Existence of a Period-Two Solution in Linearizable Difference Equations

Consider the difference equation xn+1 = f(xn, …, xn-k), n = 0, 1, …, where l, k ∈ {1, 2, . . .} and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation xn+l = Σki = 1–l gixn-1, n = 0, 1, . . . , where l, k ∈ {1, 2, . . .} and the functions gi : ℝk+l → ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution when l = 1

Global Asymptotic Stability for Quadratic Fractional Difference Equation

Consider the difference equation [Mathematical equations cannot be displayed here, refer to PDF] where all parameters α, β,ai,bi,aij,bij, i, j = 0,1,…, k, and the initial conditions xi, i ∈{−k,…,0}, are nonnegative. We investigate the asymptotic behavior of the solutions of the considered equation. We give simple explicit conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation

Poverty and the rural non-farm economy in Armenia, Georgia and Romania: a synthesis of findings (NRI report no. 2773)

The focus of this paper is on rural non-farm livelihoods in economies in transition. It looks at key factors affecting the ability and motivation of rural dwellers to become involved in the non-farm economy. The intended outputs of this study are: (i) to improve understanding of the dynamics of the RNFE in providing employment and income diversification opportunities in Armenia, Georgia and Romania; and (ii) to promote mechanisms for integrating research results into relevant policy processes

Electromagnetic finite-size effects to the hadronic vacuum polarization

In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach sub-percent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of $\mathcal{O}(\alpha)$ electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the $\mathrm{QED}_{\mathrm{L}}$ finite-volume corrections to the two-pion contribution to the hadronic vacuum polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order $1/L^{3}$ where $L$ is the spatial extent. A $1/L^{2}$ term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar $U(1)$ gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2-loop master integrals.Comment: 42 pages, 11 figure

Periodic One-Dimensional Hopping Model with one Mobile Directional Impurity

Analytic solution is given in the steady state limit for the system of Master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile, directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.Comment: 31 LaTex pages, 5 Postscript figures included, to appear in Journal of Statistical Physic

Spatial and Temporal Changes of Tidal Inlet Using Object-Based Image Analysis of Multibeam Echosounder Measurements: A Case from the Lagoon of Venice, Italy

Scientific exploration of seabed substrata has significantly progressed in the last few years. Hydroacoustic methods of seafloor investigation, including multibeam echosounder measurements, allow us to map large areas of the seabed with unprecedented precision. Through time-series of hydroacoustic measurements, it was possible to determine areas with distinct characteristics in the inlets of the Lagoon of Venice, Italy. Their temporal variability was investigated. Monitoring the changes was particularly relevant, considering the presence at the channel inlets of mobile barriers of the Experimental Electromechanical Module (MoSE) project installed to protect the historical city of Venice from flooding. The detection of temporal and spatial changes was performed by comparing seafloor maps created using object-based image analysis and supervised classifiers. The analysis included extraction of 25 multibeam echosounder bathymetry and backscatter features. Their importance was estimated using an objective approach with two feature selection methods. Moreover, the study investigated how the accuracy of classification could be affected by the scale of object-based segmentation. The application of the classification method at the proper scale allowed us to observe habitat changes in the tidal inlet of the Venice Lagoon, showing that the sediment substrates located in the Chioggia inlet were subjected to very dynamic changes. In general, during the study period, the area was enriched in mixed and muddy sediments and was depleted in sandy deposits. This study presents a unique methodological approach to predictive seabed sediment composition mapping and change detection in a very shallow marine environment. A consistent, repeatable, logical site-specific workflow was designed, whose main assumptions could be applied to other seabed mapping case studies in both shallow and deep marine environments, all over the world

Measurement of 131I activity in thyroid of nuclear medical staff and internal dose assessment in a Polish nuclear medical hospital

This paper presents results of 131I thyroid activity measurements in 30 members of the nuclear medicine personnel of the Department of Endocrinology and Nuclear Medicine Holy Cross Cancer Centre in Kielce, Poland. A whole-body spectrometer equipped with two semiconductor gamma radiation detectors served as the basic research instrument. In ten out of 30 examined staff members, the determined 131I activity was found to be above the detection limit (DL = 5 Bq of 131I in the thyroid). The measured activities ranged from (5 ± 2) Bq to (217 ± 56) Bq. The highest activities in thyroids were detected for technical and cleaning personnel, whereas the lowest values were recorded for medical doctors. Having measured the activities, an attempt has been made to estimate the corresponding annual effective doses, which were found to range from 0.02 to 0.8 mSv. The highest annual equivalent doses have been found for thyroid, ranging from 0.4 to 15.4 mSv, detected for a cleaner and a technician, respectively. The maximum estimated effective dose corresponds to 32% of the annual background dose in Poland, and to circa 4% of the annual limit for the effective dose due to occupational exposure of 20 mSv per year, which is in compliance with the value recommended by the International Commission on Radiological Protection