A series of monomial representations of SL2(p) is used to construct a new series of self-dual ternary codes of length 2(p + 1) for all primes p ≡ 5 (mod 8). In particular we find a new extremal self-dual ternary code of length 60.

Example 4.31. (K16 , P) : P = {(1, 3,5,10,16,15), (1, 4, 6,13,14,11), (1,5, 7,12, 15,10),(1,16,12,10,9,14),(2,3,6,9,11,13),(2,4, 7,10,13,9), (2,5,13,7,11,10), (1, 6, 2, 7,3,8), (1, 7, 8, 11,6,12), (3, 13, 1,9,7,14), (2,11,3,10,6,14),(3,15,14,16,8,12),(4,9,16,7,15,11),(4,10,14,8,13,15), (4,13,16,11,5,14),(8,2,12,5,9,15),(16,3,9,12,4,5),(5,15,6,16,4,8)}; L {(5, 6), (6,7), (6, 8), (8,9), (8, 10), ...

where 〈. . .〉 here denotes an average over many particles and events. In particular, elliptic flow v2 is recognized as a sensitive probe of thermalization at RHIC [2]. While anisotropic flow is by definition a collective effect that involves many particles, it has mostly been analyzed using methods based either on a study of twoparticle correlations [3–5] or on the cumulants of correlations bet...

Consider a random walk on the mapping class group, and let wn be the location of the random walk at time n. A random Heegaard splitting M(wn) is a 3-manifold obtained by using wn as the gluing map between two handlebodies. We show that the joint distribution of (wn, w −1 n ) is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by th...

Let M be a surface sum of 3-manifolds M1 and M2 along a bounded connected surface F and ∂i be the component of ∂Mi containing F . If Mi has a high distance Heegaard splitting, then any minimal Heegaard splitting of M is the amalgamation of those of M,M and M∗, where M i = Mi \ ∂i × I, and M∗ = ∂1 × I ∪F ∂2 × I. Furthermore, once both ∂i \ F are connected, then g(M) = Min {

Introduction: Magnetic resonance elastography (MRE) is a non invasive method that combines externally applied vibrations with the motion sensitivity of MRI to measure the shear elasticity soft tissues [1]. In MRE this is traditionally achieved by solving an inverse problem with MRE shear wave images as input data [2]. A complementary approach, which does not require the solution of an inverse p...

Non-invasive methods for liver stiffness assessment have been introduced over recent years. Of these, two main methods for estimating liver fibrosis using ultrasound elastography have become established in clinical practice: shear wave elastography and quasi-static or strain elastography. Shear waves are waves with a motion perpendicular (lateral) to the direction of the generating force. Shear...

Douglas H. Jones, Donald C. Anderson, Bean L. Burr, Helen E. Rudloff, C. Wayne Smith, Sharon S. Krater, and Frank C. Schmalstieg Departments of Pediatrics (D.H.J., D.C.A., B.L.B., C.W.S., S.S.K.) and Microbiology and Immunology and Cell Biology (D.C.A.), Baylor College of Medicine, and the Speros P. Martel Leukocyte Biology Laboratory, Texas Children’s Hospital, Houston, and Department of Pedia...

Elastography is a modality that estimates tissue stiffness and, thus, provides useful information for clinical diagnosis. Attention has focused on the measurement of shear wave propagation; however, many methods assume shear wave propagation is unidirectional and aligned with the lateral imaging direction. Any deviations from the assumed propagation result in biased estimates of shear wave spee...

This paper is concerned with the effect of pure shear on the reflection from a plane boundary of infinitesimal plane waves propagating in a half-space of incompressible isotropic elastic material. For a special class of constitutive laws it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave (with angle o...