Consider the collection of all integer partitions, whose part sizes lie in a given set. Such a set is called monotone if the generating function has weakly increasing coefficients. The monotone subsets are classified, assuming an open conjecture.

Assumptions on a likelihood function, including a local GlivenkoCantelli condition, imply the existence of M-estimators converging to an Mfunctional. Scatter matrix-valued estimators, defined on all empirical measures on R for d ≥ 2, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

‎The main goal of this paper is to introduce and study two new class of functions‎, ‎called weakly $e^*$-irresolute functions and strongly $e^*$-irresolute functions‎, ‎via the notion of $e^*$-open set defined by Ekici [7]. ‎We obtain several fundamental properties and characterizations of these functions‎. ‎Moreover‎, ‎we investigate not only some of their basic properties but also their relat...

Although OSER formation does not appear overtly harmful to cultured cells, nondimerizing forms of the tag are probably a more prudent choice for most studies. ᭿ lthough normally seen as a branching network of membranes, the endo-plasmic reticulum can quickly and dramatically reorganize into a variety of regular, tightly stacked arrays. Referring to these structures collectively as organized smo...

Although OSER formation does not appear overtly harmful to cultured cells, nondimerizing forms of the tag are probably a more prudent choice for most studies. ᭿ lthough normally seen as a branching network of membranes, the endo-plasmic reticulum can quickly and dramatically reorganize into a variety of regular, tightly stacked arrays. Referring to these structures collectively as organized smo...