Let be a smooth domain on the unit sphere S whose closure is contained in an open hemisphere and denote by H the mean curvature of ∂ as a submanifold of with respect to the inward unit normal. It is proved that for each real number H that satisfies inf H > −H ≥ 0, there exists a unique radial graph on bounded by ∂ with constant mean curvature H . The orientation on the graph is based on the nor...

We develop the geometry of the Cayley graph of the lamplighter group with respect to the generating set rising from its interpretation as an automata group [4]. We find metric behavior with respect to this generating set analogous to the metric behavior in the standard group theoretic generating set. This includes expressions for normal forms and geodesic paths, and families of ‘dead-end’ words...

Power law distributions are an increasingly common model for computer science applications; for example, they have been used to describe file size distributions and inand out-degree distributions for the Web and Internet graphs. Recently, the similar lognormal distribution has also been suggested as an appropriate alternative model for file size distributions. In this paper, we briefly survey s...

Letting τ denote the inverse transpose automorphism of GL(n, q), a formula is obtained for the number of g in GL(n, q) so that gg is equal to a given element h. This generalizes a result of Gow and Macdonald for the special case that h is the identity. We conclude that for g random, gg behaves like a hybrid of symplectic and orthogonal groups. It is shown that our formula works well with both c...

Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley ...

The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula...

We solve the isomorphism problem for certain classes of unary automatic structures: unary automatic equivalence relations, unary automatic linear orders, and unary automatic trees. That is, we provide algorithms which decide whether two given elements of these classes are isomorphic. In doing so, we define new finite representations for these structures which give normal forms. 1

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

This paper continues the line of research on knowledge compilation in the context of Negation Normal Forms (NNF) and Binary Decision Diagrams (BDD). The idea is to analyze different target languages according to their succinctness and the classes of queries and transformations supported in polytime. We identify a new property called simple-negation, which is an implicit restriction of all NNFs ...

The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula...