A simple (inductive) proof for the non-existence of 2-cycles of the 3x+1 problem

A 2-cycle of the 3x + 1 problem has two local odd minima x(0) and x(1) with x(1) = a(i)2(ki) - 1. Such a cycle exists if and only if an integer solution exists of a diophantine system of equations in the coefficients a(i). We derive a numerical lower bound for a(0) center dot a(1), based on Steiner's proof for the non-existence of 1-cycles. We derive an analytical expression for an upper bound for a(0) center dot a(1) as a function of K and L (the number of odd and even numbers in the cycle). We apply a result of de Weger on linear logarithmic forms to show that these lower and upper bounds are contrary. The proof does not use exterior lower bounds for numbers in a cycle and for the cycle length. (c) 2006 Elsevier Inc. All rights reserved.</p

Assessing the Effects of Ownership Change on Women and Minority Employees: Evidence from Matched Employer-Employee Data

While there have been numerous papers on the employment and wage effects of mergers and acquisitions, there has been no direct analysis of the impact of such ownership changes on minority and female workers. This is an unexplored "equity" dimension of these transactions. We fill this gap by analyzing linked employer-employee data for the entire population of Swedish workers and approximately 16,000 manufacturing plants for the period 1985-1998. For each worker employed in these establishments (as well as the entire population of workers), we have data on gender, age, national origin, level of education, type of education, location, industrial sector, annual earnings, as well as each employee's complete work history during the period. We also have data on numerous plant and firm-level characteristics, which allows us to control for additional factors that might result in changes in labor composition and relative compensation. Our findings suggest that ownership change does not significantly alter the relative earnings and employment status of minority and female workers.

An analysis of the concept of equilibrium in organization theory

This article analyzes how the equilibrium concept is used in four organization theories: the theories of Fayol, Mintzberg, Morgan, and Volberda. Equilibrium can be defined as balance, fit or requisite variety. Equilibrium is related to observables dependent on the definition of organization as work organization, formal organization or artifact organization. The discussed theories can be mapped on a state space model in a way that clarifies the equilibrium concept.\ud The equilibrium concept in organization theory in general can be formalized mathematically using concepts from systems theory. The equilibrium condition can be formulated in terms of a difference function that has to be zero at equilibrium. A central idea is the necessity to maintain equilibrium by actions. This is done by means of a circular causal mechanism that reinforces equilibrium once it has been established as long as the organization conforms to the Law of Requisite Variety. The difference function on which the condition of organizational equilibrium is based takes different forms for each of the four organization theories studied. The establishment of these difference functions enables a comparison with the types of fit described by Venkatraman. It turns out that all types of fit described by Venkatraman are gamma-space based. The analysis of the four theories leads to five equilibrium types, of which two (the Gestalt type and the Matching type) have been described by Venkatraman. Three types of equilibrium that were found have not been covered by Venkatraman: Fayol’s balance / mu-space type, Volberda’s gamma-space/ variety type and Morgan’s mu-space / variety type

Desktop review of groundwater prospectivity for irrigation in the lower De Grey River area

The Department of Primary Industries and Regional Development (DPIRD) has identified priority areas in the Pilbara that warrant further investigation into their capacity for irrigated agriculture and related businesses. The De Grey River area is one of these. The lower De Grey River area, upstream of the De Grey River Water Reserve, was identified by the Transforming Agriculture in the Pilbara (TAP) project for staged investigations of viability. Progression through these stages, each with increasingly detailed groundwater and soil suitability investigations, is dependent on prospectivity. This document provides a summary of DPIRD’s initial desktop groundwater evaluation in the lower De Grey River area. It uses existing information on groundwater depth, quality and yield to indicate the prospectivity for sustainable groundwater abstraction for irrigation. While there are isolated areas of groundwater with suitable quality in the evaluation area, these seem unlikely to provide sufficient supply for even a moderately sized irrigated agriculture enterprise. Further groundwater investigations could be undertaken, but combined with the low likelihood of finding a significant fresh groundwater resource, we believe this would represent an uncertain investment at a significant cost. Given the relatively high reliability of river flows, further investigations could instead focus on the feasibility of off-stream capture and storage of floodwaters into retention basins for irrigation

Measurement of Radio-Frequency Radiation Pressure

We perform measurements of the radiation pressure of a radio-frequency (RF) electromagnetic field which may lead to a new SI-traceable power calibration. There are several groups around the world investigating methods to perform more direct SI traceable measurement of RF power (where RF is defined to range from 100s of MHz to THz). A measurement of radiation pressure offers the possibility for a power measure traceable to the kilogram and to Planck's constant through the redefined SI. Towards this goal, we demonstrate the ability to measure the radiation pressure/force carried in a field at 15~GHz.Comment: 2 pages 4 figure

Hydrological impacts of integrated oil mallee farming systems

This study reports on the results from investigations at four sites into the effect of commercial-scale oil mallee systems on localised groundwater systems over seven years. It also reports the results of the use of a numerical model to forecast potential longer term impacts

Interferon signaling patterns in peripheral blood lymphocytes may predict clinical outcome after high-dose interferon therapy in melanoma patients

<p>Abstract</p> <p>Background</p> <p>High-dose Interferon (HDI) therapy produces a clinical response and achieves relapse-free survival in 20-33% of patients with operable high risk or metastatic melanoma. However, patients may develop significant side effects frequently necessitating dose reduction or discontinuation of therapy. We recently showed that peripheral blood lymphocytes (PBL) from some melanoma patients have impaired interferon (IFN) signaling which could be restored with high concentrations of IFN. This exploratory study evaluated IFN signaling in PBL of melanoma patients to assess whether the restoration of PBL IFN signaling may predict a beneficial effect for HDI in melanoma patients.</p> <p>Methods</p> <p>PBL from 14 melanoma patients harvested on Day 0 and Day 29 of neoadjuvant HDI induction therapy were analyzed using phosflow to assess their interferon signaling patterns through IFN-α induced phosphorylation of STAT1-Y701.</p> <p>Results</p> <p>Patients who had a clinical response to HDI showed a lower PBL interferon signaling capacity than non-responders at baseline (Day 0). Additionally, clinical responders and patients with good long-term outcome showed a significant increase in their PBL interferon signaling from Day 0 to Day 29 compared to clinical non-responders and patients that developed metastatic disease. The differences in STAT1 activation from pre- to post- HDI treatment could distinguish between patients who were inclined to have a favorable or unfavorable outcome.</p> <p>Conclusion</p> <p>While the sample size is small, these results suggest that interferon signaling patterns in PBL correlate with clinical responses and may predict clinical outcome after HDI in patients with melanoma. A larger confirmatory study is warranted, which may yield a novel approach to select patients for HDI therapy.</p

Cockatoo Sands in the Victoria Highway and Carlton Hill areas, East Kimberley: hydrogeology, aquifer properties and groundwater chemistry

Cockatoo Sands are recognised as potentially suitable for irrigated agriculture because they are generally well drained and not subject to waterlogging or inundation. These characteristics allow them to be cultivated and prepared for planting various crops during the wet and dry seasons of northern Australia. Expanding agricultural production onto the Cockatoo Sands around Kununurra will increase opportunities for agriculture by increasing the overall scale of agriculture, allowing year-round agricultural enterprise, new crops and new market opportunities. DAFWA has assessed the soil characteristics and agriculturally suitable areas of Cockatoo Sands in the Victoria Highway and Carlton Hill areas near Kununurra. Potential development areas (PDAs) comprising 6538 hectares (ha) at Victoria Highway and 2571ha at Carlton Hill were identified. DAFWA has also assessed the baseline surface water characteristics of run-off from catchments that contain the PDAs. This report describes the methodology, data and analyses used to derive the baseline hydrogeological conditions and physicochemical groundwater conditions that underlie the Victoria Highway and Carlton Hill PDAs

Gibson oil mallee study : drill completion and preliminary hydrogeological interpretation report

Oil mallees are being planted in Western Australian wheatbelt farms with the expectation that they will reduce land salination by lowering watertables as well as providing income from combinations of eucalyptus oil distillation, power generation, activated carbon production and carbon sequestration in the future