Robust Statistics considers the quality of statistical decisions in the presence of deviations from the ideal model. Usually these deviations are neighborhoods of a certain size about the ideal model. We introduce a new concept of optimality if this size or radius is not (precisely) known: We determine the increase of the maximum risk over the minimax risk in the case that the optimally robust ...

Ideal carving occurs when a snowboarder or skier, equipped with a snowboard or carving skis, describes a perfect carved turn in which the edges of the ski alone, not the ski surface, describe the trajectory followed by the skier, without any slipping or skidding. In this article, we derive the " ideal-carving " equation which describes the physics of a carved turn under ideal conditions. The la...

A parameter, U(cp), that quantifies the distortion of the anion skeleton in a crystal from ideal closest-packing has been developed. It is a measure of the average isotropic displacement of the observed anions from their ideal equivalents. An ideal closest-packed structure can be fit to an observed structure by varying the radius of the ideal spheres, orientation and translation, such that U(cp...

In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that is modeled by an ideal nonstandard physical world transformation process that yields a connection between an exterior Schwarzschild line eleme...

In this study, we consider the ideal aggregate with quadratically increasing permeability kappa = k2r2 and derive the analytical expression of the stream function within the porous aggregate by incorporating the Brinkman and continuity equations. The hydrodynamic properties of the aggregate are investigated by taking account of the hydrodynamic radius, settling velocity, and fluid collection ef...

The dynamics of the partially ionized solar atmosphere is controlled by frequent collision and charge exchange between predominant neutral Hydrogen atoms charged ions. At signal frequencies below or order either magnetic stress {\it felt} both particles simultaneously. resulting neutral-mass loading ions leads to rescaling effective ion-cyclotron frequency-it becomes Hall frequency, resultant L...

We consider the problem of an ideal polymer confined in a droplet. When the droplet radius is smaller than the (unconfined) polymer radius of gyration, the polymer entropy will depend on the droplet shape. We compute the resulting surface free

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...

Room-temperature small-signal intensity-modulation frequency response of InGaAs/InGaAsP multiple quantum well microdisk lasers depends on disk radius. For frequencies up to 2 GHz the measured response of a small radius microdisk laser is closer to an ideal laser compared to larger devices. The dynamic response of larger radius lasers is strongly in¯uenced by the presence of a reservoir of carri...