Kenneth Jacobson serves as Chief of the Laboratory of Bioorganic Chemistry and the Molecular Recognition Section at the National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health in Bethesda, Maryland, USA. Dr. Jacobson is a medicinal chemist with interests in the structure and pharmacology of G-proteincoupled receptors, in particular receptors for adenosine...

We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by which to bound graph invariants by certain indices in the ordered degree sequence. As an illustration of the DSI strategy, we show how it can be used to give new upper and lower bounds on the k-independence and the k-domination numbers. These include, among other things, a double generalization of the annihilation num...

Object-oriented software development process, such as the Unified Process [Jacobson 99], Catalysis [D ́Souza 98] and Fusion [Coleman 94] among others, is a set of activities needed to transform user’s requirements into a software system. A software development process typically consists of a set of software development artifacts together with a graph of tasks and activities. Software artifacts a...

We introduce a notion of depth three tower C ⊆ B ⊆ A with depth two ring extension A|B being the case B = C . If A = End BC and B|C is a Frobenius extension with A|B|C depth three, then A|C is depth two. If A, B and C correspond to a tower G > H > K via group algebras over a base ring F , the depth three condition is the condition that K has normal closure KG contained in H . For a depth three ...

We prove a coordinatization theorem for unital alternative algebras containing $2\\times 2$ matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on description of generalized quaternion $\\mathbb{H}$ 1, case when is split. In particular, this basic field finite or algebraically closed.

The edge clique cover number ecc ( G ) of a graph is the size smallest collection complete subgraphs whose union covers all edges G. Chen, Jacobson, Kézdy, Lehel, Scheinerman, and Wang conjectured in 2000 that if claw-free, then bounded above by its order (denoted n). Recently, Javadi Hajebi verified this conjecture for claw-free graphs with an independence at least three. We study two, which a...