We consider a two-dimensional steady motion of an inviscid incompressible fluid described by the equation &UDelta; u(x,y) = F(u(x,y)), where u(x,y) is the streamfunction, &UDelta; is the Laplace operator, and F((.)) an arbitrary function measuring the flow vorticity. Apparently, until now, the only way to treat an equation of the above type with nontrivial function F analytically is to use the algebro-geometric method for integrable equations. In particular, we investigate the Cosh-Laplace equation (ChL) &UDelta; u(x,y) = ± 4cosh(u(x,y)) by means of the special technique of finite-gap integration, which allows us to obtain real solutions of the ChL equation by using a Riemann surface with appropriate symmetry. We study the first nontrivial case corresponding to a Riemann surface of genus g = 3. The hydrodynamical interpretation of finite-gap solutions is meaningful, and we try to understand the fluid processes described by these solutions. To this end, we take a Riemann surface with additional symmetry properties. We present four five-parameter families of exact solutions. These solutions are given in terms of Jacobi elliptic functions, which enables us to directly investigate the relevant properties. We also find explicit formulas for the lines of singularity. It is of interest from the point of view of algebraic geometry that the structure of the theta divisor can be described.

We analyze the stability of a Taylor-Couette flow under the imposition of a weak axial flow in the case of a very short cylinder with a narrow annulus gap. We consider an incompressible viscous fluid contained in the narrow gap between two concentric short cylinders, in which the inner cylinder rotates with constant angular velocity. The caps of the cylinders have narrow tubes conically tapering to very narrow slits, allowing an axial flow along the surface of the inner cylinder. The approximated solution for the Taylor-Couette flow for short cylinders was found and used for the stability analysis instead of the precise but bulky solution. The sensitivity of the Taylor-Couette flow to small perturbations and to weak axial flow was studied. We demonstrate that perturbations coming from the axial flow cause the propagation of dispersive waves in the Taylor-Couette flow. While in long cylinders the presence of an axial flow leads to the breaking of axial symmetry, in small cylinders it leads to the breaking of mirror symmetry. The coexistence of a rotation and an axial flow requires that, in addition to the energy and the angular momentum of the flow, the helicity must also be studied. The approximated form for the helicity formula in the case of short cylinders was derived. We found that the axial flow stabilizes the Taylor-Couette flow. The supercritical flow includes a rich variety of vortical structures, including a symmetric pair of Taylor vortices, an anomalous single vortex and quasiperiodic oscillating vortices. Pattern formation was studied at large for rated ranges of azimuthal and axial Reynolds numbers. A region where three branches of different states occur was localized. Numerical simulations in 3-D and in the axisymmetrical case of the model flow are presented, which illustrate the instabilities analyzed.

On an upward curve? The curvature of an elastically deformed nanowire pinned to a flat surface contains information about the maximum static friction force, and hence the shear stress, between the nanowire and the surface. Here, InAs nanowires are bent in a controlled manner using the tip of an atomic force microscope (see image). The shear stress can be obtained from a simple analysis according to the standard theory of elasticity.

A study was conducted to perform friction measurements of InAs nanowires (NW) on silicon nitride (Si ₃N ₄) through atomic force microscopy (AFM) manipulation. The investigations revealed the friction force per unit length for sliding and static friction over a range of nanowire diameters. It was found that there is a significant difference between the coefficients of the two sliding modes for large wires. It was also found that the difference between the two sliding modes disappears at smaller diameters and the sliding friction becomes equal with the static friction. The AFM investigations were performed on a Nanoscope IIIa Dimension 3100, using rectangular cantilevers, with a nominal spring constant of 30 N m ^-1. The nanowires were manipulated, using the 'Retrace Lift' mode of the AFM controller. The friction force per unit length was gathered from the local curvature of the NWs, using standard elasticity theory.

This study is based on three models, Markov model, Hidden Markov model and the Radial basis function neural network. A number of work has been done before about application of these three models to the stock market. Though, individual researchers have developed their own techniques to design and test the Radial basis function neural network. This paper aims to show the different ways and precision of applying these three models to predict price processes of the stock market. By comparing the same group of data, authors get different results. Based on Markov model, authors find a tendency of stock market in future and, the Hidden Markov model behaves better in the financial market. When the fluctuation of the stock price index is not drastic, the Radial basis function neural network has a nice prediction.

The performance of quantum dots-in-a-well infrared photodetectors (DWELL IPs) has been studied by means of interband and intersubband photocurrent measurements as well as dark current measurements. Using interband photocurrent measurements, substantial escape of electrons from lower lying states in the DWELL structure at large biases was revealed. Furthermore, a significant variation in the escape probability from energy states in the DWELL structure with applied bias was observed. These facts can explain the strong temperature and bias dependence of both photocurrent and dark currents in DWELL IPs.

Bias-mediated tuning of the detection wavelength within the infrared wavelength region is demonstrated for quantum dots-in-a-well and dots-on-a-well infrared photodetectors. By positioning the InAs quantum dot layer asymmetrically in an 8 nm wide In_0.15Ga_0.85As/GaAs quantum well, a shift in the peak detection wavelength from 8.4 to 10.3 μm was observed when reversing the polarity of the applied bias. For a dots-on-a-well structure, the peak detection wavelength was tuned from 5.4 to 8 μm with small changes in the applied bias. These tuning properties could be essential for applications such as modulators and dual-color infrared detection.

Resonant optical pumping across the band gap was used as artificial doping in InAs/In_0.15Ga_0.85As/GaAs quantum dots-in-a-well infrared photodetectors. A selective increase in the electron population in the different quantum dot energy levels enabled the low temperature photocurrent peaks observed at 120 and 148 meV to be identified as intersubband transitions emanating from the quantum dot ground state and the quantum dot excited state, respectively. The response was increased by a factor of 10 through efficient filling of the quantum dot energy levels by simultaneous optical pumping into the ground states and the excited states of the quantum dots.

We observe spin-valve-like effects in nanoscaled thermally evaporated Co/AlOx/Au tunnel junctions. The tunneling magnetoresistance is anisotropic and depends on the relative orientation of the magnetization direction of the Co electrode with respect to the current direction. We attribute this effect to a two-step magnetization reversal and an anisotropic density of states resulting from spin-orbit interaction. The results of this study points to future applications of novel spintronics devices involving only one ferromagnetic layer.

The authors report on magnetotransport investigations of nanoscaled ferromagnetic Co/Ni/Co single electron transistors. As a result of reduced size, the devices exhibit single electron transistor characteristics at 4.2 K. Magnetotransport measurements carried out at 1.8 K reveal tunneling magnetoresistance (TMR) traces with negative coercive fields, which the authors interpret in terms of a switching mechanism driven by the shape anisotropy of the central wirelike Ni island. A large TMR of about 18% is observed within a finite source-drain bias regime. The TMR decreases rapidly with increasing bias, which the authors tentatively attribute to excitation of magnons in the central island.

We report on magnetoresistance (MR) studies on CoAl OX Au and CoAl OX NiAu magnetic tunnel junctions. In spite of the fact that the difference between the two samples is merely a 3 nm thick Ni layer, there is a sharp contrast in MR behavior indicating that the electronic structure at the interface between the ferromagnetic electrodes and the insulating barrier dominates the MR signal. The former sample exhibits a clear tunneling anisotropic MR (TAMR), with the characteristic correlation between resistance and current direction, in contrast to the latter sample which displays a conventional tunneling MR (TMR) dominated by the relative orientation between the magnetization directions of the two electrodes. In addition, the TAMR has a much stronger temperature dependence than the TMR, indicating a much faster drop-off of the tunneling density of states anisotropy than the tunneling electron spin polarization with increasing temperature. Finally, we propose a possible simple way to distinguish TAMR from normal TMR by measuring the resistance of the device at different angles of the external magnetic field. 2008 American Institute of Physics.

We demonstrate the assembly of nanoscale ferromagnetic single-electron transistors using atomic force microscopy for imaging as well as for nanoscale manipulation. A single 30 nm Au disc, forming the central island of the transistor, is manipulated with angstrom precision into the gap between a plasma-oxidized Ni source and drain electrodes. The tunnel resistances can be tuned in real time during the device fabrication by repositioning the Au disc. Transport measurements reveal long-term stable single-electron transistor characteristics at 4.2 K. The well-controlled devices with very small central islands facilitate future in-depth studies of the interplay between Coulomb blockade, spin-dependent tunnelling and spin accumulation in ferromagnetic single-electron transistors at elevated temperatures.

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication.

Mn-doped GaAs semiconductors have generated great interest in current research regarding the evolution from a paramagnetic insulator to a ferromagnetic metal governed by a carrier mediated exchange interaction. The interplay between the charge carriers in a semiconductor and the electron spin of incorporated ferromagnetic metals can be utilized for novel spin-sensitive spintronic devices. We have fabricated highly Mn-doped, single-crystalline GaAs nanowires (NWs) by ion implantation at elevated temperatures to facilitate in-situ dynamic annealing. To exploit these nanowires in spintronic applications, a detailed understanding of fundamental charge transport mechanisms is however necessary. It is generally expected that new features, different from any bulk counterparts, will emerge in systems with reduced dimensionality e.g. quasi-1D NWs. Here we report on a detailed study of different charge transport mechanisms and localization-related effects in single Mn-doped GaAs NWs in the temperature range from 300K to 1.6K, and with magnetic fields ranging from 0T to 8T. In general, the resistance of the nanowires increases strongly from a few M* at 300K to several G* at 1.6 K. More specially, the temperature dependence displays several different interesting regimes described by distinctly different models. Furthermore, the current-voltage (I-V) characteristics becomes strongly non-linear as the temperature decreases and shows apparent power-law behavior at low temperatures. In particular, we interpret our transport data in the temperature range from 80K to 275K in terms of a variable range hopping process influenced by Mn-induced disorder in the NWs. Below 50K the magnetotransport data reveals a large negative magnetoresistance (MR) under both paralleland perpendicular magnetic fields. We are presently developing models to explain this large MR signal, including low-temperature transport mechanisms and possible magnetic interaction between Mn ions.

Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.

In this thesis a new method for the option pricing will be introduced with

the help of the Mellin transforms. Firstly, the Mellin transform techniques for

options on a single underlying stock is presented. After that basket options

will be considered. Finally, an improvement of existing numerical results

applied to Mellin transforms for 1-basket and 2-basket American Put Option

will be discussed concisely. Our approach does not require either variable

transformations or solving diusion equations.