In many different contexts, decision-making is improved by the availability of probabilistic predictions. The accuracy forecasting methods can be compared using scoring functions and insight provided calibration tests. These tests evaluate consistency predictions with observations. Our main agenda in this paper interval forecasts their evaluation. Such are usually bounded two quantile forecasts...

‎Assume that $A$ is a Banach algebra‎. ‎We define the‎ ‎$beta-$topology and the $gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$‎ ‎We establish further properties of $(QM_{el}(A^{*}),gamma)$ when $A$ is a $C^{*}-$algebra‎. ‎In particular‎, ‎we characterize the $gamma-$dual‎ ‎of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),gamma)^{*},$...

In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...