One-sided classiiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 ii the set on the input belongs to the given class. Such a classiier is two-sided if the sequence of its output in addition converges to 0 on sets not belonging to the class. The present work obtains the below mentioned results for one-sided classes (...

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai's generalize central approximate identities in ideals in C *-algebras, for it is proved that if X admits an M-cai in Y , then X is a complete M-ideal in Y. It is proved, using " special " M-cai's, that if J is a nuclear ideal in a C *-algebra A, then J is ...

We examine inference on conditional quantiles from the nonparametric perspective of local smoothing. This paper develops a framework for translating the powerful, high-order accurate IDEAL results (Goldman and Kaplan, 2012) from their original unconditional context into a conditional context, via a uniform kernel. Under mild smoothness assumptions, our new conditional IDEAL method’s two-sided p...

For four wide classes of topological rings $\mathfrak R$, we show that all flat left R$-contramodules have projective covers if and only are descending chains cyclic discrete right R$-modules terminate the quotient R$ perfect. Three for which this holds complete, separated associative with a base neighborhoods zero formed by open two-sided ideals such either ring is commutative, or it has count...

AV In the analysis of the Cancer and Leukemia Group B (CALGB)/SWOG 80405 trial that we presented at the 2016 annual meeting of the American Society of Clinical Oncology (ASCO), we defined right-sided colon cancer as cancer of the cecum and the ascending colon up to the hepatic flexure. Left-sided colon cancer comprises cancer of the splenic flexure and cancer in regions distal to the splenic fl...