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.     

Electronic structure of the benzene–tetracyanoethylene complex: A synthesis of molecular orbital and density functional descriptions

The electronic structure of the benzene–tetracyanoethylene electron donor–acceptor complex is investigated at the HF /6-311G ^** level of theory. The computed electronic wave function is analyzed with rigorous interpretive tools that involve both molecular orbital and density functional approaches. The in situ electronegativity difference is calculated at 3.32 eV, resulting in a charge transfer of 0.016. This extent of charge transfer is found to account for only ca. 17% of the interaction energy of ca. 33% of the dipole moment. The remaining part of the dipole moment originates from buckling of the tetracyanoethylene moiety. The dependence of the electronegativity difference on the magnitude of charge transfer is found to be highly nonlinear. © 1994 John Wiley & Sons, Inc.     

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.     

Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.