We construct a uniform model for highest weight crystals and $B(\infty)$ generalized Kac--Moody algebras using rigged configurations. also show an explicit description of the $\ast$-involution on configurations $B(\infty)$: that interchanges rigging corigging. do this by giving recognition theorem $\ast$-involution. As consequence, we characterize $B(\lambda)$ as subcrystal

Mammary gland involution represents one of the most dramatic examples of programmed cell death/apoptosis and tissue regression during development, yet large gaps still exist in the understanding of the mechanisms involved, and the key factors that trigger involution, are not yet identified. With the focus on identifying "novel" genes associated with mammary gland regression, we used microarray ...

It truly is a remarkable event when traditional pathologic observations lead to new ideas about the prevention of cancer. In this issue of the Journal , Milanese et al. (1) , through a histologic review of breast biopsy specimens, show that the extent of age-related lobular involution is strongly associated with a reduced risk of breast cancer. Breast cancer risk decreased with increasing exten...

Let T be an orientation-preserving Lipschitz expanding map of the circle T. A pre-image selector is a map τ : T → T with finitely many discontinuities, each of which is a jump discontinuity, and such that τ (x) ∈ T(x) for all x ∈ T. The closure of the image of a pre-image selector is called a flower, and a flower with p connected components is called a p-flower. We say that a real-valued Lipsch...

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.  

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.

The method of forming complex algebras of finite ternary relations will produce all finite nonassociative relation algebras. We use this method to construct many interesting algebras. Every atomic NA determines an involution on atoms, which in turn determines both the cycles of the algebra and also the missing, or forbidden cycles. So we begin by studying the cycles of an arbitrary involution. ...

The Lalanne–Kreweras involution is an on the set of Dyck paths which combinatorially exhibits symmetry number valleys and major index statistics. We define piecewise-linear birational extensions involution. Actually, we show that a special case more general operator, called rowvacuation, acts antichains any graded poset. Rowvacuation, like closely related studied rowmotion composition toggles. ...