Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

Holography and Cosmological Singularities

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area.Comment: Anomaly equation corrected. References adde

Reflections of Culture in Global Corporate Web Sites

Hofstede (1980) found that national cultures differ along several dimensions. He believed that national cultural values and differences have existed for a long period of time and are stable. Subsequent research has both confirmed and challenged the validity of Hofstede’s conclusions for the long term. With the advent of the Internet and related networking and communication technologies, many have speculated that the ubiquitous nature of these technologies has a homogenizing effect and contributes to cultural convergence. The main objective of this study is to determine if differences in national culture are evident in the web sites of global corporations or if national cultures, as reflected through these web sites, have converged as a result of Internet usage

Radiation Nephropathy: A Review

The marked radiosensitivity of renal tissue represents a limitation on the total radiotherapeutic dose that safely can be applied to treatment volumes that include the kidneys. Radiation nephropathy is characterized by a progressive reduction in renal hemodynamics associated with a severe anemia. The latter is often normochromic normocytic in character, but can progress to a microangiopathic hemolytic anemia. The pathogenic mechanisms responsible for the development of radiation nephropathy remain ill-defined. Experimental studies which allow serial determinations of functional, morphologic, and cell kinetic radiation-induced changes indicate that primarily glomerular but also tubular alterations occur in the primary stages of radiation nephropathy. Glomerular capillary endothelial cell loss is seen within several weeks of irradiation. Remaining endothelial cells exhibit increased permeability leading to a subendothelial transudate. Mesangiolysis also is observed. In contrast, podocytes appear to be relatively unaffected at this stage. The endothelial changes appear to resolve, but the mesangial lesions progress, with hypercellularity and/or hypertrophy, increased mesangial matrix, mesangial sclerosis, and ultimately, glomerulosclerosis. These mesangial changes are similar to those observed in other chronic glomerulopathies. Dietary protein restriction, corticosteroids, and ACE-inhibitors all can reduce the severity of experimental radiation nephropathy

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Variations in Flight Patterns of European Corn Borer (Lepidoptera: Pyralidae) in New York

Seasonal flights of Ostrinia nubilalis (Hübner) were monitored in 1981, using blacklight traps in 28 locations in central and western New York state. Calendar date of peak catch and heat unit accumulations indicated the presence of both univoltine and bivoltine biotypes, although before this study, only the latter was assumed to be present in these regions. Both biotypes were evident at 16 of the 28 trapping sites. Trap catches during the last 5 years of a 15-year study (1967-1981), at a fixed location near Geneva, N. Y., indicated the recurrence of a univoltine population that had last been noted in this region before 1964. Losses due to larval contamination of processed snap beans are reported for 1979 and 1980. Growers of susceptible crops must be aware of local flights and the potential for shifts in peak moth emergence before insecticides are applie

Hoplia equina (Coleoptera: Scarabaeidae) and Nontarget Capture Using 2-Tetradecanone-Baited Traps

Using bucket traps baited with 2-tetradecanone, the sex pheromone of Hoplia equina LeConte, an important pest of cranberries in Massachusetts, we investigated the effect of trap height, color, pheromone load, and lure aging on male capture, as well as captures of nontarget arthropods including pollinators. Male capture was inversely related to height of traps over the four heights tested (0, 20, 60, and 100 cm). Captures increased with increasing pheromone load over the doses of 0, 100, 300, and 600 μg, but captures at the highest load, 1,000 μg, were not significantly different from 300 or 600 μg. H. equina captures were strongly diurnal, with a flight period spanning ≈6 wk starting in mid-June. Vane color of traps (white, yellow, green, blue, red, black) did not affect H. equina capture but significantly influenced capture of nontargets, including pollinators. A bucket trap with the funnel opening at 20 cm, and green (or red) vanes, baited with 600 μg of 2-tetradecanone, was the optimal design for high male capture and low nontarget capture. The low-cost capture of over 50,000 H. equina on a 2.4-ha commercial bog in Massachusetts with this lure-trap combination indicates the feasibility of mass trapping for managing established infestations of H. equin