Geometric existence theory for the control-affine nonlinear optimal regulator

For infinite horizon nonlinear optimal control problems in which the control term enters linearly in the dynamics and quadratically in the cost, well-known conditions on the linearised problem guarantee existence of a smooth globally optimal feedback solution on a certain region of state space containing the equilibrium point. The method of proof is to demonstrate existence of a stable Lagrangian manifold M and then construct the solution from M in the region where M has a well-defined projection onto state space. We show that the same conditions also guarantee existence of a nonsmooth viscosity solution and globally optimal set-valued feedback on a much larger region. The method of proof is to extend the construction of a solution from M into the region where M no-longer has a well-defined projection onto state space.     

Synthese und Metallierung des Diaminosiloxans O(SiiPr2NH2)2

Synthesis and Metalation of the Diaminosiloxane O(SiiPr₂NH₂)₂ The 1,3‐diaminoldisiloxane O(SiiPr₂NH₂)₂ ( 1 ) was obtained from the reaction of O(SiiPr₂Cl)₂ with NH₃. The reactions of 1 with AlEt₃ or GaEt₃ produced the compounds [O{SiiPr₂N(H)MEt₂}{SiiPr₂NMEt}]₂ ( 2 : M = Al; 3 : M = Ga). The crystal structures of 2 and 3 were determined by single crystal X‐ray diffraction, showing a polycyclic M₄N₄Si₄O₂ core structure of these molecules.     

Synthesis,Structure, and Properties of the High‐Pressure Modification of CePdSn – a 5 K Antiferromagnet

The high‐pressure (HP) modification of CePdSn was synthesized under multianvil high‐pressure (10.5 GPa) high‐temperature (1100 °C) conditions from the normal‐pressure (NP) modification. The structures of both modifications were studied by X‐ray powder and single crystal diffraction: TiNiSi type, Pnma, a = 754.1(2), b = 470.6(1), c = 798.4(3) pm, wR2 = 0.0333, 945 F² values, 20 variables for NP‐CePdSn and ZrNiAl type, , a = 760.03(5), c = 416.06(3) pm, wR2 = 0.0443, 248 F² values, 13 variables for HP‐CePdSn. The structural chemistry of both modifications is goverened by platinum centered trigonal prisms. The platinum and tin atoms in NP‐CePdSn and HP‐CePdSn build up a three‐dimensional [PdSn] network in which the cerium atoms fill channels. Susceptibility measurements on HP‐CePdSn reveal an experimental magnetic moment of 2.55(1) μ_B/Ce atom in the paramagnetic region. At 5 K a paramagnetic‐to‐antiferromagnetic transition is evident from magnetization and specific heat measurements.     

New Silver Tellurates – The Crystal Structures of a Third Modification of Ag2Te2O6 and of Ag4TeO5

Single crystals of a third modification of Ag₂Te₂O₆ (denoted as Ag₂Te₂O₆–III) and of Ag₄TeO₅ have been obtained as minor by‐products during hydrothermal phase formation experiments in the system Ag‐Hg‐Te‐O. The crystal structure of Ag₂Te₂O₆–III (P2₁/c, Z = 4, a = 6.4255(10), b = 6.9852(11), c = 13.204(2) Å, β = 90.090(3)°, 1885 independent reflections, R[F² > 2σ(F²)] = 0.0334, wR2(F² all) = 0.0817) comprises tellurium in oxidation states +IV and +VI and is topologically related to the structure of the Ag₂Te₂O₆–I modification, which consists of similar layers and interjacent layers of Ag⁺ cations. Ag₄TeO₅ (C2/c, Z = 8, a = 16.271(2), b = 6.0874(10), c = 11.4373(16) Å, β = 106.730(10)°, 2372 independent reflections, R[F² > 2σ(F²)] = 0.0288, wR2(F² all) = 0.0737) is made up of a layer‐like arrangement of isolated [Te^VI₂O₁₀] double octahedra and of Ag⁺ cations situated both in layers parallel and inside the layers of the anionic moieties.     

Synthetic Activators of Cell Migration Designed by Constructive Machine Learning

Constructive machine learning aims to create examples from its learned domain which are likely to exhibit similar properties. Here, a recurrent neural network was trained with the chemical structures of known cell-migration modulators. This machine learning model was used to generate new molecules that mimic the training compounds. Two top-scoring designs were synthesized, and tested for functional activity in a phenotypic spheroid cell migration assay. These computationally generated small molecules significantly increased the migration of medulloblastoma cells. The results further corroborate the applicability of constructive machine learning to the de novo design of druglike molecules with desired properties.     

New Rare‐Earth Metal Germanides RE2Ge9 (RE = Nd,Sm) by Thermal Decomposition of High‐Pressure Phases REGe5

The rare‐earth metal germanides RE₂Ge₉ (RE = Nd, Sm) have been prepared by thermal decomposition of the metastable high‐pressure phases REGe₅ at ambient pressure. The compounds adopt an orthorhombic unit cell with a = 396.34(4) pm; b = 954.05(8) pm and c = 1238.4(1) pm for Nd₂Ge₉ and a = 395.46(7) pm; b = 946.4(2) pm and c = 1232.1(3) pm for Sm₂Ge₉. Crystal structure refinements reveal space group Pmmn (No. 59) for Nd₂Ge₉. The atomic pattern resembles an ordered defect variety of the pentagermanide motif REGe₅ (RE = La; Nd, Sm, Gd, Tb) comprising corrugated germanium layers. These condense into a three‐dimensional network interconnected by eight‐coordinated germanium atoms. The resulting framework channels along [100] enclose the neodymium atoms. With respect to the atomic arrangement of the pentagermanides, half of the interlayer germanium atoms are eliminated in an ordered way so that occupied and empty germanium columns alternate along [001]. The rare‐earth metal atoms of both types of compounds, REGe₅ and RE₂Ge₉, exhibit the electronic states 4f ³ and 4f ⁵ (oxidation state +3) for neodymium and samarium, respectively, evidencing that the modification of the germanium network leaves the electron configuration of the metal atoms unaffected.     

Luminescence of ion-pair states of halogens in liquid perfluorocarbons

The I(2)(D'-A') luminescence in liquid C(7)F(16), C(8)F(18), C(9)F(20), and C(12)F(26) has been observed following irradiation with visible (within the I(2) X → B band region) and UV (λ < 300 nm) lasers. The band is shifted by ~2000 cm(-1) to the red relative to the gas phase and is significantly broader (fwhm ≈ 3000 cm(-1) vs 500 cm(-1) in the gas phase). Two-color excitation of other halogens in C(n)F(2n+2) solvents revealed similarly shifted and strongly broadened D'-A' bands of Br(2), IBr, and BrCl. The stability of the ion-pair states of halogens in room temperature liquids opens new experimental opportunities for condensed phase studies and may be of applied interest considering the increasing industrial applications of perfluorocarbons.     

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.