On the higher eigenvalues for the \infty-eigenvalue problem

We study the higher eigenvalues and eigenfunctions for the so-called -eigenvalue problem. The problem arises as an asymptotic limit of the nonlinear eigenvalue problems for the p-Laplace operators and is very closely related to the geometry of the underlying domain. We are able to prove several properties that are known in the linear case p = 2 of the Laplacian, but are unknown for other values of p. In particular, we establish the validity of the Payne-Pólya-Weinberger conjecture regarding the ratio of the first two eigenvalues and the Payne nodal conjecture, which deals with the zero set of a second eigenfunction. The limit problem also exhibits phenomena that are not encountered for any .Received: 4 January 2004, Accepted: 9 June 2004, Published online: 3 September 2004Mathematics Subject Classification (2000): 35P30, 35J70, 49R50     

Concavity maximum principle for viscosity solutions of singular equations

We prove a concavity maximum principle for the viscosity solutions of certain fully nonlinear and singular elliptic and parabolic partial differential equations. Our results parallel and extend those obtained by Korevaar and Kennington for classical solutions of quasilinear equations. Applications are given in the case of the singular infinity Laplace operator.     

New Spectroscopic Information on 98Pd

Neutron deficient ⁹⁸Pd nuclei were produced in the ⁵⁰Cr(⁵⁸Ni,2p2α)⁹⁸Pd reaction at a beam energy of 261 MeV. A revision and extension of the level structure of ⁹⁸Pd is proposed. About 40 new transitions have been assigned to, and placed in the level scheme of this nucleus. A sequence of states are candidates for the negative parity 4—quasiparticle states built on the πg _9/2 ^?3 πp _1/2 ^?1 configuration predicted in the framework of the nuclear shell model.     

Identification of the 13/2+ isomer in 199At

The 13/2⁺ isomeric state in the ¹⁹⁹At nucleus has been identified at an excitation energy of 573 keV and its half-life measured to be 580(130) ns using the recoil-decay tagging technique. Received: 19 September 2000 / Accepted: 1 November 2000     

A pilot experiment of joint assessments by accreditation and certification bodies in clinical laboratories

When the quality system of the health care organization is certified and the laboratory accredited, two different types of assessments are also performed. To reduce the extra work caused by these different assessments the Finnish Accreditation Service FINAS and SFS-Certification have made a pilot experiment in combining the assessments. Joint assessments have been a positive experience to the laboratory as well as to the assessing bodies, and we find this operating model worth developing.     

Synthetic studies in the alkaloid field-IX: Stereospecific total synthesis of (±)-19,20-dihydro-20-desformyl-20-methoxycarbonyl-vallesiachotamine and its 20-desethyl analogue

The stereospecific total synthesis of (±) - 19,20 - dihydro - 20 - desformyl - 20 - methoxycarbonyl-vallesiachotamine and its 20-desethyl analogue has been carried out by sodium dithionite reduction of appropriate 1-[2-(3-indolyl)ethyl]-3-methoxycarbonyl pyridinium salts to the corresponding 1,4-dihydropyridine derivatives, followed by acid-induced cyclization.     

Gamma-ray spectroscopy of 192–195Po

Prompt and delayed γ-rays have been observed from very neutron deficient ^192–195Po nuclei by using the recoil-decay tagging (RDT) and recoil gating techniques. The yrast levels up to the (10⁺) state in the ¹⁹²Po were identified for the first time. Comprehensive data for ¹⁹⁴Po rendered it possible to extend the yrast line and to observe several positive and negative parity non-yrast states. In the odd-mass isotopes ¹⁹³Po and ¹⁹⁵Po, favoured and unfavoured states on top of the 13/2⁺ state have been identified. The results are discussed within the simple vibrator and rotor pictures as well as in the framework of coexisting spherical and deformed-intruder structures. Received: 5 July 1999 / Revised version: 7 September 1999     

First observation of excited states in 184Pb: spectroscopy beyond the neutron mid-shell

Excited states have been identified for the first time in ¹⁸⁴Pb, the first even-even Pb isotope beyond the 82 < N < 126 mid-shell, using the recoil-decay tagging (RDT) technique. A collective band built on the first-excited 2⁺ state has been observed. This resembles those seen in ^186,188Pb and the Hg isotones, and can thus be associated with a prolate-deformed shape. Variable moment of inertia (VMI) fits of the prolate 0⁺ level energies in ^184,186,188Pb indicate that the minimum appears at N= 103, the same neutron number at which the corresponding minimum in Hg isotopes is observed. Received: 19 May 1998 / Revised version: 1 July 1998     

In-beam gamma-ray spectroscopy of 190, 197Po

γ -ray transitions in the neutron-deficient nuclei ^{190, 197}Po have been identified using the JUROGAM Ge detector array coupled to the RITU gas-filled separator and the GREAT spectrometer. The yrast band of ¹⁹⁰Po has been firmly established through γ -γ coincidences and extended up to a spin and parity of 14⁺. It displays similar behaviour to its isotones ¹⁸⁶Hg and ¹⁸⁸Pb above the 4⁺ level, thus confirming its prolate nature. In ¹⁹⁷Po the band built upon the 13/2⁺ isomer has been extended up to a spin and parity of 33/2⁺, while the non-yrast band has been observed for the first time. The behaviour of ¹⁹⁷Po is found to be similar to that of the nearby even-mass isotopes, which is consistent with the model in which the i _13/2 neutron is weakly coupled to the states in the even-even core.