A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains

In this note we investigate the asymptotic behavior of the s-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain Ω with smooth boundary ∂Ω. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on ∂Ω. It is shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order p for which

     

K3 surfaces with non-symplectic automorphisms of 2-power order

This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Néron–Severi group. Complementing a result by Vorontsov and Kondō, we determine those K3 surfaces where the order of the automorphism is a 2-power and equals the rank of the transcendental lattice. We also study the arithmetic of these K3 surfaces and comment on relations with mirror symmetry.     

On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series

For every positive integer n, consider the linear operator U _n on polynomials of degree at most d with integer coefficients defined as follows: if we write ${\frac{h(t)}{(1 - t)^{d + 1}}=\sum_{m \geq 0} g(m) \, t^{m}}For every positive integer n, consider the linear operator U _n on polynomials of degree at most d with integer coefficients defined as follows: if we write \frach(t)(1 - t)^{d + 1}=?_{m 3 0} g(m)  t^m{\frac{h(t)}{(1 - t)^{d + 1}}=\sum_{m \geq 0} g(m) \, t^{m}} , for some polynomial g(m) with rational coefficients, then \fracU_nh(t)(1- t)^d+1 = ?_{m 3 0}g(nm)  t^m{\frac{{\rm{U}}_{n}h(t)}{(1- t)^{d+1}} = \sum_{m \geq 0}g(nm) \, t^{m}} . We show that there exists a positive integer n _d , depending only on d, such that if h(t) is a polynomial of degree at most d with nonnegative integer coefficients and h(0) = 1, then for n ≥ n _d , U _n h(t) has simple, real, negative roots and positive, strictly log concave and strictly unimodal coefficients. Applications are given to Ehrhart δ-polynomials and unimodular triangulations of dilations of lattice polytopes, as well as Hilbert series of Veronese subrings of Cohen–Macauley graded rings.     

Synthesis of New Regioselectively Sulfated Hyaluronans for Biomedical Application

Sulfated glycosaminoglycans (GAGs) display various biological effects which are strongly influenced by the degree of sulfation and the position of sulfate groups within the polymer. Hyaluronan, a non-sulfated GAG, represents a readily accessible educt to synthesize structural analogues of sulfated GAGs mimicking their biological activity. Different strategies were developed and evaluated to synthesize hyaluronan sulfates with a free primary hydroxyl group at C-6' and sulfated secondary hydroxyl groups. Applying selective desulfation methods of high-sulfated hyaluronan by means of silylating agents, products regioselectively desulfated at the primary C-6' but also partly the C-4' position were obtained. A pathway using benzoyl ester protecting groups to block the primary hydroxyl function of Hya during the sulfation resulted in a high-sulfated product, functionalized only at the secondary hydroxyl groups.     

The oracle penalty method

A new and universal penalty method is introduced in this contribution. It is especially intended to be applied in stochastic metaheuristics like genetic algorithms, particle swarm optimization or ant colony optimization. The novelty of this method is, that it is an advanced approach that only requires one parameter to be tuned. Moreover this parameter, named oracle, is easy and intuitive to handle. A pseudo-code implementation of the method is presented together with numerical results on a set of 60 constrained benchmark problems from the open literature. The results are compared with those obtained by common penalty methods, revealing the strength of the proposed approach. Further results on three real-world applications are briefly discussed and fortify the practical usefulness and capability of the method.     

Synthesis of, light emission from, and optical power limiting in soluble single-walled carbon nanotubes functionalized by disubstituted polyacetylenes

Single-walled carbon nanotubes are covalently functionalized by conjugated polyacetylenes through their cyclization reactions with poly(1-phenyl-1-alkyne) and poly(diphenylacetylene) derivatives carrying azido functional groups at the ends of their alkyl pendants. The resultant polyene nanotube addends are soluble in common solvents, emit intense visible lights and strongly attenuate the power of harsh laser pulses.     

Probing electron transfer dynamics at MgO surfaces by Mg-atom desorption

Ultraviolet excitation of high surface area MgO films using 4.7 eV femtosecond pulses results in neutral Mg-atom desorption with hyperthermal kinetic energies in the range 0.1-0.4 eV. The Mg-atom hyperthermal energies and power dependences are similar to those previously observed using nanosecond pulsed excitation. Femtosecond two-pulse correlation measurements reveal the existence of different dynamical paths for Mg-atom desorption. One mechanism displays a sub-150 fs time scale and involves the simultaneous or near-simultaneous transition of two electrons to a 3-coordinated Mg(2+) site. Other paths display picosecond time scales that we associate with dynamics following electron trapping at 3-coordinated Mg(2+) surface sites.     

New synthetic protocols for the preparation of unsymmetrical bisindoles

Novel unsymmetrical bisindoles were synthesized by a solvent-free C-C bond-formation reaction under mild conditions. Starting from aziridines or hydroxyl precursors, indoles have been used as C-nucleophiles to form new pharmacologically interesting bisindoles via an electrophilic aromatic substitution pathway in good to excellent yields. [reaction: see text]     

State tomography of capacitively shunted phase qubits with high fidelity

We introduce a new design concept for superconducting phase quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single-shot measurements.