Upper cluster algebras and choice of ground ring

We initiate a study of the dependence of the choice of ground ring on the problem on whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the cluster algebra and upper cluster algebra is given by using a variation of Muller's theory of cluster localization. An explicit example exhibiting dependence on the ground ring is provided. We also present a maximal green sequence for this example.     

Solving the spectroscopic phase: imaging excited wave packets and extracting excited state potentials from fluorescence data

We develop an inversion scheme for obtaining the signs of transition-dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained we show how to extract highly accurate excited state potential(s) and the transition-dipole(s) as a function of inter-nuclear displacements. The same dipole amplitudes can also be used to extract the phase and amplitude of unknown time-evolving wave packets, in essentially a quantum non-demolition manner. The procedure, which is demonstrated for the A((1)∑) and B((1)Π(u)) states of the Na(2) molecule, is shown to yield reliable results even when we are given incomplete or uncertain data. We also demonstrate the success of our approach in extracting double minimum potentials. The inversion scheme is in principle applicable to any polyatomic molecule.     

Forces on a porous particle in an oscillating flow

We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter beta = a/square root(k) and the frequency parameter Y = square root(a(2)omega/2nu) = a/delta, respectively. Here a is particle radius, k is its permeability, omega is the angular frequency, delta is the thickness of Stokes layer (penetration depth) and nu is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.     

Lattice dynamics and structural phase transitions

Results of lattice dynamics, or atomic motions in a solid, explain many of the thermodynamic properties of solids. Inelastic neutron scattering conveniently explores the atomic motions, quantized as phonons. Of particular interest are materials that undergo structural phase transitions. The soft mode theory has been successful in relating anomalous phonon behavior to structural changes in solids. One such example is the ferromagnetic shape memory alloy, Ni₂MnGa, which undergoes a sequence of phase transitions leading to a magnetic, incommensurate modulated, tetragonal phase as the ground state. The experiments, coupled with first principles calculations, provide evidence that strong electron–phonon coupling is the driving mechanism of the phase transformation.     

Model for evolution of periodic layered structure in the SiO2/Mg system

A mathematical model for the growth of MgO/Mg₂Si periodic layered structure (PLS) is presented based on Fick's diffusion law and conservation of matter. The model explains the temporal evolution of the width of periodic layers at different temperatures, for layers distant enough from the Mg source. It is demonstrated that the difference in thickness of a pair of any two adjacent layers decreases with increasing temperature.     

Comments on: Stability in linear optimization and related topics. A personal tour

This is a well-written compendium of both classical and recent results on qualitative and quantitative stability of linear optimization problems, where the case of infinitely many constraints is intrinsically included. The author presents basic theoretical approaches and outcomes of this area in a concise, competent and informative manner. Since this survey is almost complete, we cannot add much in our note. So, we will restrict ourselves to a discussion of two special subjects which are related to our own research, complementing thereby single aspects of the author??s presentation of Lipschitz stability analysis.     

Kinetic characteristics of the reaction of resveratrol with peroxyl radicals and natural thiols in aqueous medium

Russian Chemical Bulletin - The method of competing reactions was used to determine the rate constants of the reaction of resveratrol (RVT) with peroxyl radicals formed on decomposition of the...     

Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras

Given a PDE with real or complex partial derivatives and with constant coefficients, we propose a method of assigning to it a set of algebra‐valued functions in such a manner that the components of the latter are solutions of the PDE. Copyright © 2013 John Wiley & Sons, Ltd.