The Dold-Lashof-Fuchs construction revisited

Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire daE→B, una funzione continuaE _∞→B_∞, conE _∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli. In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche alla classificazione delleF-fibrazioni numerabili.

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Conferenza tenuta da R. Piccinini il 15 maggio 1995     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

On some properties of cohomotopy-type functors

It is shown that if II ⁿ ,n\s>2, are Chogoshvili's cohomotopy functors [1, 2, 3], then

Polar actions on Hilbert space

An isometricH-action on a Riemannian manifoldX is calledpolar if there exists a closed submanifoldS ofX that meets everyH-orbit and always meets orbits orthogonally (S is called a section). LetG be a compact Lie group equipped with a biinvariant metric,H a closed subgroup ofG ×G, and letH act onG isometrically by (h ₁,h ₂) ·x = h ₁ xh ₂ ⁻¹ · LetP(G, H) denote the group ofH ¹-pathsg: [0, 1] →G such that (g(0),g (1)) ∈H, and letP(G, H) act on the Hilbert spaceV = H ⁰([0, 1], g) isometrically byg * u = gug ⁻¹ −g′g ⁻¹. We prove that if the action ofH onG is polar with a flat section then the action ofP(G, H) onV is polar. Principal orbits of polar actions onV are isoparametric submanifolds ofV and are infinite-dimensional generalized real or complex flag manifolds. We also note that the adjoint actions of affine Kac-Moody groups and the isotropy action corresponding to an involution of an affine Kac-Moody group are special examples ofP(G, H)-actions for suitable choice ofH andG. Work supported partially by NSF Grant DMS 8903237 and by The Max-Planck-Institut für Mathematik in Bonn.     

Maximal estimates on measure spaces for weak-type multipliers

We describe sufficient conditions for transferring from locally compact abelian groups to measure spaces the weak-type bounds of maximal operators defined by multipliers of weak type. This leads to homomorphism theorems for maximal multiplier operators. Communicated by Guido Weiss     

Electromagnetic fission of238U at 600 and 1000 MeV per nucleon

Electromagnetic fission of²³⁸U projectiles at E/A =600 and 1000 MeV was studied with the ALADIN spectrometer at the heavy-ion synchrotron SIS. Seven different targets (Be, C, Al, Cu, In, Au and U) were used. By considering only those fission events where the two charges added up to 92, most of the nuclear interactions were excluded. The nuclear contributions to the measured fission cross sections were determined by extrapolating from beryllium to the heavier targets with the concept of factorization. The obtained cross sections for electromagnetic fission are well reproduced by extended Weizsäcker-Williams calculations which include E1 and E2 excitations. The asymmetry of the fission fragments' charge distribution gives evidence for the excitation of the double giant-dipole resonance in uranium.Communicated by V. Metag     

Near-barrier fission of the system12C+232Th

The fission fragment angular distributions for the system¹²C +²³²Th have been measured in the energy range 0.97<>_c.m./V_B<1.22. the=" measured=" anisotropies=" have=" been=" compared=" with=" the=" predictions=" of=" the=" standard=" saddle=" point=" statistical=" model,=" using=" the=" second=" moment=" of=" the=" compound=" nucleus=" spin=" distribution=">l² deduced from a Wong model fit to the fission excitation function. While the measured anisotropies agree with the standard saddle point statistical model for E_c.m./V_B>1.05, they are abnormally large at lower energies. This is also true for the existing measurements of¹⁶O and¹⁹F +²³²Th systems. Since for this system pre-equilibrium fission contributions are not expected, this anomaly indicates strong channel coupling effects leading to an increase in l² at sub-barrier energies.The authors thank Drs. R.K. Choudhury and A. Saxena for useful discussions, Dr. R.J. Singh for making the thorium target and the Pellectron operation staff for excellent operation of the machine.     

Investigation of the40Ca(γ,N) reaction at 60 MeV

The values of the angle-integrated cross section for the decay to various low-lying states in³⁹K following the⁴⁰Ca(,) reaction at a mean photon energy of 60 MeV are reported on, together with the values of the reduced Legendre coefficientsa _i . The⁴⁰Ca(,gp) and⁴⁰Ca(,n) reactions yield the same angular cross-section values and these agree with the corresponding RPA-calculations.Senior Research Associate NFWO     

Study of the yrast band in the doubly odd156Tm

The yrast band in the doubly odd¹⁵⁶Tm nucleus was studied through¹⁴⁴Sm(¹⁹F,2p5n)¹⁵⁶Tm reaction at beam energy of 105MeV. Several high-spin states of¹⁵⁶Tm were identified and the highest spin of the band with configuration7/2^–[523] v1/2⁺[660] could be built up to spin 25. The level structure shows the onset of a non- or weak collectivity which generally appears at neutron number of 87 in neutron-deficient rare-earth nuclei.This work was supported in part by the Fok Ying Tung Education Foundation and the Natural Science Fund of China.     

Proton-neutron interaction at N≅Z — First observation of the Tz=1 nucleus 46 94 Pd48 in-beam

The neutron deficient nucleus⁹⁴Pd was identified and studied for the first time by in-beam spectroscopy. An I=(14⁺) isomer with t_1/2=0.8 (2) s was observed in a recoil catcher setup inside the multi-detector -array OSIRIS. Filter detectors for neutrons and charged particles were used to identify the (2p2n) exit channel of the reaction⁵⁸Ni+⁴⁰Ca, populated with only 0.06% of the total evaporation residue cross section. The structure of the isomer is discussed within the frame work of shell model calculations in the (p_1/2,g_9/2) model space with emphasis on the g ₉ ^2/2 T=0, I=1,9 pairing two-body matrix elements.Communicated by: D. Schwalm