Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

Vibration-Induced Conductivity Fluctuation (VICOF) Testing of Soils

In this Letter, we propose and experimentally demonstrate a simple method to provide additional in-formation by conductivity measurements of soils. The AC electrical conductance of the soil is measured while it is exposed to a periodic vibration. The vibration-induced density fluctuation implies a corresponding conductivity fluctuation that can be seen as combination frequency components, the sum and the difference of the mean AC frequency and the double of vibration frequency, in the current response. The method is demonstrated by measurements on clayey and sandy soils

Renormalised nonequilibrium quantum field theory: scalar fields

We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium. We emphasize the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.Comment: 18 pages in revtex4, 5 figure

Stable and habitable systems with two giant planets

We have studied planetary systems which are similar to the Solar System and built up from three inner rocky planets (Venus, Earth, Mars) and two outer gas giants. The stability of the orbits of the inner planets is discussed in the cases of different masses of the gas planets. To demonstrate the results stability maps were made and it was found that Jupiter could be four times and Saturn could be three times more massive while the orbits of the inner planets stay stable. Similar calculations were made by changing the mass of the Sun. In this case the position of the rocky planets and the extension of the liquid water habitable and the UV habitable zones were studied for different masses of the Sun. It was found that the orbits of the planets were stable for values greater than 0.33 M_Sun where M_Sun is the mass of the Sun and at lower masses of the Sun (at about 0.8 M_Sun) only Venus, but for higher mass values (at about 1.2 M_Sun) Earth and also Mars are located in both habitable zones.Comment: 8 page

An approach to balance problems and falls in elderly persons

Gait instability and falls are common in elderly persons and have devastating consequences, with substantial morbidity and mortality. Furthermore, they are a precipitant for functional decline, increasing frailty and institutionalisation. The rate of falls and severity of complications increase with age and frailty. A consequence of falls with or without injury is that at least a third of persons develop a fear of falling, which leads to functional decline and a progressive decline in gait. The causes of falls in elderly persons are multifactorial and include physiological changes of ageing, frailty, pathologies, and environmental and situational factors. Maintaining postural control requires a complex integration of sensory input, central processing, motor co-ordination and musculoskeletal function, which decrease with ageing. This change, combined with sarcopenia, leads to slowed and weakened postural control and muscle responses, resulting in gait instability and falls.The assessment and management of a patient who is at risk of falls or who has fallen require a multidisciplinary approach to identify and address factors contributing to the fall. The assessment, which includes history, physical examination, and evaluation of gait, postural control and mental function, is aimed at identifying situational and associated factors surrounding a fall, intrinsic impairments in gait or pathologies that increase the risk of falls. The components of the assessment comprise a full medical evaluation for pathologies, including vision, medication review (including over-the-counter medication) with regard to polypharmacy and high-risk medications, psychogeriatric review, functional status (instrumental activities of daily living (IADLs) and activities of daily living (ADLs)), functional assessment of gait and balance, and assessment of environmental hazards in the home. Laboratory investigations are guided by clinical suspicions or diagnoses arising from the medical assessment and screening for common conditions that may increase the risk of falls.Management and prevention of falls focus on maintaining mobility and balance, and identifying those at risk of a fall for multidisciplinary assessment and intervention. Intervention to reduce the risk of subsequent falls is targeted at modification of the contributory factors. Intervention includes management of underlying pathologies, strength and balance training by a physiotherapist, assessment and modification of environmental hazards in the home by an occupational therapist, medication review and rationalisation of high-risk medications and polypharmacy, and supplementation of vitamin D where indicated

Out of Equilibrium Non-perturbative Quantum Field Dynamics in Homogeneous External Fields

The quantum dynamics of the symmetry broken lambda (Phi^2)^2 scalar field theory in the presence of an homogeneous external field is investigated in the large N limit. We choose as initial state the ground state for a constant external field J .The sign of the external field is suddenly flipped from J to - J at a given time and the subsequent quantum dynamics calculated. Spinodal instabilities and parametric resonances produce large quantum fluctuations in the field components transverse to the external field. This allows the order parameter to turn around the maximum of the potential for intermediate times. Subsequently, the order parameter starts to oscillate near the global minimum for external field - J, entering a novel quasi-periodic regime.Comment: LaTex, 30 pages, 12 .ps figures, improved version to appear in Phys Rev