We present ve axioms of name-carrying lambda-terms iden-tiied up to alpha-conversion|that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambda-abstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable free in another term. Our axioms are (1)...

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)|phi(lambda))/ that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonance...

Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerat...

Correct assembly of the heads of bacteriophages lambda and T4 requires the function of the groE gene of the Escherichia coli host. We have isolated a transducing derivative of lambda, called lambda gt-Ec.groE, that carries a functional copy of the groE gene. Unlike wild-type lambda, this phage is able to form plaques on hosts with a mutant groE gene. We have isolated an amber mutation in the gr...

Lambda lysogens of Escherichia coli reproduce more rapidly than nonlysogens during aerobic growth in glucose-limited chemostats. If the environment is changed to anaerobic growth, the situation is reversed, and the lysogen reproduces more slowly than the nonlysogen. Based on a tetrazolium dye assay, the increased fitness of the lambda lysogen during aerobic growth seems to result from a continu...

Fix coprime natural numbers a,q. Assuming the Prime k-tuple Conjecture, we show that there exist arbitrarily long arithmetic progressions of Carmichael numbers, each which lies in reduced residue class a mod q and is product three distinct prime numbers.