In the present paper, we study properties of second Dirichlet eigenvalue fractional Laplacian annuli-like domains and corresponding eigenfunctions. first part, consider an annulus with inner radius $ R outer R+1 $. We show that for sufficiently large any eigenfunction this is nonradial. investigate in form B_1(0)\setminus \overline{B_{\tau}(a)} $, where a unitary ball 0<\tau<1-|a| value m...

This paper describes the NMR/MRI magnets that are currently being developed at the MIT Francis Bitter Magnet Laboratory: 1) a 1.3 GHz NMR magnet; 2) a compact NMR magnet assembled from YBCO annuli; and 3) a persistent-mode, fully-protected 0.5-T/800-mm whole-body MRI magnet.

In this lecture we compute asumptotics estimates for the Green's function and apply it to the exiting annuli problem. Also we define Capacity, Polar set Prove the B-P-P theorem of Martin's Capacity for Markov chains[3] and use apply it on the intersection of RW problem.

We give an overview of the proof ([Sc]) that the only knots that are both tunnel number one and genus one are those that are already known: 2-bridge knots obtained by plumbing together two unknotted annuli and the satellite examples classified by Eudave-Muñoz and by Morimoto-Sakuma.

Fish retinas continue to grow throughout life by adding neurons at the margin, with the result that cells born at a peripheral site are steadily displaced toward the center of the enlarging retina. This presents a functional problem for fish with specialized temporal areas such as a fovea--how to reconcile continual growth with the maintenance of a temporal location for the fovea. One possibili...

Visible persistence refers to the continuation of visual perception after the physical termination of a stimulus. We studied an extreme case of visible persistence by presenting two matrices of randomly distributed black and white pixels in succession. On the transition from one matrix to the second, the luminance polarity of all pixels within a disk- or annulus-shaped area reversed, physically...

BACKGROUND Atherosclerosis has been implicated as a cause of valvular calcification. The aim of this study was to determine whether atherosclerotic calcification in multiple vascular areas is significantly associated with aortic or mitral annular calcification independent of traditional risk factors. METHODS AND RESULTS A total of 1242 consecutive asymptomatic patients free of clinical corona...

BACKGROUND Mitral and aortic valves are known to be coupled via fibrous tissue connecting the two annuli. Previous studies evaluating this coupling have been limited to experimental animals using invasive techniques. The new matrix array transesophageal transducer provides high-resolution real-time 3D images of both valves simultaneously. We sought to develop and test a technique for quantitati...

PURPOSE To determine the repeatability and profiles with different partition methods in intraretinal thickness layers in healthy human subjects, using optical coherence tomography (OCT). METHODS A custom-built ultrahigh-resolution OCT was used to acquire three-dimensional volume of the macula in 20 healthy subjects. The dataset was acquired twice using the macular cube 512×128 protocol in an ...