Occurrence of rotation domains in heteroepitaxy

Heteroepitaxy can involve materials with a misfit of crystal structure. Rotation domains in the epilayer are a fundamental consequence. We derive a general expression for their (minimum) number which is determined by the mismatch of the rotational symmetries of the substrate and epilayer. In the case of a mismatch of rotational symmetry, the number of rotation domains of material A on material B is different from that of B on A. A larger number of rotation domains can occur due to domain structure or nearly fulfilled additional symmetries of the substrate surface.     

Semi-internal Stabilization for a Non-linear Bernoulli–Euler Equation

We consider a non-linear plate equation of Bernoulli–Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.     

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Nonlinear Dynamics - In this paper, we consider a 5-dimensional Hindmarsh–Rose neuron model. This improved version of the original model shows rich dynamical behaviors, including a chaotic...     

Spectral analysis for the Gauss problem on continued fractions

We present a new derivation of the formula appearing in Babenko (1978) and Mayer and Roepstorff (1987) that gives the probability distribution of τ⁻ⁿ${\tau }^{-n}$ in terms of the eigenvalues of a symmetric operator. Here τ$\tau$ is the well-known Gauss-map.     

Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B _R \{0} of ? ^N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a _{i j} ) and (b _i ) stabilize at zero, and we provide some optimal conditions in this setting.     

Characterizing Methyl‐Bearing Side Chain Contacts and Dynamics Mediating Amyloid β Protofibril Interactions Using 13Cmethyl‐DEST and Lifetime Line Broadening

Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced ¹⁵N dark‐state exchange saturation transfer (DEST) and ¹⁵N lifetime line‐broadening to study solution backbone dynamics and position‐specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2–80 MDa) protofibrillar Aβ aggregates. Here we use ¹³C_methyl DEST and lifetime line‐broadening to probe the interactions and dynamics of methyl‐bearing side chains in the Aβ‐protofibril‐bound state. We show that all methyl groups of Aβ40 populate direct‐contact bound states with a very fast effective transverse relaxation rate, indicative of side‐chain‐mediated direct binding to the protofibril surface. The data are consistent with position‐specific enhancements of ¹³C_methyl‐${R{{{\rm tethered}\hfill \atop 2\hfill}}}$ values in tethered states, providing further insights into the structural ensemble of the protofibril‐bound state.     

Synthesis, structures, and strain energies of dispirophosphiranes. Comparisons with dispirocyclopropanes

Six novel dispirophosphirane complexes have been synthesized from the reaction of bicycloalkylidenes with the electrophilic phosphinidene complex PhPW(CO)(5). They contain a central phosphirane ring, which is spirofused on one side to a cyclopropane or cyclobutane ring and on the other side with a three-, four-, five-, or six-membered ring. Their crystal structures and MP2/6-31G-computed geometries for simplified parent systems suggest that spirofusion with small rings results in a tightening of the central three-membered phosphaheterocycle, while spirofusion with larger rings results in a relaxation of the phosphirane geometry. Similar theoretical predictions are made for the corresponding annulated hydrocarbons. Strain energies for both the hydrocarbon and phosphorus series of structures have been calculated at G3(MP2). Whereas the [3]triangulane hydrocarbon and phospha[3]triangulane have a significant excess strain of 8.1 and 5.2 kcal/mol per spiroatom, respectively, the excess strain for systems spirofused with larger rings are negligible for the hydrocarbons and even negative for the phosphorus-containing species because of hyperconjugative stabilization.     

Decomposition of Picolyl Radicals at High Temperature: A Mass Selective Threshold Photoelectron Spectroscopy Study

The reaction products of the picolyl radicals at high temperature were characterized by mass-selective threshold photoelectron spectroscopy in the gas phase. Aminomethylpyridines were pyrolyzed to initially produce picolyl radicals (m/z=92). At higher temperatures further thermal reaction products are generated in the pyrolysis reactor. All compounds were identified by mass-selected threshold photoelectron spectroscopy and several hitherto unexplored reactive molecules were characterized. The mechanism for several dissociation pathways was outlined in computations. The spectrum of m/z=91, resulting from hydrogen loss of picolyl, shows four isomers, two ethynyl pyrroles with adiabatic ionization energies (IE_ad) of 7.99 eV (2-ethynyl-1H-pyrrole) and 8.12 eV (3-ethynyl-1H-pyrrole), and two cyclopentadiene carbonitriles with IE′s of 9.14 eV (cyclopenta-1,3-diene-1-carbonitrile) and 9.25 eV (cyclopenta-1,4-diene-1-carbonitrile). A second consecutive hydrogen loss forms the cyanocyclopentadienyl radical with IE′s of 9.07 eV (T₀) and 9.21 eV (S₁). This compound dissociates further to acetylene and the cyanopropynyl radical (IE=9.35 eV). Furthermore, the cyclopentadienyl radical, penta-1,3-diyne, cyclopentadiene and propargyl were identified in the spectra. Computations indicate that dissociation of picolyl proceeds initially via a resonance-stabilized seven-membered ring.