We construct and test new explicit general linear Hermite–Birkhoff–Radau (HBR) methods of orders 4, 5, 8, 9 and 10 with 1, 2, 3, 4, and 4 off-step points,respectively. It is observed that the order of HBRr methods with off-step points is + (= + 1) where is the order of the predictor used to...

Let , ,…, be a sequence of independent random variables, let be a rearrangement invariant space on the underlying probability space, and let be a symmetric sequence space. This paper gives an approximate formula for the quantity whenever embeds into for some 1 ≤ ∞. This extends work of...

The theory of hypernumbers is a novel approach in functional analysis aimed at the development of such mathematically correct technique, which allows operations with divergent integrals and series. Although, it resembles nonstandard analysis, there are several distinctions between these...

Mathematical models for artificial intelligence (AI) are considered. It is assumed that AI is realized on the base of computers. Computers are controlled by algorithms in the form of software. Consequently, it is natural to assume that AI has to be realized by algorithms and it is reasonable to...

Measures of location based on the shortest half sample, including the shorth and the location of the least median of squares, are more robust than the median to outliers, but less robust to contamination near the location. Although such measures can estimate the mode, the proposed estimator of...

For each 1 < < ∞, there exists a positive constant , depending only on , such that the following holds. Let (), () be real-valued martingale difference sequences. If for for all bounded nonnegative predictable sequences () and all positive integers we havethen for all positive integers we have

We consider a finite universal set of alternatives and the set of all feasible sets are simply the set of all non-empty subsets of this universal set. A choice function assigns to each feasible set a non-empty subset of it. In such a framework we propose and study necessary and sufficient...

We prove that the threshold regime for bootstrap percolation in a -dimensional box of diameter with parameters and , where 3 ≤ ≤ , is ~ exp(), where exp is the exponential iterated — 1 times and is bounded from above and from below by two positive constants depending on , only

In any learnability setting, hypotheses are conjectured Studied herein are the influence on learnability of the in the hypothesis space. First presented are control structure of some rather specific but illustrative learnability results. The presence of these control structures is thereby shown...

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts.Building on Angluin's...