My passion for teaching began early. Throughout high school and college, I tutored English to African immigrants. Later, while student teaching remedial and gifted-and-talented mathematics at a New York City public middle school, I realized the diversity of how students learn. Some students thrive off interactive lectures, while others do not fully digest a lecture until working out examples at...

The HLA D/DR region of the human major histocompatibility complex encodes a family of highly polymorphic, human "Ia-like" molecules that function as genetic restriction elements in a variety of immune phenomena (1, 2). Correlations have been demonstrated between disease susceptibility and particular HLA D/DR antigens (1, 3, 4). Recent evidence (5-7) has demonstrated a considerable heterogeneity...

We consider a problem in extremal graph theory as introduced by Erdős, Jacobson and Lehel in [3]. That is, given an n-term graphic degree sequence, for n sufficiently large, we prove that the minimum degree sum necessary to guarantee a realization containing a t-clique, t ≥ 2, is (t − 2)(2n − t + 1) + 2. The proof involves the notion of an edge exchange, which is well-known but has not been use...

Let k be a positive integer and G = (V,E) be a simple graph. A subset S ⊆ V is dominating in G, if for each vertex v ∈ V \ S, N(v) ∩ S 6= ∅. In 1985, Fink and Jacobson gave a generalization of the concept of dominating sets in graphs. A subset S of V is kdominating in G, if every vertex of V \ S is adjacent to at least k vertices in S. In this paper, we characterize vertices that are in all or ...

Let R be a ring with identity. The unitary Cayley graph of a ring R, denoted by GR, is the graph, whose vertex set is R, and in which {x, y} is an edge if and only if x − y is a unit of R. In this paper we find chromatic, clique and independence number of GR, where R is a finite ring. Also, we prove that if GR ' GS , then GR/JR ' GS/JS , where JR and JS are Jacobson radicals of R and S, respect...

Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V − S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number γ2(G) and the maximum cardinality of a 2-independent set of G is the 2-independence number β2(G). Fink and Jaco...

Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n− 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most (n− 3)/(δ − 1) components, unless G is...

The concept of the Jacobson radical of a ring is generalized to semirings. A semiring is a system consisting of a set S together with two binary operations, called addition and multiplication, which forms a semigroup relative to addition, a semigroup relative to multiplication, and the right and left distributive laws hold. The additive semigroup of S is assumed to be commutative. The right ide...