Multiply union families in Nn

Let An Nn be an r-wise s-union family, that is, a family of sequences with n components of non-negative integers such that for any r sequences in A the total sum of the maximum of each component in those sequences is at most s. We determine the maximum size of A and its unique extremal configuration provided (i) n is sufficiently large for fixed r and s, or (ii) n = r + 1. © 2016 Elsevier Ltd

Longitudinal Analyses of the Effects of Trade Unions

This paper examines how measurement error biases longitudinal estimates of union effects. It develops numerical examples, statistical models, and econometric estimates which indicate that measurement error is a major problem in longitudinal data sets, so that longitudinal analyses do not provide the research panacea for determining the effects of unionism (or other economic forces) some have suggested. There are three major findings:1) The difference between the cross-section and longitudinal estimates is attributable in large part to random error in the measurement of who changes union status. Given modest errors of measurement, of the magnitudes observed,and a moderate proportion of workers changing union status, also of the magnitudes observed, measurement error biases downward estimated effects of unions by substantial amounts. 2) Longitudinal analysis of the effects of unionism on nonwage and wage outcomes tends to confirm the significant impact of unionism found in cross-section studies, with the longitudinal estimates of both nonwage and wage outcomes lover in the longitudinal analysis than in the cross-section analysis of the same data set. 3) The likely upward bias of cross-section estimates of the effect of unions and the likely downward bias of longitudinal estimates suggests that,under reasonable conditions, the two sets of estimates bound the "true" union impact posited in standard models of what unions do.

Singularity analysis, Hadamard products, and tree recurrences

We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relationsComment: 47 pages. Submitted for publicatio

Generalized moonshine II: Borcherds products

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster simple group. We introduce vector-valued modular functions attached to families of modular functions of different levels, and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half-planes. We recast this result using the Borcherds-Harvey-Moore singular theta lift, and show that the vector-valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps. For each element of the monster simple group, we construct an infinite dimensional Lie algebra, such that its denominator formula is an infinite product expansion of the automorphic function arising from that element's McKay-Thompson series. These Lie algebras have the unusual property that their simple roots and all root multiplicities are known. We show that under certain hypotheses, characters of groups acting on these Lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group.Comment: v3: final version, minor corrections and explanations added, 41 page

Complex patterns on the plane: different types of basin fractalization in a two-dimensional mapping

Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins' bifurcations. According to the already established nomenclature in the literature, we present the relevant phenomenology organised in different scenarios: fractal islands disaggregation, finite disaggregation, infinitely disconnected basin, infinitely many converging sequences of lakes, countable self-similar disaggregation and sharp fractal boundary. By use of critical curves, we determine the influence of zones with different number of first rank preimages in the mechanisms of basin fractalization.Comment: 19 pages, 11 figure

The Relational Blockworld Interpretation of Non-relativistic Quantum Mechanics

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality