For weak solutions of the incompressible Euler equations, there is energy conservation if the velocity is in the Besov spaceB3 s with s greater than 1/3. B p s consists of functions that are Lip(s) (i.e., Hölder continuous with exponent s) measured in the L norm. Here this result is applied to a velocity field that is Lip(α0) except on a set of co-dimension κ1 on which it is Lip(α1), with unifo...

We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals, associated primes, leading term ideals, and the minimal number of generators. In contrast, the reduction number of the Ratliff-Rush filtration behaves better...

For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of...

In this paper, a realistic simulation model for Wheeled Mobile Robot (WMR) is given by a dynamical system that switches between three models corresponding to three different tire/road contact conditions: ideal condition, skidding condition and slipping condition. Then, an algebraic based numerical identification for the discrete state (tire/road contact condition) of this switching system is pr...

PhysIcs of Fluids B. Results of extended research should not be presented as a series of letters in place of comprehensive articles. Letters cannot exceed three printed pages in length, including space allowed for title, figures, tables, references and an abstract limited to about 100 words. There is a three-month time limit, from date of receipt to acceptance, for processing Letter manuscripts...

The explosive growth of mobile technologies combined with the rapid rise of aging populations fearful of their risk for Alzheimer’s disease has led to a number of marketed products aimed at enhancing cognitive health. However, an increasing number of product claims that are not substantiated has led regulatory agencies, such as the Federal Trade Commission (FTC), to issue warnings or penalties ...

Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also gener...