Plane Sections of Convex Bodies of Maximal Volume

Let K = {K ₀ ,... ,K _k } be a family of convex bodies in R ⁿ , 1≤ k≤ n-1 . We prove, generalizing results from [9], [10], [13], and [14], that there always exists an affine k -dimensional plane A _k (subset, dbl equals) R ⁿ , called a common maximal k-transversal of K , such that, for each i∈ {0,... ,k} and each x∈ R ⁿ , where V _k is the k -dimensional Lebesgue measure in A _k and A _k +x . Given a family K = {K _i } _i=0 ^l of convex bodies in R ⁿ , l < k , the set C _k ( K ) of all common maximal k -transversals of K is not only nonempty but has to be ``large' both from the measure theoretic and the topological point of view. It is shown that C <sub>k</sub> ( K ) cannot be included in a ν -dimensional C <sup>1</sup> submanifold (or more generally in an ( H <sup>ν</sup> , ν) -rectifiable, H <sup>ν</sup> -measurable subset) of the affine Grassmannian AGr <sub>n,k</sub> of all affine k -dimensional planes of R <sup>n</sup> , of O(n+1) -invariant ν -dimensional (Hausdorff) measure less than some positive constant c <sub>n,k,l</sub> , where ν = (k-l)(n-k) . As usual, the ``affine' Grassmannian AGr _n,k is viewed as a subspace of the Grassmannian Gr _n+1,k+1 of all linear (k+1) -dimensional subspaces of R ⁿ⁺¹ . On the topological side we show that there exists a nonzero cohomology class θ∈ H ^n-k (G _n+1,k+1 ;Z ₂ ) such that the class θ ^l+1 is concentrated in an arbitrarily small neighborhood of C _k ( K ) . As an immediate consequence we deduce that the Lyusternik—Shnirel'man category of the space C _k ( K ) relative to Gr _n+1,k+1 is ≥ k-l . Finally, we show that there exists a link between these two results by showing that a cohomologically ``big' subspace of Gr _n+1,k+1 has to be large also in a measure theoretic sense. Received May 22, 1998, and in revised form March 27, 2000. Online publication September 22, 2000.     

Field Effect and Local Gating in Nitrogen-Terminated Nanopores (NtNP) and Nanogaps (NtNG) in Graphene

Functionalization of electrodes is a wide-used strategy in various applications ranging from single-molecule sensing and protein sequencing, to ion trapping, to desalination. We demonstrate, employing non-equilibrium Green′s function formalism combined with density functional theory, that single-species (N, H, S, Cl, F) termination of graphene nanogap electrodes results in a strong in-gap electrostatic field, induced by species-dependent dipoles formed at the electrode ends. Consequently, the field increases or decreases electronic transport through a molecule (benzene) placed in the nanogap by shifting molecular levels by almost 2 eV in respect to the electrode Fermi level via a field effect akin to the one used for field-effect transistors. We also observed the local gating in graphene nanopores terminated with different single-species atoms. Nitrogen-terminated nanogaps (NtNGs) and nanopores (NtNPs) show the strongest effect. The in-gap potential can be transformed from a plateau-like to a saddle-like shape by tailoring NtNG and NtNP size and termination type. In particular, the saddle-like potential is applicable in single-ion trapping and desalination devices.     

A Counter-Example to Hausmann’s Conjecture

Foundations of Computational Mathematics - In 1995 Jean-Claude Hausmann proved that a compact Riemannian manifold X is homotopy equivalent to its Rips complex $${\text {Rips}}(X,r)$$ for small...     

Σ-Hypernuclear (π−,K +) production

The (π ^?,K ⁺) reaction is proposed as an optimalσ-hypernuclear production process on nuclear tagets. Several ingredients of this process are discussed in connection with the choice of appropriate target nuclei. For demonstration, the excitation functions are calculated for the (π ^?,K ⁺) reaction on the⁵⁶Fe and²⁸Si targets by assuming a shallowσ well depth, varying the spin-orbit strength and smearing (conversion) widths.     

14N NQR study of the structural phase transitions in NH4NO3

The temperature dependences of the¹⁴N nuclear quadrupole resonance frequencies have been measured in phases II, III, IV and V of ammonium nitrate with the help of the¹H–¹⁴H nuclear quadrupole double resonance technique. The experimental results are related to the proposed crystal structures and disorder in the various crystallographic phases.     

Kinetics and Mechanism of the Oxidation of Molybdenum Sulphide

This paper reports on the results attained in the determination of the mechanism of oxidation of molybdenum sulphide under non-isothermal conditions in an air atmosphere. The mechanism of the process was determined by simultaneous DTA-TG-DTG, and the kinetic parameters of the reactions involved were obtained according to the methods of Kissinger and Ozawa. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the configurational splitting of strangeness analog state

Signatures and behaviour of s^–1s configurations are qualitatively discussed. Suppression of baryon-decay channels and an enhancement of cluster-decay channels are the relevant signals. The hypernuclear-quanta from constitute a novel example of the decay of s^–1 s^–1s configuration.Dedicated to the memory of M. Gmitro.We dedicate this article to our colleague and friend Dr. Marian Gmitro, whose premature death brought a profound grief upon our community. During years, his activities and knowledge in meson-nuclear physics have been very helpful in further development of hypernuclear physics. Also, his role in an efficient topical collaboration between Soviet and Czechoslovak physicists is to be greatly acknowledged.     

Anomalous bootstrap current estimates from experimentally found values of the radial electron transport

A method of computation of anomalous bootstrap current is suggested which uses calculated or experimentally found values of the radial transport velocity. The underlying theory is the drift kinetic equation approach of Shaing to anomalous plasma transport in a toroidal configuration and/or the MHD approach of Klíma and Petrílka to convection and diffusion in a plasma cylinder under the influence of RF fields.The author thanks R. Klíma and the referee for valuable comments.