Aspects of operator theory in hereditarily indecomposable Banach spaces

We examine certain special features exhibited by various classes of linear operators acting in a hereditarily indecomposable Banach space. For instance, we show that the family of all Riesz operators in a H.I. space forms a closed, 2-sided ideal. We also give further characterizations of the class of scalar-type spectral operators (to those already given in [16]). The final section discusses some properties of the spectral maximal spaces of (necessarily decomposable) linear operators in such spaces. Conferenza tenuta il 16 settembre 1997 The support of the German Academic Exchange Scheme (DAAD) is gratefully acknowledged     

An apparent momentum balance anomaly in the plasma focus

The validity of the snowplow model of plasma sheath propagation in a plasma focus (PF) and the localization of the magnetic field in the low density region behind the dense plasma sheath are two well-established experimental facts. It is shown that, when taken together, these two imply a deficiency in the momentum balance. The hypothesis that the current-carrying plasma layer is rotating while the dense plasma layer is not rotating is shown not only to resolve this momentum balance anomaly (MBA), but also to explain many observed phenomena in a unified manner     

An electro-optic holographic technique for the measurement of the components of the strain tensor on three-dimensional object surfaces

An electro-optic holographic technique (also called electronic speckle pattern interferometry or TV holography) for the measurement of displacements and strains on three-dimensional object surfaces is presented. The three components of the displacement vector, in a fixed coordinate system, are separated using four independent illumination beams. The interferometric phase for each illumination beam is extracted using the phase stepping technique. Displacements in the fixed coordinate system are projected on to the object surface using the tensor transformation law. Equations for the computation of surface strains using the projected displacements and the surface geometry are developed. The technique is applied for the measurement of strains on the surface of a cylindrical vessel subjected to internal pressure.     

Optical bistability in an all-optical fiber nonlinear fabry-perot resonator with linear absorption

An all-optical fiber nonlinear Fabry-Perot resonator is proposed. The steady-state model for describing this resonator is developed. The transmission and refection bistabilities are shown numerically. Our results show that the bistability in this system is similar to that in a normal nonlinear Fabry-Perot etalon, except that the characteristics of the bistability can be changed not only by the cavity length but also by the phase shifts of the fiber loop mirrors.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

The accurate dimensional measurements within small internal structures

This paper shows that the dimension of internal structure of a component can be measured remotely to a resolution better than 5 μm by use of the combination of high resolution optical microscopy and image processing.A specialised high resolution, long working distance and diffraction limited lens was used to image within the component. A series of digital images were made to map spatially the interior of the component. An edge detector was then used to localise the specific location of features in order that an accurate internal measurement could be made. A visualisation of the internal surface finish was also achieved.     

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators     

Influence of isovalent substitutions on absorption spectra of orthoferrities

The role of impurity ions in formation of the optical properties of rare-earth orthoferrites is investigated. Optical spectra of the substituted against unsubstituted orthoferrites are presented. The influence of different isovalent substitutions on the optical absorption of orthoferrites that are promising for magnetooptics is studied. Institute of Solid-State and Semiconductor Physics of the Academy of Sciences of Belarus, 17, P. Brovka St., Minsk, 220072, Belarus. Translated from zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 5, pp. 642–645, September–October, 1997.