We show that the binary homogeneous nucleation (BHN) of H2SO4-H2O can be treated as quasi-unary nucleation of H2SO4 in equilibrium with H2O vapor. A scheme to calculate the evaporation coefficient of H2SO4 molecules from H2SO4-H2O clusters is presented and a kinetic model to simulate the quasi-unary nucleation of H2SO4-H2O is developed. In the kinetic model, the growth and evaporation of sulfur...

In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical quantization condition. Properties of this quantization condition are compared with those derived from the standard WKB approach.

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasiYang-Baxrer algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and nd an unexpected and remarkable applications in quantum inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter algebras the standard proced...

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

Two important classes of manifolds of quantum states, the locally quasi-classical manifold and the quasi-classical manifold, are introduced from the estimation theoretical viewpoint, and they are characterized geometrically by the vanishing conditions of the relative phase factor (RPF), implying the close tie between Uhlmann parallel transport and the quantum estimation theory.

We know that tilesets that can tile the plane always admit a quasiperiodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasiperiodic tiling. We prove that the tilings by a tileset that admits only quasiperiodic tilings have a recursively (and uniformly) bounded quasi-periodicity function. Thi...

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these converge superlinearly, corresponding rates still remain unknown. In this paper, we address problem. obtain first explicit non-asymptotic superlinear standard methods, which are based on updating formulas from convex Broyden clas...