Some relations concerning k-chordal and k-tangential polygons

In papers [6] and [7] the k-chordal and the k-tangential polygons are defined and some of their properties are proved. In this paper we shall consider some of their other properties. Theorems 1-4 are proved

Some relations and properties concerning tangential polygons

The k-tangential polygon is defined, and some of its properties are proved

On algebraic equations concerning semi-tangential polygons

Some properties of equations (5) and (6) are proved (Theorem 1-2) and it was established that the positive roots of these equations are radii of a sequence of tangential semi-polygons which have the same lengths of tangents

Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder

We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled disorder. That is, we investigate the evolution of the single particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons

Thermoelectrical manipulation of nanomagnets

We investigate the interplay between the thermodynamic properties and spin-dependent transport in a mesoscopic device based on a magnetic multilayer (F/f/F), in which two strongly ferromagnetic layers (F) are exchange-coupled through a weakly ferromagnetic spacer (f) with the Curie temperature in the vicinity of room temperature. We show theoretically that the Joule heating produced by the spin-dependent current allows a spin-thermo-electronic control of the ferromagnetic-to-paramagnetic (f/N) transition in the spacer and, thereby, of the relative orientation of the outer F-layers in the device (spin-thermo-electric manipulation of nanomagnets). Supporting experimental evidence of such thermally controlled switching from parallel to antiparallel magnetization orientations in F/f(N)/F sandwiches is presented. Furthermore, we show theoretically that local Joule heating due to a high concentration of current in a magnetic point contact or a nanopillar can be used to reversibly drive the weakly ferromagnetic spacer through its Curie point and thereby exchange couple and decouple the two strongly ferromagnetic F-layers. For the devices designed to have an antiparallel ground state above the Curie point of the spacer, the associated spin-thermionic parallel-to-antiparallel switching causes magneto-resistance oscillations whose frequency can be controlled by proper biasing from essentially DC to GHz. We discuss in detail an experimental realization of a device that can operate as a thermo-magneto-resistive switch or oscillator.Comment: This paper, published in J. Appl. Phys. 107, 123706 (2010), is an expanded version of arXiv:0710.5477 (8 pages, 12 figures, two additional authors and experimental section added

DC spin generation by junctions with AC driven spin-orbit interaction

An unbiased one-dimensional weak link between two terminals, subjected to the Rashba spin-orbit interaction caused by an AC electric field which rotates periodically in the plane perpendicular to the link, is shown to inject spin-polarized electrons into the terminals. The injected spin-polarization has a DC component along the link and a rotating transverse component in the perpendicular plane. In the adiabatic, low rotation-frequency regime, these polarization components are proportional to the frequency. The DC component of the polarization vanishes for a linearly-polarized electric field.Comment: published versio

Competition and risk-taking in investment banking

How does competition affect the investment banking business and the risks individual institutions are exposed to? Using a large sample of investment banks operating in seven developed economies over 1997-2014, we apply a panel VAR model to examine the relationships between competition and risk without assuming any a priori restrictions. Our main finding is that investment banks’ higher risk exposure, measured as a long-term capital-at-risk and return volatility, was facilitated by greater competitive pressures for both boutique investment banks and full service investment banks. Overall, we find some evidence that more competition leads to more fragility before and during the recent financial crisis

Spin-thermo-electronic oscillator based on inverse giant magnetoresistance

A spin-thermo-electronic valve with the free layer of exchange-spring type and inverse magnetoresistance is investigated. The structure has S-shaped current-voltage characteristics and can exhibit spontaneous oscillations when integrated with a conventional capacitor within a resonator circuit. The frequency of the oscillations can be controlled from essentially dc to the GHz range by the circuit capacitance.Comment: 7 pages, 9 figure

On some algebraic equations in connection with one kind of tangential polygons

This article can be considered as an appendix to article [1]. Here article [1] is completed and extended, where some new relations concerning one kind of tangential polygons and algebraic equations are established