In 1999, Frank Schmidt noted that the number of partitions integers with distinct parts in which first, third, fifth, etc., summands add to n is equal p(n), n. The object this paper provide a context for result leads directly many other theorems nature and can be viewed as continuation our work on elongated partition diamonds. Again generating functions are infinite products built by Dedekind e...

[Reaction: see text]. The photolysis of CpW(CO)3Me has been shown to produce methyl radicals and to cleave DNA in a single-stranded manner, and preliminary evidence implicated a carbon-centered radical in this process. In this work, the mechanism of strand scission in this reaction was determined to occur by hydrogen atom abstraction from the 4'- and 5'-positions of the deoxyribose moiety of th...

Boosting is a generic learning method for classification and regression. Yet, as the number of base hypotheses becomes larger, boosting can lead to a deterioration of test performance. Overfitting is an important and ubiquitous phenomenon, especially in regression settings. To avoid overfitting, we consider using l1 regularization. We propose a novel Frank-Wolfe type boosting algorithm (FWBoost...

In the early 60s, Harary and Hill conjectured H(n) := 1 4b2 cbn−1 2 cbn−2 2 cbn−3 2 c to be the minimum number of crossings among all drawings of the complete graph Kn. It has recently been shown that this conjecture holds for so-called shellable drawings of Kn. For n ≥ 11 odd, we construct a non-shellable family of drawings of Kn with exactly H(n) crossings. In particular, every edge in our dr...

On utilising an identity from [5], some weighted Ostrowski type inequalities are established.

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In this paper we derive weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev type inequalities on time scales. We also give some other interesting inequalities on time scales as special cases.

In this paper we derive new weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales. Some other interesting inequalities on time scales are also given as special cases.

The Ostrowski theorem in question is that an additive function bounded (above, say) on a set T of positive measure is continuous. In the converse direction, recall that a topological space T is pseudocompact if every function continuous on T is bounded. Thus theorems of ‘converse Ostrowski’type relate to ‘additive (pseudo)compactness’. We give a di¤erent characterization of such sets, in terms ...