Trace Inequalities,Maximal Inequalities,and Weighted Fourier Transform Estimates

In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality $\Big(\int_{{\Bbb R}_d} \vert\hat{f}\vert^q d\mu\Big)^{1/q} \leq C\Big(\int_{{\Bbb R}_d} \vert f\vert^p v\Big)^{1/p}$ provided v is a radial weight for which v^?1/p is convexly decreasing and μ is a suitable measure. We also establish alternative conditions for such inequalities by proving corresponding trace type inequalities and maximal function inequalities that underlie the Fourier transform estimates. Our conditions are relatively simple to compute. Among applications we give extensions of a Sobolev restriction theorem.     

Self-avoiding walks and trees in spread-out lattices

LetG _R be the graph obtained by joining all sites ofZ ^d which are separated by a distance of at mostR. Let (G _R ) denote the connective constant for counting the self-avoiding walks in this graph. Let (G _R ) denote the coprresponding constant for counting the trees embedded inG _R . Then asR, (G _R ) is asymptotic to the coordination numberk _R ofG _R , while (G _R ) is asymptotic toek _R. However, ifd is 1 or 2, then (G _R )-k _R diverges to –.Dedicated to Oliver Penrose on this occasion of his 65th birthday.     

Automated millimeter-wave-therapy devices of the “BAYuR” series and diagnostic and therapeutic systems based on them

The devices and systems for EHF therapy and diagnosis of the BAYuR series are examined and compared with known analogs.Scientific-Research Measuring-Systems Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 1, pp. 155–157, January, 1994.     

Mass dependent αs evolution and the light gluino existence

There is an intriguing discrepancy between values measured directly at the CERNZ ₀-factory and low-energy (at few GeV) measurements transformed toQ=M _z0 by a massless QCD evolution relation. There exists and attempt to reconcile this discrepancy by introducing a light gluinog in the MSSM. We study in detail the influence of heavy thresholds on evolution. First, we construct the exact explicit solution to the mass-dependent two-loop RG equation for the running . This solution describes heavy thresholds smoothly. Second, we use this solution to recalculate a new values corresponding to low-energy input data. Our analysis demonstrates that usingmass-dependent RG procedure generally produces corrections of two types: Asymptotic correction due to effective shift of threshold position; Local threshold correction only for the case when input experiment lies in the close vicinity of heavy particle threshold:Q _expt -M _h . Both effects result in the effective shift of the values of the order of 10^–3. However, the second one could be enhanced when the gluino mass is close to a heavy quark mass. For such a case the sum effect could be important for the discussion of the light gluino existence as it further changes theg mass.Work supported in part by INTAS-93-1180     

An investigation of intermittency in proton-gold, oxygen-gold, sulphur-gold and sulphur-sulphur interactions at 200 GeV per nucleon

The intermittency phenomenon is investigated in proton-gold, oxygen-gold, sulphur-gold and sulphur-sulphur collisions at 200 GeV per nucleon. The data were taken with the NA 35 streamer chamber detector at the CERN SPS. The data samples are carefully corrected for double counting of tracks and for contamination from photon conversions, particle decays and secondary interactions. The analysis is carried out in terms of factorial moments, using a new definition, and of correlation integrals. Both methods show the presence of nonstatistical fluctuations (intermittency). The main conclusions are: The observation of the effect for pairs of hadrons with negative charges and its near absence for pairs of opposite charges is consistent with the assumption that Bose-Einstein correlations yield the dominant contribution. The intermittency effect is not proportional to (dn/dy)^–1 which would be expected in superposition models. The measured relation between the second and third factorial moment for negative hadrons indicates that genuine 3-particle correlations are small. The predictions of a Monte Carlo simulation which is based on the Lund Fritiof model with the inclusion of Bose-Einstein correlations agree with the experimental results.Deceased     

Excitonic detectors of infrared and submillimeter radiation

The theory of new type detectors based on the quenching of secondary emission in direct-gap semiconductors (lines of Raman light scattering due to interaction between free and bound excitons in the crystal, and also bands of edge radiation) caused by IR or submillimeter radiation is proposed. The results obtained are confirmed by the experiment performed for CdS crystal excited by ultraviolet radiation of mercury lamp, at liquid helium temperature.     

Mössbauer studies on the series La1-xSrxFeO3

Mössbauer spectra have been recorded at 4.2 and 300 K on the series La_1–x Sr _x FeO₃, wherex varies from 0 to 1.0 in steps of 0.1. Neutron diffraction experiments have shown that the crystal structure is orthorhombic for 0x<0.3, rhombohedral for 0.4x0.7, and cubic for 0.8<x1.0. Mössbauer spectra at 4.2 K are composed of magnetic sextet components arising from different charge states of iron ions. In the orthorhombic and rhombohedral phases, the charge states Fe³⁺ and Fe⁵⁺ coexist. In the cubic phase, iron is present as Fe³⁺ and Fe⁴⁺ states. At 300 K, the samples are magnetically ordered in the range 0 x0.3 and the coexistence of Fe³⁺ and Fe⁵⁺ remains. For samples 0.4x1.0, the samples are paramagnetic. Fits to these spectra require two components, one corresponding to an Fe⁴⁺ state, the other being best described as an Fe³⁺ ion forx0.7 but forx>0.7 having a mean charge state which increases to 3.5 forx=1.0.