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The energy of graphs containing self-loops is considered. If the graph G of order n contains σ self-loops, then its energy is defined as E(G) = |λ i − σ/n| where λ 1 , λ 2 , . . . , λ n are the eigenvalues of the adjacency matrix of G. Some basic properties of E(G) are established, and several open problems pointed out or conjectured.

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It is shown that a theorem, recently obtained by Dixon, is a special case of the Cauchy inequalities. Several additional applications of these inequalities in the simple molecular orbital theory are pointed out.

Neuroeconomics has the potential to fundamentally change the way economics is done. This article identifies the ways in which this will occur, pitfalls of this approach, and areas where progress has already been made. The value of neuroeconomics studies for social policy lies in the quality, replicability, and relevance of the research produced. While most economists will not contribute to the neuroeconomics literature, we contend that most economists should be reading these studies.

A simple methods that extends earlier work by Vemulapalli in 1986 (in this journal) regarding how to demonstrate in an undergraduate course of physical chemistry that entropy is a state function without exploiting the concept of the Carnot engine.

By connecting two identical bivalent constituent fragments in two different ways S and T isomers are obtained. The following interlacing theorem:is proved, where sj and fj, j = 1,2, . . . ,2n, stand for the molecular orbital energies (calculated within the simple tight-binding approximation) of the S and T isomers, respectively. In addition, some new topological functions are studied and a number of statements concerning the location of their zeros as well as their relation to the location of the sj and ti are deduced.

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