My views on the semantic and pragmatic interpretation of natural language were influenced a lot by the works of Martin, Jeroen and Frank. What attracted me most is that although their work is always linguistically relevant, it still has a philosophical point to make. As a student (not in Amsterdam), I was already inspired a lot by their work on dynamics semantics, and by Veltman’s work on data ...

We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on n vertices. The two players take turns choosing edges within Kn, building up a simple graph. The edges must be chosen according to a set of restrictions R. The winner is the last player to choose an edge that does no...

In a paper of Harary and Plantholt, they concluded by noting that they knew of no generalization of the leaf edge exchange (LEE) transition sequence result on spanning trees to other natural families of spanning subgraphs. Now, we give two approaches for such a generalization. We define two kinds of LEE-graphs over the set of all connected spanning k-edge subgraphs of a connected graph G, and s...

Consider the Parzen-Rosenblatt kernel estimate f. = (l/n) ~ Kh (x-Xi), where h > 0 is a constant, K is an absolutely integrable i=1 function with integral one, Kh(X)=(1/ha)K(x/h), and X1 ..... X. are iid random variables with common density f on R d. We show that for all e > 0, n8 2 2 sup P(lSlf.-fl-E~lf.-fll>e)<Ze 32~1KI. whenever liminfl~E~lf,-f]=oo. We also study what happens when h is allow...

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.

A graph G=(V; E) is said to be an integral sum graph (sum graph) if its vertices can be given a labeling with distinct integers (positive integers), so that uv ∈ E if and only if u+ v ∈ V . The integral sum number (sum number) of a given graph G, denoted by (G) ( (G)), was de:ned as the smallest number of isolated vertices which when added to G result in an integral sum graph (sum graph). In th...

A quantification of the Frank and McFee-Parungao orthogonal electrocardiogram of 175 normal children, ages 2-10 years is presented. There are significant differences in age groups 2-5 and 6-10. The QRS voltages of the younger group demonstrate 1) greater Z anterior, 2) greater initial X right, 3) greater terminal X right, 4) smaller Y inferior, and 5) the T vector is oriented more posteriorly. ...

With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4, and thus show that the exact value of it is equal to 9. The Ramsey multiplicity M(G) of a graph G is defined as the smallest number of monochromatic copies ofG in any two-coloring of edges of KR(G), whereR(G) is the Ramsey number of G, i.e. the smallest integer n such that any two-coloring of edge...

We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost c...