Methoxymethylation of a variety of alcohols was performed using formaldehyde dimethyl acetal in the presence of 1,3-dichloro-5,5-dimethyl hydantoin [DCDMH] and Poly N,N′-dibromo-N-ethyl naphthyl-2,7-disulfonamide [PBNS] as catalysts at room temperature and under solvent-free conditions. Our experiments show that primary and secondary alcohols can be smoothly converted into the corresponding MOM...

The topic of repeating segments in words is one of major interest in combinatorics on words. The topic has been studied for more than a century by many authors after the seminal work [9] which described infinite words containing no consecutive occurrences of the same factor. Beyond the theoretical aspect of questions related to redundancies in words, repetitions, also called repeats in the foll...

This paper proves sharp inequalities for the frequencies of vibration of strings and cylindrical membranes, under either fixed or fixed-free boundary conditions. We establish such inequalities also on the "generalized" cylinder, which is the cross-product of an interval with a homogeneous Riemannian manifold. The goal is to better understand the effect that inhomogeneities in the mass distribut...

We study zero-temperature Ising Glauber Dynamics, on 2D slabs of thickness k ≥ 2. In this model, ±1-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for k = 2 under free boundary conditions and for k = 2 or 3 under periodic boundary conditions. For thicker slabs there are sites ...

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

The three–dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection (or density stratification) equation. In this paper we prove...

The probability of observing a large deviation (LD) in the number of particles in a region L in a dilute quantum gas contained in a much larger region V is shown to decay as exp[− |L| DF], where |L| is the volume of L and DF is the change in the appropriate free energy density, the same as in classical systems. However, in contrast with the classical case, where this formula holds at all temper...