Coupled Nosé-Hoover equations of motions without time scaling

The Nosé-Hoover (NH) equation of motion is widely used in molecular dynamics simulations. It enables us to set a constant temperature and produce the canonical distribution for a target physical system. For the purpose of investigating the physical system under fluctuating temperature, we have introduced a coupled Nosé-Hoover equation in our previous work [J. Phys. A 48 455001 (2015)]. The coupled NH equation implements a fluctuating heat-bath temperature in the NH equation of the physical system, and also keeps a statistically complete description via an invariant measure of the total system composed of the physical system and a “temperature system”. However, a difficulty lies in that the time development of the physical system may not correspond to the realistic physical process, because of the need of a scaled time average to compute thermodynamical quantities. The current work gives a solution by presenting a new scheme, which is free from the scaled time but retains the statistical description. By use of simple model systems, we validate the current scheme and compare with the original scheme. The sampling property of the current scheme is also clarified to investigate the effect of function setting used for the distribution of the total system.

BALANCED INTERPOLATORY MULTIWAVELETS WITH MULTIPLICITY r

Vector-valued refinable interpolatory functions with multiplicity r are discussed in this paper. This kind of refinable functions have a sampling property like Shannon's sampling theorem, and corresponding matrix-valued refinable masks possess special structure. In the context of multiwavelets, some properties of multifilter banks related will be present. Based on these properties, it will be shown that there are no symmetric (or antisymmetric) vector-valued refinable functions with interpolatory property. In the practical application, multiwavelets are always required to possess a certain degree of smoothness, which is related to three different concepts: balancing order, approximation order and analysis-ready order. In the general case, three notions are different. But if the scaling function is interpolatory, three concepts will be verified to equal to each other. Finally, a complete characterization of multifilter banks {H, G} will also be given and it will be used to construct some new balanced multiwavelets with interpolatory property for case r = 2, corresponding to which, multifilter banks have rational coefficients.

Strong Convergence of Pramarts in Banach Spaces

Let E be a Banach space and be an adapted sequence on the probability space We denote by T the set of all bounded stopping times with respect to . is called a pramart ifconverges to zero in probability, uniformly in τ ≧ σ. The notion of pramart was introduced in [6]. A good property is the optional sampling property (see Theorem 2.4 in [6]). Furthermore the class of pramarts intersects the class of amarts, and every amart is a pramart if and only if dim E < ∞ ([2], see also [4]). Pramarts behave indeed quite differently than amarts. Although the class of pramarts is large, they have good convergence properties as is seen in the next two results of Millet-Sucheston, [6], [7].THEOREM 1.1. Let be a real-valued pramart of class (d), i.e.,