We find necessary and sufficient conditions for almost sure finiteness of integral functionals spectrally positive Lévy processes under conditional probabilities. Via Lamperti-type transforms, these results can be applied to obtain new tests on extinction explosion behaviors a class continuous-state nonlinear branching processes.

In this paper we consider the expected value function of a stochastic simple recourse program with random technology matrix and integer variables in the second stage. Due to its separability the analysis is straightforward. Conditions for finiteness, continuity, Lipschitz continuity and differentiability are derived by conditioning upon the technology matrix. The corresponding results for a fix...

We analyze the periodicity of optimal long products of matrices. A set of matrices is said to have the finiteness property if the maximal rate of growth of long products of matrices taken from the set can be obtained by a periodic product. It was conjectured a decade ago that all finite sets of real matrices have the finiteness property. This conjecture, known as the “finiteness conjecture”, is...

A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renor-malized Green functions is deduced from the Polchinski equation of renormal-ization group. The resulting Feynman graphs are organized in such a way that the loop m...

There are numerous occasions on which we need to reason about a finite number of events. And we often need to consider only those events which are given or which we perceive. These give rise to the Criteria of Finiteness and Closedness. Allen’s logic provides a way of reasoning about events. In this paper I examine Allen and Hayes’ axiomatisation of this logic, and develop two other axiomatisat...

The most general version of a renormalizable d = 4 theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains 12 independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

Does a given system of linear equations with nonnegative constraints have an integer solution? This is a fundamental question in many areas. In statistics this problem arises in data security problems for contingency table data and also is closely related to non-squarefree elements of Markov bases for sampling contingency tables with given marginals. To study a family of systems with no integer...

In this paper we study different conditions whose presence is required for A. the admissibility and stability of large shocks present in solutions of a strictly hyperbolic n × n system of conservation laws in one space dimension ut + f(u)x = 0, B. the solvability and L well posedness of the Cauchy problem for the above equation, near solutions containing large and stable, but noninteracting sho...

As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N = 1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the β-functions at all orders) in N = 1 SYM. Finally, we apply this finiteness criterion to an SU(5) SGUT. The latter turns out to be all-order finite if one imposes additional sy...