We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set. Key words Doob Meyer decomposition, natural increasing processes, potentials, supermartingales. Mathematics Subject Classi…cation (2000): : 28A12, 60G07, 60G20.

We discuss recent work of several authors on the Kakeya nee dle problem and other related problems involving nonexistence of small sets containing large families of one dimensional objects Mathematics Subject Classi cation B

The main result of the present paper is that the projective line over a ring R is connected with respect to the relation ``distant'' if, and only if, R is a GE2-ring. 2000 Mathematics Subject Classi®cation. 51C05, 20H25.

We examine the impact of retirement exibility and the constraint against borrowing from future labor income on optimal consumption, optimal investment, and optimal retirement policy. We solve three alternative models almost explicitly in parametric forms (up to at most a constant) and provide veri cation theorems for the claimed solutions. In addition, we also obtain analytical comparative stat...

Suppose that G is a …nite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether is primitive or not. Mathematics Subject Classi…cation 2000...

To decompose solution sets of polynomial systems into irreducible components, homotopy continuation methods generate the action of a natural monodromy group which partially classi es generic points onto their respective irreducible components. As illustrated by the performance on several test examples, this new method achieves a great increase in speed and accuracy, as well as improved numerica...

N grams o er fast language independent multi-class text categorization. Text is reduced in a single pass to ngram vectors. These are assigned to one of several classes by a) nearest neighbour (KNN) and b) genetic algorithm operating on weights in a nearest neighbour classi er. 91% accuracy is found on binary classi cation on short multi-author technical English documents. This falls if more cat...

This report about research in mathematics and Mathematics Education in the Republic of Srpska is a resource for the international academic society. In this paper we expose the capacity for research in mathematics and Mathematics Education and scientific competence of researches in the Republic of Srpska during 2012-2014, as an example. Mathematics Subject Classification (2010): 97A40, 97A50 Did...

Let S be a scheme, and letGbe a ¢nite, £at, commutative group scheme over S. In this paper we show that (subject to a mild technical assumption) every primitive class in Pic(G) is realisable. This gives an af¢rmative answer to a question of Waterhouse. We also discuss applications to locally free classgroups and to Selmer groups of Abelian varieties. Mathematics Subject Classi¢cations (2000). 1...

Abstract. Enumeration schemes were developed by Zeilberger, Vatter, and Pudwell as automatable methods to enumerate the set of permutations of length n which avoid a set of patterns B, Sn(B). In this paper we show how their schemes may be re ned to enumerate Sn(B) according to the inversion number of each permutation. Mathematics Subject Classi cation(2000). 05A05, 05A15, 05A30, 68R15.