How fat is a fat bundle?

Let P M be a principal G-bundle with connection 1-form and curvature . For a subset S of g^* the given connection is S-fat (Weinstein, [5]) if for every in S the form ° is nondegenerate on each horizontal subspace in TP.Let K be a compact group and K/H be its coadjoint orbit. The orthogonal projection t h defines a connection on the principal H-bundle K K/H. We show that this connection is fat off certain walls of Weyl chambers in h^*. We then apply the result to the construction of symplectic fiber bundles over K/H. As an example, we show how higher-dimensional coadjoint orbits fiber symplectically over lower-dimensional orbits.     

On the existence of acetyl hypofluorite

¹H and ¹⁹F NMR spectra along with GC studies of the oxidizing solution obtained from the reaction of F₂ with NaOAc, support the notion that a single compound with molecular structure CH₃COOF indeed exists.     

r-Maximal major subsets

The question of which r.e. setsA possess major subsetsB which are alsor-maximal inA (A⊂_rm B) arose in attempts to extend Lachlan’s decision procedure for the αε-theory of ℰ^*, the lattice of r.e. sets modulo finite sets, and Soare’s theorem thatA andB are automorphic if their lattice of supersets ℒ^*(A) and ℒ^*(B) are isomorphic finite Boolean algebras. We characterize the r.e. setsA with someB⊂_rm A as those with a Δ₃ function that for each recursiveR _i specifiesR _i or as infinite on and to be preferred in the construction ofB. There are r.e.A andB with ℒ^*(A) and ℒ^*(B) isomorphic to the atomless Boolean algebra such thatA has anrm subset andB does not. Thus 〈ℰ^*,A〉 and 〈ℰ^*,B〉 are not even elementarily equivalent. In every non-zero r.e. degree there are r.e. sets with and withoutrm subsets. However the classF of degrees of simple sets with norm subsets satisfies . The authors were partially supported by NSF Grants MCS 76-07258, MCS 77-04013 and MCS 77-01965 respectively.     

Determination of rate constants for quenching singlet oxygen by chemiluminescence technique

Overall rate constants have been found for quenching¹O₂ generated under thermal decomposition of hydrotrioxides ROOOH, by several unsaturated species at 0°C. CH₃CH(OH)OOOHm (CH₃)₂C(OH)OOOH, CH₃C(OC₂H₅)₂OOOH and CH₃C(O) CH(OOOH) (CH₂)₂CH₃ were used as ROOOH; unsaturated compounds were 1,3-diphenylisobenzofurane, 2-methylfurane, 2,3,4,5-tetraphenylfurane, furfuroldiacetate, tetramethylethylene, adamantylideneadamantane, exo,-exo-2,3-dioxymethyl-7-adamantylidenenorbornane, exo,-exo-2,3-(2¹-oxatrimethylene)-7-adamantylidenenorbornane, 1,3-cyclohexadiene, (E,E)-8, 10-dodecadienol, cyclooctatetraene and isoprene.

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¹O₂, ROOOH O°C. ROOOH CH₃CH(OH)OOOH, (CH₃)₂C(OH)OOOH, CH₃C(OC₂H₅)₂OOOH, CH₃C(O)CH(OOOH) (CH₂)₂CH₃; -1,3-, 2-, 2,3,4,5-, , , . , -2,3-(2¹-)-7-, 1,3-, (,)-8,10-, , .

     

Neutron generation in massive Cu-targets during the irradiation with 22 and 44 GeV carbon ions

An extended Cu-target was irradiated with 22 and 44 GeV carbon ions for about 11.3 and 14.7 hours, respectively. The upper side of the target was in contact with a paraffin-block for the moderation of secondary neutrons. Small holes in the moderator were filled with either lanthanum salts or uranium oxide. The reaction was studied via the decay of¹⁴⁰La(40h) using radiochemical methods, as has been published. The reaction was studied via the decay of²³⁹Np(2.3 d) as well as the reaction U(n,f) using radiochemical methods. In addition, solid state nuclear track detectors were used for fission studies in gold. The yields for the formation of (n,) products agree essentially with other experiments on extended targets carried out at the Dubna Synchrophasotron (LHE, JINR). To a first approximation, the breeding rate of (n, ) products doubles when the carbon energy increases from 22 to 44 GeV. If, however, results at 44 GeV are compared in detail to those at 22 GeV, we observe an excess of (37±9)% in the experimentally observed²³⁹Np-breeding rate over theoretical estimations. Experiments using solid state nuclear track detectors give similar results. We present a conception for the interpretation of this fact: There is the evident connection between anomalies we observe in the yield of secondary particles in relativistic heavy ion interactions above a total energy of approximately 30–35 GeV and increased yield of neutrons in this energy region.     

Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory

Background  

Although a large body of knowledge about both brain structure and function has been gathered over the last decades, we still have a poor understanding of their exact relationship. Graph theory provides a method to study the relation between network structure and function, and its application to neuroscientific data is an emerging research field. We investigated topological changes in large-scale functional brain networks in patients with Alzheimer's disease (AD) and frontotemporal lobar degeneration (FTLD) by means of graph theoretical analysis of resting-state EEG recordings. EEGs of 20 patients with mild to moderate AD, 15 FTLD patients, and 23 non-demented individuals were recorded in an eyes-closed resting-state. The synchronization likelihood (SL), a measure of functional connectivity, was calculated for each sensor pair in 0.5–4 Hz, 4–8 Hz, 8–10 Hz, 10–13 Hz, 13–30 Hz and 30–45 Hz frequency bands. The resulting connectivity matrices were converted to unweighted graphs, whose structure was characterized with several measures: mean clustering coefficient (local connectivity), characteristic path length (global connectivity) and degree correlation (network 'assortativity'). All results were normalized for network size and compared with random control networks.     

Harmonic Vibrations of Shells with Cutouts Under Kinematic Conditions at Their Periphery

Problems on harmonic vibrations of shells with openings are considered for the case where displacements and angles of turn are specified at their periphery. A technique for determination of the natural frequencies and modes of vibrations is stated. The technique replaces the unknown peripheral forces and moments by a system of local statically equivalent loads. The intensity of these loads is found from the boundary conditions at the opening periphery. The solutions of the equations of shell theory for local loads are constructed by expanding the sought-for quantities into series in terms of the natural modes of the shell without openings. The performance of the approach developed is illustrated by calculating the natural frequencies and modes of shallow shells with a rectangular planform and various Gaussian curvatures     

Contact cuts

We describe a contact analog of the symplectic cut construction [L]. As an application we show that the group of contactomorphisms for certain overtwisted contact structures on lens spaces contains countably many non-conjugate two tori. Supported by the NSF grant DMS-980305.     

Iterated trees of strategies and priority arguments

We describe the motivation for the construction of a general framework for priority arguments, the ideas incorporated into the construction of the framework, and the use of the framework to prove theorems in computability theory which require priority arguments. Received: August 1, 1994