alkaline deprotection conditions was examined. The results clearly demonstrate that a significant acceleration of phosphinate cleavage occurs due to the intermediacy of a five-membered, mixed anhydride-type species. This was supported by the observation that similar interactions were not observed in the case of hindered alpha-carboxyphosphinate homologous derivatives.     

Hybridization of mismatched or partially matched DNA at surfaces

We investigate how probe density influences hybridization for unlabeled target oligonucleotides that contain mismatched sequences or targets that access different binding locations on the immobilized probe. We find strong probe density effects influencing not only the efficiency of hybridization but also the kinetics of capture. Probe surfaces are used repeatedly, and the potentially large contributions of sample-to-sample variations in surface heterogeneity and nonspecific adsorption are addressed. Results of kinetic, equilibrium, and temperature-dependent studies, obtained using in-situ surface plasmon resonance (SPR) spectroscopy, show that hybridization for surface immobilized DNA is quite different from the well-studied solution-phase reaction. Surface hybridization depends strongly on the target sequence and probe density. Much of the data can be explained by the presence of steric crowding at high probe density; however, the behavior of mismatched sequences cannot be understood using standard models of hybridization even at the lowest density studied. In addition to unusual capture kinetics observed for the mismatched targets, we find that the binding isotherms can be fit only if a heterogeneous model is used. For mismatched targets, the Sips model adequately describes probe-target binding isotherms; for perfectly matched targets, the Langmuir model can be used.     

Products from Furans. XVI . Novel synthetic routes to sympathomimetic amine analogues via 6-hydroxy-2H-pyran-3(6H)-ones

Novel heterocyclic analogues mimicking compounds with antipsychotic activity (sympathomimetic amines) were synthesized. These compounds contain the phenyl-substituted pyran ring system as a consequence of their common route of preparation. Furthermore an example of the synthetic route for preparing compounds having the features of both β-hydroxy-β-phenylethylamine and GABA is also presented.     

Stability of token passing rings

A sufficient stability condition for the standard token passing ring has been known since the seminal paper by Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to the research community. In fact, Watson observed that in the performance evaluation of token passing rings, it is convenient to derive stability conditions ... (without proof). Our intention is to fill this gap, and to provide a formal proof of thesufficient and necessary stability condition for the token passing ring. In this paper, we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth a gatedl-limited (l ) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.This research was supported by NSF Grant CCR-8900305, and in part by AFOSR Grant 90-0107, and by Grant R01 LM05118 from the National Library of Medicine.     

An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity

The technique of distributed dislocations proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work is intended to extend this technique in studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. This extension is not an obvious one since rotations and couple-stresses are involved in the theory employed to analyze the crack problems. Here, the technique is introduced to study the case of a mode I crack. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack is modeled by a continuous distribution of climb dislocations and constrained wedge disclinations (the concept of ‘constrained wedge disclination’ is first introduced in the present work). These distributions create both standard stresses and couple stresses in the body. In particular, it is shown that the mode-I case is governed by a system of coupled singular integral equations with both Cauchy-type and logarithmic kernels. The numerical solution of this system shows that a cracked solid governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a solid governed by classical elasticity. Also, the stress level at the crack-tip region is appreciably higher than the one predicted by classical elasticity.     

A Method Based on the Radon Transform for Three-Dimensional Elastodynamic Problems of Moving Loads

An integral transform procedure is developed to obtain fundamental elastodynamic three-dimensional (3D) solutions for loads moving steadily over the surface of a half-space. These solutions are exact, and results are presented over the entire speed range (i.e., for subsonic, transonic and supersonic source speeds). Especially, the results obtained here for the tangential loads (one of these loads is along the direction of motion and the other is orthogonal to the direction of motion) are quite new in the literature. The solution technique is based on the use of the Radon transform and elements of distribution theory. It also fully exploits as auxiliary solutions the ones for the corresponding plane-strain and anti-plane shear problems (the latter problems are 2D and uncoupled from each other). In particular, it should be noticed that the plane-strain problem here is completely analogous to the original 3D problem, not only with respect to the field equations but also with respect to the boundary conditions. This makes the present technique more advantageous than other techniques, which require first the determination of a fictitious auxiliary plane-strain problem through the solution of an integral equation. Our approach becomes particularly simple when there is no angular dependence in the boundary conditions (i.e., when axially symmetric problems regarding their boundary conditions are considered). On the contrary, no such constraint needs to be fulfilled as regards the material response (and, therefore, the governing equations of the problem) and/or also possible loss of axisymmetry due to the generation of shock (Mach-type) waves in the medium. Therefore, the solution technique can easily deal with general 3D problems having a largely arbitrary radial dependence in the boundary conditions and involving: (i) material anisotropy in static and dynamic situations, and (ii) asymmetry caused by changes in the nature of governing PDEs due to the existence of different velocity regimes (super-Rayleigh, transonic, supersonic) in dynamic situations. This revised version was published online in July 2006 with corrections to the Cover Date.