Circular autocorrelation of stationary circular Markov processes

The stationary Markov process is considered and its circular autocorrelation function is investigated. More specifically, the transition density of the stationary Markov circular process is defined by two circular distributions, and we elucidate the structure of the circular autocorrelation when one of these distributions is uniform and the other is arbitrary. The asymptotic properties of the natural estimator of the circular autocorrelation function are derived. Furthermore, we consider the bivariate process of trigonometric functions and provide the explicit form of its spectral density matrix. The validity of the model was assessed by applying it to a series of wind direction data.     

<Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains

We consider the C ¹-classification of gapped Hamiltonians introduced in Fannes et al. (Commun Math Phys 144:443–490, 1992) and Nachtergaele (Commun Math Phys 175:565–606, 1996) as parent Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the ‘bulk’ ground state does not need to be broken to establish C ¹-equivalence, namely that the spin chain does not need to be blocked.     

Nickel metallisation of Si by dynamic ion-beam mixing

Abstract

Thin Ni films were prepared at room temperature by Ni metal vapour deposition and simultaneous irradiation by Ar ions with an energy of 2–20 keV. The reaction of Ni with Si during dynamic ion-beam mixing was studied. The fluences of the ion beam were 4.7 × 10¹⁷ and 8.9 × 10¹⁷ cm^?2, and arrival rate ratios Ni/Ar were 9.7 and 5.1. Concentration profiles of Ni, Si, C, and O were analysed with Auger electron spectroscopy; the surface morphology and the crystalline structure were investigated with a cross-sectional scanning electron microscope and X-ray diffractometry. The theoretical profiles were calculated with the dynamic Monte Carlo simulation T-DYN for comparison with the experimentally obtained profiles. It was possible to observe the ballistic mixing effects and also thermally activated formation of nickel silicide.     

Proposal for generation of high-intensity monochromatic Cherenkov radiation in THz range by femtosecond electron bunches in impurity-doped semiconductor tube

A novel method to generate high-power THz radiation is proposed. If a beam with a bunch length on the order of 100 fs is injected into an electron–hole plasma of a semiconductor with a plasma frequency on the order of THz, THz wake fields are coherently generated. If the beam moves on the axis of a hollow tube covered by a metal, the frequency spectrum of the radiation is composed of discrete components. Monochromatic radiation is obtained by making only the lowest frequency component coherent.     

Asymmetric synthesis of bicyclo[n.1.0]alkanes by the enantioselective 1,3-CH insertion reaction of chiral magnesium carbenoids

Treatment of enantiomerically pure 1-chlorovinyl p-tolyl sulfoxides, derived from cyclic ketones and (R)-chloromethyl p-tolyl sulfoxide, with the lithium enolate of tert-butyl carboxylates gave adducts in quantitative yields as single diastereomers. The adducts were treated with i-PrMgCl in toluene to afford optically active bicyclo[n.1.0]alkanes bearing a tert-butyl carboxylate moiety in up to 99% enantiomeric excess through the enantioselective 1,3-CH insertion reaction of the generated chiral magnesium carbenoids. This is the first example of the enantioselective 1,3-CH insertion reaction of magnesium carbenoid.     

Four-Body CDCC Analysis for Breakup Reactions of Three-Body Projectiles

We present a new method of smoothing discrete breakup cross sections calculated by the continuum-discretized coupled-channels method based on the complex-scaling method. One of the advantages of this approach is to be applicable to many-body breakup reaction systems. In this work, we apply the new smoothing method to analyses of ¹²C(⁶He, nn ⁴He) and ²⁰⁸Pb(⁶He, nn ⁴He) reactions at 240 MeV/A.     

2-Dimensional complete self-shrinkers in $$\mathbf {R}^3$$

It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for \(\mathcal {L}\)-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \(\mathbb R^3\). Ding and Xin (Trans Am Math Soc 366:5067–5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.