Synopsis. A slotted surface coil, inspired on the cavity magnetron was developed for magnetic resonance imaging (MRI) at 4T. Imaging tests using a saline phantom demonstrated that the slotted surface coil has deeper RF-sensitivity than the single-loop RF-coil. High quality images of two rats were acquired simultaneously using standard spin-echo pulse sequences, demonstrating that the slotted su...

Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte − d2 4t ≤ pt ≤ C2Qte d2 4t where pt is the heat kernel, and d the Carnot-Carathéodory distance on G. We also obtain similar bounds on the norm of its subellip...

In the development of the Drosophila central nervous system, some of the neuroblasts designated as neuroglioblasts generate both glia and neurons. Little is known about how neuroglioblasts produce these different cell types. NB6-4 in the thoracic segment (NB6-4T) is a neuroglioblast, although the corresponding cell in the abdominal segment (NB6-4A) produces only glia. Here, we describe the cell...

Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

A small-scale synthesis of the four sphingosine stereoisomers (d-erythro, l-erythro, d-threo, and l-threo) and lignoceroyl d- and l-erythro-sphingosines, which is suitable for synthesis of tritium-labeled compounds, is described. Ethyl dl-erythro-2-acetamino-3-hydroxy-4t-octadecenoate was esterified with l(+)-acetylmandeloyl chloride and the two diastereomers obtained were separated from each o...

Fix n. Let r(n) denote the largest number r for which there is an r × n (1, −1)-matrix H satisfying the matrix equation HH ⊤ = nIr. The Hadamard conjecture states that for n divisible by 4 we have r(n) = n. Let ǫ > 0. In this paper, we show that the Extended Riemann Hypothesis and recent results on the asymptotic existence of Hadamard matrices imply that for n sufficiently large r(n) > 1 2 − ǫ ...