Minimum of the modulus of an entire function on the sequence of Polya peaks

Let f be an entire function of genus zero, let (r_k) be a sequence of Pólya peaks for N(r, f) of order <1. Then there exists a sequence r _k ~r_k such that If for (r_k) one takes a sequence of Pólya peaks for ln M(r, f) or for T(r, f), 1/2<<1, then the result ceases to be true.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 45, pp. 26–40, 1986.     

Weak matching rules for quasicrystals

Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in perp-space are uniformly bounded. It is shown here that weak matching rules exist forN-fold symmetric tilings, whereN is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules forN-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well.     

Area-preserving diffeomorphisms and higher-spin algebras

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonicd=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphereS ² as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS ^1,1, and can be rewritten as . As an application of our results, we formulate a newd=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms ofS ^1,1.     

Comparative analysis of (p,d), (d,t) and (3He, α) reactions on13C nucleus

The angular distributions of the (p, d), (d, t) and(³He, ) reactions on¹³C have been analysed within the framework of DWBA in which additional information on nuclear vertex constants was introduced. Although all these reactions seem to be similar single nucleon transfer, their mechanism is shown to be quite different and so is the information extracted thereof. While from the (p, d) reactions spectroscopic factors may be extracted unambiguously, from the (d, t) reactions it is possible to obtain directly the values of vertex constants only, which in turn are consistent with those determined by extrapolation of the experimental cross sections of the (p, d) reactions to the pole.In the case of (³He, ) reactions, however, the analysis indicates inadequacy of the DWBA concerning the calculations of central partial amplitudes. For a more reliable extraction of structural information, besides the correct normalization of peripheral amplitudes, a contribution of more complex mechanisms must be taken into account.     

Inclusive\bar K^{0*} (892) andK 0*(892) production on silicon by 200 GeVK − andπ −

The production of the neutralK ^? (892) resonances by 200 GeVK ^? andπ ^? has been studied over the kinematic range 0.0<x _f<1.0 andp _t ² <5.0 GeV². Longitudinal and transverse momentum distributions are presented. In addition the decay angular distributions inK ^? fragmentation to \(\bar K^{0*} \) have been investigated.     

High dose iron implantation into silicon and metals

High dose implantations of Fe into metals and semiconductors have been performed with beam energies up to 1 MeV at the UNILAC-injector at GSI. Unusual high concentrations of 70 atomic % for Si and 20 atomic % for Cu have been obtained, with doses of 10¹⁸ Fe/cm² in the case of Si and several 10¹⁷ Fe/cm² in the case of Cu. For Si the thickness of the layers were determined by Rutherford backscattering to be 4500 Å. These results are consistent with calculations, which show that these high concentrations are due to the reduction of the sputter yield at the relative high particle energies. Samples have been characterized using several complementary methods (Mössbauer Spectroscopy (MS), Rutherford Backscattering Spectroscopy (RBS), Auger electron Spectroscopy (AES). Scanning Electron Microscopy (SEM), X-ray diffraction (XRD)).     

A193Ir Mössbauer study of Pt−Ir catalysts prepared by impregnantion of silica with H2MCl6

The state of iridium on Pt?Ir catalysts prepared by impregnation of amorphous silica with H₂IrCl₆ and H₂PtCl₆ was studied by¹⁹³Ir Mössbauer spectroscopy after different steps of preparation. The Ir is adsorbed in its trivalent state, presumably as [IrCl₆]^3?. Calcination in air at 450°C converts this to IrO₂. The metallic clusters formed by subsequent reduction in H₂ at 200°C show a strong tendency towards segregation of Ir and Pt and re-oxidize partially when exposed to air at ambient temperature. In both respects the behaviour is similar to that of samples prepared by co-exchange from [Ir(NH₃)₅Cl]Cl₂ and Pt(NH₃)₄Cl₂. H₂O.     

Mössbauer and infrared spectroscopic studies of novel mixed valence states in cobaltous ferrocyanides and ferricyanides

Novel mixed valence states have been obtained by the treatment of cobaltous ferrocyanides (Co⁺²Fe^II) and ferricyanides (Co⁺²Fe^III) in an ozone flow. The CN stretching bands occur at 2085 cm^–1 for Co⁺²Fe^II and at 2160 cm^–1 for Co⁺²Fe^III. After the ozonization process of Co⁺²Fe^II, an intense band approximately at 2125 cm^–1 is detected. This intermediate band must correspond to a mixed valence state of the type: Fe^II–CN–Co²⁺–NC–Fe^III Mössbauer spectra recorded in situ during the ozonization of Co⁺²Fe^II show the presence of two components: a doublet with isomer shift and quadrupole splitting values close to the cobalti ferricyanide and a very broad line for the mixed valence state. From the Mössbauer and infrared spectra of the aged samples of the Co⁺²Fe^II after ozonization, a relaxation process to the initial state of the samples is observed but the mixed valence state is stable.     

Solution of the inverse problem for an evolution equation in a Banach space

For the equationdy (t)/dt=Ay(t) + p, t [0, ), where A is a closed linear operator on a Banach space , p is an unknown parameter from , we consider the problem

Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Ordinary differential equations with impulse action are considered at fixed moments of time when finite limits points are admitted to the set of moments of the shocks. The topological structure of this set is clarified: it must be resolvable, in particular nowhere dense in R.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 378–383, March, 1990.