A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.Comment: 2 page

Asymptotic expansion of the minimum covariance determinant estimators

In arXiv:0907.0079 by Cator and Lopuhaa, an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a first-order Taylor expansion. In this paper, we prove the existence of this derivative for multivariate distributions that have a density and provide an explicit expression. Moreover, under suitable symmetry conditions on the density, we show that this derivative is non-singular. These symmetry conditions include the elliptically contoured multivariate location-scatter model, in which case we show that the minimum covariance determinant (MCD) estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent identically distributed vector and matrix valued random elements, respectively. This provides a proof of asymptotic normality and a precise description of the limiting covariance structure for the MCD estimators.Comment: 21 page

Energy storage apparatus

A high efficiency, flywheel type energy storage device which comprises an electronically commutated d.c. motor/generator unit having a massive flywheel rotor magnetically suspended around a ring shaped stator is presented. During periods of low energy demand, the storage devices were operated as a motor, and the flywheel motor was brought up to operating speed. Energy was drawn from the device functioning as a generator as the flywheel rotor rotated during high energy demand periods

Logarithmic circuit with wide dynamic range

A circuit deriving an output voltage that is proportional to the logarithm of a dc input voltage susceptible to wide variations in amplitude includes a constant current source which forward biases a diode so that the diode operates in the exponential portion of its voltage versus current characteristic, above its saturation current. The constant current source includes first and second, cascaded feedback, dc operational amplifiers connected in negative feedback circuit. An input terminal of the first amplifier is responsive to the input voltage. A circuit shunting the first amplifier output terminal includes a resistor in series with the diode. The voltage across the resistor is sensed at the input of the second dc operational feedback amplifier. The current flowing through the resistor is proportional to the input voltage over the wide range of variations in amplitude of the input voltage

Theory of the spatial structure of non-linear lasing modes

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have non-trivial spatial structure even in the single-mode limit. In the multi-mode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic and random laser media.Comment: 4 pages, 3 figure

The Deep X-ray Radio Blazar Survey (DXRBS). II. New Identifications

We have searched the archived, pointed ROSAT Position Sensitive Proportional Counter data for blazars by correlating the WGACAT X-ray database with several publicly available radio catalogs, restricting our candidate list to serendipitous X-ray sources with a flat radio spectrum (alpha_r <= 0.70). This makes up the Deep X-ray Radio Blazar Survey (DXRBS). Here we present new identifications and spectra for 106 sources, including 86 radio-loud quasars, 11 BL Lacertae objects, and 9 narrow-line radio galaxies. Together with our previously published objects and already known sources, our sample now contains 298 identified objects: 234 radio-loud quasars (181 flat-spectrum quasars: FSRQ [alpha_r <= 0.50] and 53 steep-spectrum quasars: SSRQ), 36 BL Lacs, and 28 narrow-line radio galaxies. Redshift information is available for 96% of these. Thus our selection technique is ~ 90% efficient at finding radio-loud quasars and BL Lacs. Reaching 5 GHz radio fluxes ~ 50 mJy and 0.1-2.0 keV X-ray fluxes a few x 10^-14 erg/cm^2/s, DXRBS is the faintest and largest flat-spectrum radio sample with nearly complete (~ 85%) identification. We review the properties of the DXRBS blazar sample, including redshift distribution and coverage of the X-ray-radio power plane for quasars and BL Lacs. Additionally, we touch upon the expanded multiwavelength view of blazars provided by DXRBS. By sampling for the first time the faint end of the radio and X-ray luminosity functions, this sample will allow us to investigate the blazar phenomenon and the validity of unified schemes down to relatively low powers.Comment: 33 pages, 5 figures. Accepted for publication in MNRAS. Postscript file also available at http://www.stsci.edu/~padovani/survey.htm

Dynamical breakdown of the Ising spin-glass order under a magnetic field

The dynamical magnetic properties of an Ising spin glass Fe$_{0.55}$Mn$_{0.45}$TiO$_3$ are studied under various magnetic fields. Having determined the temperature and static field dependent relaxation time $\tau(T;H)$ from ac magnetization measurements under a dc bias field by a general method, we first demonstrate that these data provide evidence for a spin-glass (SG) phase transition only in zero field. We next argue that the data $\tau(T;H)$ of finite $H$ can be well interpreted by the droplet theory which predicts the absence of a SG phase transition in finite fields.Comment: 4 pages, 5 figure

On the penetration of meridional circulation below the solar convection zone

Meridional flows with velocities of a few meters per second are observed in the uppermost regions of the solar convection zone. The amplitude and pattern of the flows deeper in the solar interior, in particular near the top of the radiative region, are of crucial importance to a wide range of solar magnetohydrodynamical processes. In this paper, we provide a systematic study of the penetration of large-scale meridional flows from the convection zone into the radiative zone. In particular, we study the effects of the assumed boundary conditions applied at the convective-radiative interface on the deeper flows. Using simplified analytical models in conjunction with more complete numerical methods, we show that penetration of the convectively-driven meridional flows into the deeper interior is not necessarily limited to a shallow Ekman depth but can penetrate much deeper, depending on how the convective-radiative interface flows are modeled.Comment: 13 pages, 5 figures. Subitted to Ap