A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning

Journal of Optimization Theory and Applications - We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...     

Dichlorocarbene and analogs: discovery,properties and reactions

Russian Chemical Bulletin - The discovery and studies of chemistry of dichlorocarbene and other electron deficient carbenes are discussed.     

Experimental and Theoretical Mechanistic Study on the Thermal Decomposition of 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline

The present paper is a continuation of comprehensive study regarding to synthesis and properties of pyrazoles and their derivatives. In its framework an experimental and theoretical studies of thermal decomposition of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline were performed. It was found, that the decompositions of the mentioned pyrazoline system in the solution and at the melted state proceed via completely different molecular mechanisms. These mechanisms have been explained in the framework of the Molecular Electron Density Theory (MEDT) with the computational level of B3LYP/6-31G(d). A Bonding Evolution Theory (BET) examination of dehydrochlorination of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline permits elucidation of the molecular mechanism. It was found, that on the contrary for most known HCl extrusion processes in solution, this reaction is realised via single-step mechanism.     

Synthesis and Properties of Azoles and Their Derivatives. Part 70. Nitroallylic Systems in [2 + 3] Cycloaddition Reactions with Nitrones: A DFT Computational Study

The analysis of electrophilicity indexes and the results of potential energy surface (PES) simulations for the reaction pathways proved that the [2 + 3] cycloadditions of nitroallylic systems with nitrones should be considered nonpolar reactions. Our simulations proved that the reactions always proceed via a one‐step mechanism through a prereaction complex. Although the symmetry of respective transition states is quite varied, their polarity is low and does not change when a polar medium is introduced to the reaction environment. When the polarity of the reaction medium increases, the kinetic pathway preference does not change. The regiochemistry of the cycloadditions tested may, however, be controlled to some extent by steric effects.     

Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

Measurement of the Seperation between Atoms beyond Diffraction Limit

We propose a scheme to obtain the distance of two identical atoms placed inside the standing wave field by monitoring the collective resonance fluorescence spectrum emitted by the two particles. We find three different parameter ranges, depending on the distance of the atoms as compared to the transition wavelength. For large interparticle distances, dipole-dipole coupling is negligible, and the main system evolution arises from the interaction with the standing wave field. In the small-distance limit, the dynamics is dominated by the dipole-dipole interaction. Finally, in the intermediate region, a rich interplay of the various couplings arises, which however is lifted for strong driving laser fields. The present measurement procedure allows us to distinguish the three cases. In each of the cases, we show how to determine the distance of the two particles and their respective positions relative to the nodes of the standing wave field with fractional-wavelength precision.