Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.Comment: 5 pages; accepted for publication in A&

Keynesian Dynamics and the wage price spiral. A baseline disequilibrium approach

We reformulate the AS-AD growth model of the Neoclassical Synthesis (Stage I) with its traditional microfoundations. The model still has an LM curve in the place of a Taylor interest rate rule, exhibits sticky wages as well as sticky prices, myopic perfect foresight of current inflation rates and adaptively formed medium run expectations concerning the investment and inflation climate in which the economy is operating. The resulting nonlinear 5D model of labor and goods market disequilibrium dynamics avoids striking anomalies of the standard model of the Neoclassical synthesis. It exhibits instead Keynesian feedback dynamics proper with in particular asymptotic stability of its unique interior steady state for low adjustment speeds and with cyclical loss of stability -- by way of Hopf bifurcations -- when adjustment speeds are made sufficiently large, even leading to purely explosive dynamics sooner or later. In such cases downward money wage rigidity can be used to make the dynamics bounded and thus viable. In this way we obtain and analyze a baseline DAS-AD model with Keynesian feedback channels whose rich set of stability features is the source of business cycle fluctuations. These outcomes of the model stand in contrast to those of the currently fashionable New Keynesian alternative (the Neoclassical Synthesis, Stage II) that we suggest is more limited in scopeDAS-AD growth, wage and price Phiilips curves, real interest rate effects, real wage effects, instability, persistent cycles

Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

Simplified solution to determination of a binary orbit

We present a simplified solution to orbit determination of a binary system from astrometric observations. An exact solution was found by Asada, Akasaka and Kasai by assuming no observational errors. We extend the solution considering observational data. The generalized solution is expressed in terms of elementary functions, and therefore requires neither iterative nor numerical methods.Comment: 15 pages; text improved, Accepted for publication in the Astronomical Journa

R&D Status of Nuclear Emulsion For Directional Dark Matter Search

In this study, we are doing R&D for directional dark matter search with nuclear emulsion. First of all, higher resolution nuclear emulsion with fine silver halide crystals was developed in the production facility of emulsion at Nagoya university, and we confirmed that it can detect the expected nuclear recoil tracks. The readout of submicron tracks was required the new technology. We developed the expansion technique, and could readout the signal by shape analysis with optical microscopy. The two dimensional angular resolution is 36 degrees at the original track length of range from 150nm to 200nm with optical microscopy. Finally we demonstrated by using recoiled nuclei induced by 14.8MeV neutron, and confirmed the technique.Moreover, we developed the X-ray microscope system with SPring-8 as final check with higher resolution of selected candidate tracks with optical microscopy. The angular resolution was improved from 31 degrees with optical microscopy to 17degrees with X-ray microscopy at the track length of range from 150nm to 250nm. We are developing the practical system and planning for start of the test running with prototype detector.Comment: Proceedings of the 3rd International conference on Directional Detection of Dark Matter (CYGNUS 2011), Aussois, France, 8-10 June 201

Distances in Inhomogeneous Cosmological Models

Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced gravitationally by the inhomogeneities in the universe. In this paper we first give the basic optical relations and the definitions of different distances in inhomogeneous universes. Next we show how the observational relations depend quantitatively on the distances. Finally, we give results for the frequency distribution of different distances and the shear effect on distances obtained using various methods of numerical simulation

Wearable Conductive Fiber Sensors for Multi-Axis Human Joint Angle Measurements

BACKGROUND: The practice of continuous, long-term monitoring of human joint motion is one that finds many applications, especially in the medical and rehabilitation fields. There is a lack of acceptable devices available to perform such measurements in the field in a reliable and non-intrusive way over a long period of time. The purpose of this study was therefore to develop such a wearable joint monitoring sensor capable of continuous, day-to-day monitoring. METHODS: A novel technique of incorporating conductive fibers into flexible, skin-tight fabrics surrounding a joint is developed. Resistance changes across these conductive fibers are measured, and directly related to specific single or multi-axis joint angles through the use of a non-linear predictor after an initial, one-time calibration. Because these sensors are intended for multiple uses, an automated registration algorithm has been devised using a sensitivity template matched to an array of sensors spanning the joints of interest. In this way, a sensor array can be taken off and put back on an individual for multiple uses, with the sensors automatically calibrating themselves each time. RESULTS: The wearable sensors designed are comfortable, and acceptable for long-term wear in everyday settings. Results have shown the feasibility of this type of sensor, with accurate measurements of joint motion for both a single-axis knee joint and a double axis hip joint when compared to a standard goniometer used to measure joint angles. Self-registration of the sensors was found to be possible with only a few simple motions by the patient. CONCLUSION: After preliminary experiments involving a pants sensing garment for lower body monitoring, it has been seen that this methodology is effective for monitoring joint motion of the hip and knee. This design therefore produces a robust, comfortable, truly wearable joint monitoring device

Anderson transition in the three dimensional symplectic universality class

We study the Anderson transition in the SU(2) model and the Ando model. We report a new precise estimate of the critical exponent for the symplectic universality class of the Anderson transition. We also report numerical estimation of the $\beta$ function.Comment: 4 pages, 5 figure