On the number of solutions of an algebraic equation on the curve , and a consequence for o-minimal structures

We prove that every polynomial of degree has at most zeros on the curve . As a consequence we deduce that the existence of a uniform bound for the number of zeros of polynomials of a fixed degree on an analytic curve does not imply that this curve belongs to an o-minimal structure.

     

Anisochronism of large geminal groups in the 1H and 13C nuclear magnetic resonance spectra

The role of steric factors in magnetic non-equivalence anisochronism of complex geminal groups and of their fragments in compounds of the general formula RCH(Ph)CH(COOR′)₂ has been investigated. CMR anisochronism is more sensitive to conformational and other steric changes than is PMR.     

Addition of hot hydrogen atoms to 1-butene in the gas phase and dissociation of excited butyl radicals

The reaction of hot hydrogen atoms originating from 253.7- and 228.8-nm photolyses of hydrogen sulfide with 1-butene was investigated. Of the hydrogen atoms undergoing addition a substantial part undergoes it in a first collision (37 and 48% at 253.7 and 228.8 nm, respectively) yielding highly excited butyl radicals. The ratio of nonterminal to terminal addition is 0.5 and practically does not depend on the energy of the hydrogen atoms over the range of 15–33 kcal/mol. Comparing the results of 229- and 254-nm photolyses of hydrogen sulfide with those of 313- and 334-nm photolyses of hydrogen iodide with the use of the decomposition rate constants of n-butyl radicals calculated by the RRKM methods, the conclusion is reached that the hydrogen atom from H₂S photodissociation has 90–95% of the available energy.     

New evidence of the intrinsic chemical shift non-equivalence

Carbinols of the general formulae R·CHOH·C(NO₂)Me₂ exhibit increasing values of chemical shift non-equivalence for the geminal methyl groups with rise of temperature. This phenomenon furnishes indirect evidence for the intrinsic non-equivalence.     

Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies

We experimentally demonstrate subwavelength resolution imaging at microwave frequencies by a three-dimensional (3D) photonic-crystal flat lens using full 3D negative refraction. The photonic crystal was fabricated in a layer-by-layer process. A subwavelength pinhole source and a dipole detector were employed for the measurement. By point-by-point scanning, we obtained the image of the pinhole source shown in both amplitude and phase, which demonstrated the imaging mechanism and subwavelength feature size in all three dimensions. An image of two pinhole sources with subwavelength spacing showed two resolved spots, which further verified subwavelength resolution.     

The converse theorem for Minkowski's inequality

Let (Ω, Σ, μ) be a measure space and ?, ψ : (0, ∞) → (0, ∞) some bijective functions. Suppose that the functional _?,ψ defined on class of μ-integrable simple functions χ : Ω → [0, ∞), μ({? : χ(?) > 0} > 0, by the formula

     

Crown Inclusion Compounds with 3,4-Diamino-1,2,5-Oxadiazole. X-Ray Structures of Its 1:1 Inclusion Complexes with 15-Crown-5 and Benzo-15-crown-5

The X-ray crystal structures of two closely related molecular complexes of 15-crown-5 and benzo-15-crown-5 with 3,4-diamino-1,2,5-oxadiazole are reported (I and II). Both complexes are of 1:1 stoichiometry with the host–guest alternation in the infinitechains formed due to the unsymmetrical H-bonding patterns between the components. Crystals of I are monoclinic, P2_1/c, a = 7.856(3), b = 12.994(1), c = 16.033(1) , = 94.79(2)°, Z = 4, final R-factor is 0.0488. Crystals of II are orthorhombic, P2₁2₁2₁, a = 8.260(4), b = 15.692(5),c = 13.955(7) , Z = 4, final R-factor is 0.0522.     

Eta physics at threshold

The production of - and -mesons in elementary nucleon-nucleon collisions has been investigated at the synchrotrons CELSIUS, COSY and SATURNE. The high-quality proton beam with low emittance and small momentum spread permits to study the creation of these mesons very close to the kinematical threshold, where --due to the rapid growth of the phase space volume-- the total cross-section increases by orders of magnitude over a few MeV range of the excess energy. The magnitude and energy dependence of the total cross-section as well as the occupation distribution of the phase space serve as observables for investigating the mechanisms underlying the production processes and the interaction of mesons with nucleons. The precise data on the and creation via the reactions allowed to settle the general features of the - and -meson production and revealed the sensitivity of the mentioned observables to the nucleon-nucleon-meson final-state interaction. The particular production properties, like for example, the determination of the dominating exchange processes which lead to the excitation of the S ₁₁ nucleon isobar in the case of creation, must be established by confrontation with other observables. The present status of this investigation with an emphasis on the results of the COSY-11 Collaboration is briefly presented. The available data are interpreted in view of the production mechanism and the meson-nucleon interaction.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Le Meson production - 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.85.Lg Total cross sections - 25.40.-h Nucleon-induced reactions