We consider an extremal problem for graphs as introduced by Erdős, Jacobson and Lehel in [7]. Let π be an n-element graphic sequence. Let H be a graph. We wish to determine the smallest m such that any nterm graphic sequence π whose terms sum to at least m has some realization containing H as a subgraph. Denote this value m by σ(H, n). For an arbitrarily chosen H, we give a construction that yi...

There are many representations of planar graphs, but few are as elegant as Turán’s (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main disadvantage has been that “it does not allow efficient searching” (Jacobson, 1989). In this paper we show how to add a sublinear number of bits to Turán’s represen...

Problem 2. Let A be a central division algebra (of finite dimension) over a field k. Let [A, A] be the k-subspace of A spanned by the elements ab − ba with a, b ∈ A. Show that [A, A] = A. Solution. Let K be the algebraic closure of k, and consider B = A ⊗ k K. Then B ∼ = M n (K) for some n ∈ N, and thus we can understand [B, B] ∼ = [A, A] ⊗ k K. In this case, [B, B] contains only matrices of tr...

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cians in behavioral activation methods aimed at palliating depressive symptoms, including graded task assignment, goal setting scheduling, reinforcement of social contact behaviors or performance of gratifying activities (Kanter, Busch, & Rusch, 2009; Lejuez, Hopko, & Hopko, 2002; Martell, Addis, & Jacobson, 2001). In fact, there was always a place for these strategies in the most serious cases...

We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson radical of any locally finite profinite ring is nil of finite nilexponent. Our results apply to the context of small compact G-rings, where we also obtain a...

In 1990, Jacobson and colleagues at the University of Washington began a dismantling study where they tested competing hypotheses about the basis for the effects of cognitive therapy ( Jacobson et al., 1996). In particular, they isolated the behavioral activation (BA) component of cognitive therapy (CT) to determine whether simply activating depressed people, and thereby helping them make conta...

We investigate the structure of incidence rings of group automata over finite fields. One of the major tools used in research on the structure of ring constructions is the Jacobson radical. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of (possibly nondeterministic) group automata over finite fields in the important special case where the input group ...

Jacobson, Levin, and Scheinerman introduced the fractional Ramsey function rf (a1,a2, . . . ,ak) as an extension of the classical definition for Ramsey numbers. They determined an exact formula for the fractional Ramsey function for the case k=2. In this article, we answer an open problem by determining an explicit formula for the general case k>2 by constructing an infinite family of circulant...

We study symmetric algebras $A$ over a field $F$ in which the Jacobson radical of center $A$, socle or Reynolds ideal are ideals.