Design of Selective Adiabatic Inversion Pulses Using the Adiabatic Condition

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in the presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion along it. In this paper, we describe a method by which optimized modulation functions can be constructed to render insensitivity toB₁inhomogeneity over a predeterminedB₁range and over a wide band of frequencies. This is accomplished by requiring that the optimized pulse fulfill the adiabatic condition over this range ofB₁inhomogeneity and over the desired frequency band for the complete duration of the pulse. A trajectory similar to the well-known sech/tanh adiabatic pulse, i.e., a half-ellipse, is used. The optimization process improves the slice profile by optimizing the rate of motion along this trajectory. The optimized pulse can be tailored to the specific design requirements; in particular, the transition sharpness may be traded off against the inverted bandwidth. Two design examples, including experimental results, demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse: in the first example, a large frequency band is to be inverted using a weak RF amplitude in a short time. In the second example, a pulse with a very sharp transition is required.     

Comments on `Dihedral corner reflector backscatter using higherorder reflections and diffractions' [and reply]

The commenter presents arguments to show that although the above paper (see ibid., vol.AP-35, no.11, p.1235-47, Nov. 87) demonstrates reasonable agreement between the calculated and measured results, the accuracy and practical usefulness of its approach are highly questionable. The authors discuss the comments, agreeing with some and disagreeing with others, and providing further support of their work     

Comments on "A New CT-Aided Stereotactic Neurosurgery Technique"

The method given for finding the position of a target in three-dimensional space from a CT image is incorrect. The solution is based on representation of the target vector as a linear combination of two coplanar nonparallel vectors. This results in a single linear equation with two unknowns. An alternative formulation is offered, solved, and the existence and uniqueness of the solution is proved.     

The problems in quantum foundations in the light of gauge theories

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.Work supported in part by U.S. DOE Grant DE-FG05-85ER40200.Wolfson Chair Extraordinary in Theoretical Physics, TAUP N-161-85.     

On the symmetric square Unstable twisted characters

We provide a purely local computation of the (elliptic) twisted (by “transpose-inverse”) character of the representationπ=I(1) of PGL(3) over ap-adic field induced from the trivial representation of the maximal parabolic subgroup. This computation is independent of the theory of the symmetric square lifting of [IV] of automorphic and admissible representations of SL(2) to PGL(3). It leads — see [FK] — to a proof of the (unstable) fundamental lemma in the theory of the symmetric square lifting, namely that corresponding spherical functions (on PGL(2) and PGL(3)) are matching: they have matching orbital integrals. The new case in [FK] is the unstable one. A direct local proof of the fundamental lemma is given in [V].     

A simple derivation of Borland's locality result

A new proof of Borland's localization theorem is given, which is simpler, less rigorous, but gives more quantitative results.