Shore platforms and mass movement phenomena are important elements in the coastal scenery of the British Isles. Both features are particularly well developed along the English Channel coast. Where mass movement is of major importance it tends to inhibit the exposure of shore platforms. Under certain conditions it may temporarily protect the platform from further erosion. The factors which encou...

Veblen has given a set of axioms for geometry.!. The first eight of these are as follows : % Axiom I. There exist at least two distinct points. Axiom II. If points A, B, C are in the order ABC, they are in the order CBA. Axiom III. If points A, B, C are in the order ABC, they are not in the order BCA. Axiom IV. If points A, B, C are in the order ABC, then A is distinct from C. Axiom V. If A and...

Let a1, a2, . . . , ak be positive integers. An (a1, a2, . . . , ak)-packing coloring of a graph G is a mapping from V (G) to {1, 2, . . . , k} such that vertices with color i have pairwise distance greater than ai. In this paper, we study (a1, a2, . . . , ak)packing colorings of several lattices including the infinite square, triangular, and hexagonal lattices. For k small, we determine all ai...

In [l] Bagchi and Bagchi conjectured that one of the hypotheses of their theorem 2(d) is superfluous. This turns out to be true: PROPOSITION. Let 4 = 9 mod 16 be a prime power such that 2 is a fourth power in Fq. Then 1 f fi are nonsquares in Fp. Pruc$ Let p be a primitive eighth root of unity in Fq (note that /3 is a nonsquare). Because of (02 + 1)2 = p4 + 202 + 1 = 202 we obtain that (0 * + 1...

In the Einstein stat ic Universe the gravit ational self-attract ion of homogeneously dist ribut ed matter and the cosmological repulsion implied by the cosmological constant balance each other. Eddington [1] showed in 1930 that this balance is unstable: any departure from it will cause the Universe to either expand or collapse away from the init ial state. The perturbed solut ions are the Frie...

In his classic book, Risk, Uncertainty, and Profit [9] , F.H . Knight proposed that one should distinguish sharply between "risk" and "uncertainty" as descriptions of imperfect knowledge about the economic environment ; risk being a quantitative measure and uncertainty a non-quantitative one . These two concepts have since become standard in microeconomics, especially in the theory of profit (5...

This paper analyses the declarative readings of logic programming. Logic programming and negation as failure has no unique declarative reading. One common view is that logic programming is a logic for default reasoning, a sub-formalism of default logic or autoepistemic logic. In this view, negation as failure is a modal operator. In an alternative view, a logic program is interpreted as a defin...

where Vg(M, P) denotes the gradient of the Green's function with pole at M, is bounded, independently of the position of M in T. A corresponding result holds for convex regions in three dimensions. It is the purpose of this note to bring out some of the differences between the twoand three-dimensional situations by a comparison of the analyses for the general plane simply connected region and t...

We give a new proof of the classical Dalang-Morton-Willinger theorem.