Pseudohalogeno-Metallverbindungen. LXXV. Pentacarbonylrhenium-und Triphenylphosphangold-Komplexe mit Pseudohalogeniden: (OC)5ReX,Ph3PAuX (X = ONC(CN)2, o-MeC6H4SO2C(CN)2,o-MeC6H4SO2NCN,Ph2(S)PNCN)

Pseudohalogeno Metal Compounds. LXXV. Pentacarbonylrhenium and Triphenylphosphinegold Complexes of Pseudohalide Anions: (OC)₅ReX, Ph₃PAuX (x = ONC(CN)₂, o-MeC₆H₄SO₂C(CN)₂, o-MeC₆H₄SO₂NCN, Ph₂(S)PNCN) The pseudohalides (X^?) nitrosodicyanmethanide, o-tosyldicyanmethanide, o-tosylcyanamide and diphenylthiophosphinylcyanamide react with the Organometallic Lewis Acids (OC)₅Re⁺ (as (OC)₅ReFBF₃) and Ph₃PAu⁺ (as Ph₃PAuNO₃) to give the neutral title complexes (OC)₅Re—X and Ph₃PAu? X, respectively. X-ray diffraction shows that nitroso-dicyanmethanide is coordinated through the nitroso N-atom to the Re(CO)₅ fragment. Cyanide-N-coordination is observed for the complexes with o-tosyldicyanmethanide and o-tosylcyanamide whereas diphenylthiophosphinylcyanamide is S-coordinated to the gold atom. Spectroscopic data (IR, NMR) of 1–6 are described.     

“Integer-making” theorems

Let X = {x₁, x₂,…} be a finite set and associate to every x_i a real number α_i. Let f(n) [g (n)] be the least value such that given any family $\text{F}$ of subsets of X having maximum degree n [cardinality n], one can find integers α_i, i=1,2,… so that α_i ? α_i|<1 and

$\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤?(n)}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤}\text{g(n)}$

for all $\text{E ?}\text{F}$. We prove

$\text{f(n)≤n ? 1 and g(n)≤c(n}\text{log}\text{n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

.     

Functionalization of cellulose nanocrystal powder by non-thermal atmospheric-pressure plasmas

Cellulose - Despite promising characteristics such as the biodegradability and the environmentally benign nature of cellulose nanocrystal (CNC) based composites, their poor dispersion and...     

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work, we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (1) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (2) a merged formulation of the PDE and the 2BSDE problem, (3) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (4) a stochastic gradient descent-type optimization procedure. Numerical results obtained using TensorFlow in Python illustrate the efficiency and the accuracy of the method in the cases of a 100-dimensional Black–Scholes–Barenblatt equation, a 100-dimensional Hamilton–Jacobi–Bellman equation, and a nonlinear expectation of a 100-dimensional G-Brownian motion.

     

On the Influence of Polynomial De-aliasing on Subgrid Scale Models

In this work we investigate the interplay of polynomial de-aliasing and sub-grid scale models for large eddy simulations based on discontinuous Galerkin discretizations. It is known that stability is a major concern when simulating underresolved turbulent flows with high order nodal collocation type discretizations. By changing the interpolatory character of the nodal collocation type discretization to a projection based discretization by increasing the number of quadrature points (polynomial de-aliasing), one is able to remove the aliasing induced stability problems. We focus on this effect and on the consequence for large eddy simulations with explicit subgrid scale models. Often, subgrid scale models have to achieve two possibly conflicting tasks in a single simulation: firstly stabilizing the numerics and secondly modeling the physical effect of the missing scales. Within a discontinuous Galerkin approach, it is possible to use either a fast (but potentially aliasing afflicted) nodal collocation discretization or a projection-based (but computationally costly) variant in combination with an explicit subgrid scale model. We use this framework to investigate the effect on the appropriate model parameter of a standard Smagorinsky subgrid scale model and of a Variational Multiscale Smagorinsky formulation. For this we first consider the 3-D viscous Taylor-Green vortex example to investigate the impact on the stability of the method and second the turbulent flow past a circular cylinder to investigate and compare the accuracy of the results. We show that the aliasing instabilities of collocative discretizations severely limit the choice of the model constant, in particular for high order schemes, while for de-aliased DG schemes, the closure model parameters can be chosen independently from the numerical scheme. For the cylinder flow, we also find that for the same model settings, the projection-based results are in better agreement with the reference DNS than those of the collocative scheme.     

Contamination of therapeutic human immunoglobulin preparations with apolipoprotein H (β2‐glycoprotein I)

Polyclonal immunoglobulin (Ig) concentrates are important biological medicinal products and the assurance of their quality and safety is crucial. In our present approach we used proteomic methods to check the purity of commercial Ig products of different origin. The experimental setup included nonreducing 2DE or DIGE combined with MALDI‐TOF and the thrombin generation assay, a routine safety test for pharmaceutical Ig preparations, and was complemented by a specific immunoassay. 2DE patterns displayed contaminations with trace amounts of human apolipoprotein H (Apo‐H), transferrin, albumin, and its fragments. In contrast to the latter, Apo‐H is a protein that is active in the coagulation cascade, and thus a potential involvement in thromboembolic events in vivo cannot be excluded. It was found by 2DE and MALDI‐TOF to be a contaminant of several Ig preparations. Spiking experiments of Ig preparations with pure Apo‐H demonstrated an Apo‐H concentration dependent increase in thrombin generation assay values. Traces of Apo‐H are possibly also contributing to unwanted side effects, as already known for factor XIa. The significance of Apo‐H contaminations for these side effects might be verified by detailed analyses of pharmacovigilance data.