In a 1985 paper, Berthold J. Maier gave necessary and sufficient conditions for the weak embeddability of amalgams of two nilpotent groups of class two over a common subgroup. Then he derived simpler conditions for some special cases. One of his subsequent results is incorrect, and we provide a counterexample. Finally, we provide a fix for the result. In this note, N2 denotes the variety of nil...

Let 51 be a generalized Hilbert algebra and let 5 be a closed right ideal of S. Let J-1 denote the pre-Hilbert space orthogonal complement of 3 inï. The problem investigated in this paper is: for which algebras % is it true that SI = J ffi ¡f^for every closed right ideal 3"of 8? In the case that % is achieved, a slightly stronger property is characterized and these characterizations are then us...

We announce some new results about systems of residue sets. A residue set R C Z is an arithmetic progression R = {a,a±n,a± 2n,...}. The positive integer n is referred to as the modulus of R. Following Znam [21] we denote this set by a(n). We need several number-theoretic functions. p(ra)-the least prime divisor of a natural number ra, P(m)-the greatest prime divisor of ra, A(m)-the greatest div...

Discrete dynamical systems defined on the state space Π = {0, 1, . . . , p − 1}n have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale and Hirsch, which form part of the theory of (continuous) monotone dynamical systems, generalize or fail to do so in the discrete case. We show tha...

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to a sub-polynomial factors. As an additional resul...

Ordinary computations can be characterised by register machines working with natural numbers. We study ordinal register machines where the registers can hold arbitrary ordinal numbers. The class of sets of ordinals which are computable by such machines has strong closure properties and satisfies the set theoretic axiom system SO. This implies that ordinal computability is equivalent to Gödel’s ...

In this letter we provide a reformulation of the strong cosmic censor conjecture taking into account recent results on Malament–Hogarth space-times. We claim that the strong version of the cosmic censor conjecture can be formulated by postulating that a physically reasonable space-time is either globally hyperbolic or possesses the Malament–Hogarth property. But it is well-known that a Malament...

wall street is sometimes compared to a darwinian jungle. Nice guys finish last, it is said, and only the strong survive. This is an adequate enough description, but not entirely true, neither for the stock market nor for life in the jungle. When Richard Grasso, head of the New York Stock Exchange, revealed a pay package for himself of close to $200 million, there was public outcry. As it happen...

The orbital instability of ground state standing waves eφω(x) for the nonlinear Klein-Gordon equation has been known in the domain of all frequencies ω for the supercritical case and for frequencies strictly less than a critical frequency ωc in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equ...

Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language Γ, a fixed, finite set of relations over a finite domain D. An instance of the problem uses these relations to constrain an arbitrarily large finite set of variables. Bulatov showed that the problem of counting the satisfying assignments of instanc...