The additivity principle in pyrolysis—gas chromatography of brown coal

Pyrolysis—gas chromatography of brown coal exhibits additive properties and it is therefore possible to construct the pyrogram of the original coal from the individual pyrograms of the bitumen, humic acids, lignin and humin fractions. The contents of phenols in the pyrograms are typical for all of the above classes except bitumen and are in agreement with the contents of the individual groups in the original coal. The results suggest that the separation does not bring about significant chemical changes in individual brown coal fractions.     

Tree Oriented Pullback

Given two epimorphisms of algebras A ? B and C ? B, we consider the pullback R. We introduce a particular class of algebras, the tree oriented pullback, where there is a close relationship between the category of indecomposable modules of these algebras. This leads us to prove that if A and C are hereditary algebras, then R is a tilted algebra.     

Metric Möbius geometry and a characterization of spheres

We obtain a Möbius characterization of the n-dimensional spheres S ⁿ endowed with the chordal metric d ₀. We show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is Möbius equivalent to (S ⁿ , d ₀) for some n ≥ 1.     

Möbius characterization of hemispheres

In this paper we generalize the Möbius characterization of metric spheres as obtained in Foertsch and Schroeder [4] to a corresponding Möbius characterization of metric hemispheres.     

Embedding of Hyperbolic Spaces in the Product of Trees

We show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space Hⁿ in the product Tⁿ=T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding for any metric tree T and any m ≥ 0.Mathematics Subject classification (2000). 54Exx.Supported by RFFI Grant 02-01-00090, CRDF Grant RMI-2381-ST-02 and SNF Grant 20-668 33.01. Supported by Swiss National Science Foundation.     

Internal gravity–capillary solitary waves in finite depth

We consider a two‐dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and interfacial tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a spatial dynamics approach and formulate the steady Euler equations as a Hamiltonian system, where we consider the unbounded horizontal coordinate x as a time‐like coordinate. The linearization of the Hamiltonian system is studied, and bifurcation curves in the (β,α)‐plane are obtained, where α and β are two parameters. The curves depend on two additional parameters ρ and h, where ρ is the ratio of the densities and h is the ratio of the fluid depths. However, the bifurcation diagram is found to be qualitatively the same as for surface waves. In particular, we find that a Hamiltonian‐Hopf bifurcation, Hamiltonian real 1:1 resonance, and a Hamiltonian 0²‐resonance occur for certain values of (β,α). Of particular interest are solitary wave solutions of the Euler equations. Such solutions correspond to homoclinic solutions of the Hamiltonian system. We investigate the parameter regimes where the Hamiltonian‐Hopf bifurcation and the Hamiltonian real 1:1 resonance occur. In both these cases, we perform a center manifold reduction of the Hamiltonian system and show that homoclinic solutions of the reduced system exist. In contrast to the case of surface waves, we find parameter values ρ and h for which the leading order nonlinear term in the reduced system vanishes. We make a detailed analysis of this phenomenon in the case of the real 1:1 resonance. We also briefly consider the Hamiltonian 0²‐resonance and recover the results found by Kirrmann. Copyright © 2016 John Wiley & Sons, Ltd.     

Power variation from second order differences for pure jump semimartingales

We introduce power variation constructed from powers of the second-order differences of a discretely observed pure-jump semimartingale processes. We derive the asymptotic behavior of the statistic in the setting of high-frequency observations of the underlying process with a fixed time span. Unlike the standard power variation (formed from the first-order differences of the process), the limit of our proposed statistic is determined solely by the jump component of the process regardless of the activity of the latter. We further show that an associated Central Limit Theorem holds for a wider range of activity of the jump process than for the standard power variation. We apply these results for estimation of the jump activity as well as the integrated stochastic scale.