Crystal Structure and Mass-, Electronic-, Infrared Spectral Studies on Hexaaqua Ni(II) Bis(O-Tolylazo-Citrazinate) Hexahydrate Complex

A new crystalline octahedral hexaaqua Ni(II) bis(o-tolylazo-citrazinate)hexahydrate complex was synthesized. The analytical data proved the formation of 1:2 stoichiometry. An X-ray structure investigation has been carried out. The triclinic space group is p and the unit cell parameters are a = 585.5 pm, b = 993 pm, c = 1139.4 pm, α = 101.6°, β = 97.4°, γ = 102.4°. Evaluation of intensity data revealed the structure with an R-value of 0.03 (2316 observed independent reflections). The compound consists of hexaaqua nickel(2+) ions, univalent anions of the carboxylic acid and six additional water molecules per     

Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.     

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

This paper identifies an industrially relevant class of linear hybrid automata (LHA) called reasonable LHA for which parametric verification of convex safety properties with exhaustive entry states can be verified in polynomial time and time-bounded reachability can be decided in nondeterministic polynomial time for non-parametric verification and in exponential time for parametric verification. Properties with exhaustive entry states are restricted to runs originating in a (specified) inner envelope of some mode-invariant. Deciding whether an LHA is reasonable is shown to be decidable in polynomial time.     

Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the Cartesian product of several standard simplices (of possibly different dimensions). Among many other applications, multi-StQPs occur in Machine Learning Problems. Several converging monotone interior point methods are established, which differ from the usual ones used in cone programming. Further, we prove an exact cone programming reformulation for establishing rigorous yet affordable bounds and finding improving directions.     

Duality and Hidden Symmetries in Interacting Particle Systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.     

Binding free energies in the SAMPL5 octa-acid host–guest challenge calculated with DFT-D3 and CCSD(T)

We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO–CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11–16 kJ/mol. DLPNO–CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum–mechanical methods.     

Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality

We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.