Abstract:
The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the J-symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is obtained in the set of associated matrix Riccati equations. This inconsistency is interpreted as a no-go theorem which forbids the construction of isospectral alpha^2-dynamo operator classes with the help of first-order differential intertwining operators.

Abstract:
This communication deals with a theoretical study of the hot spot onset (HSO) in cellular bipolar power transistors. This well-known phenomenon consists of a current crowding within few cells occurring for high power conditions, which significantly decreases the forward safe operating area (FSOA) of the device. The study was performed on a virtual sample by means of a fast, fully analytical electro-thermal simulator operating in the steady state regime and under the condition of imposed input base current. The purpose was to study the dependence of the phenomenon on several thermal and geometrical factors and to test suitable countermeasures able to impinge this phenomenon at higher biases or to completely eliminate it. The power threshold of HSO and its localization within the silicon die were observed as a function of the electrical bias conditions as for instance the collector voltage, the equivalent thermal resistance of the assembling structure underlying the silicon die, the value of the ballasting resistances purposely added in the emitter metal interconnections and the thickness of the copper heat spreader placed on the die top just to the aim of making more uniform the temperature of the silicon surface.

Abstract:
The provision of services as e-commodities and the wide use of networked business models have driven buyer experience to new heights. Innovation, coupled with quality is the competitive advantage e-commerce vendors strive to achieve when designing or re-designing their software. In terms of quality, evaluation stood in the spotlight for many years. However, software analysis and design based on quality models have been used mostly for understanding, rather than improving. In this work, we present a new model for the analysis and design of e-commerce software systems mapped to the software life-cycle process. Quality control procedures are mapped to every phase, from initiation and design to delivery. Based on current ISO standards such as ISO25000 series, this work discusses technical and managerial principles that need to be applied in order to obtain quality e-commerce software.

Abstract:
Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

Abstract:
A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac equation and to extract non-numerical information about the dynamo spectrum.

Abstract:
The present paper deals with an application of the analytical thermal simulator DJOSER. It consist of the characterization of a water speed sensor realized in hybrid technology. The capability of the thermal solver to manage the convection heat exchange and the effects of the passivating layers make the simulation work easy and fast.

Abstract:
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust and accurate tools for the numerical solution of many problems in other fields of physics. The paper is intended to facilitate the use of integral equation solvers in dynamo theory. In concrete, the integral equation method is employed to solve the eigenvalue problem for a hydromagnetic dynamo model with a spherically symmetric, isotropic helical turbulence parameter alpha. Three examples of the function alpha(r) with steady and oscillatory solutions are considered. A convergence rate proportional to the inverse squared of the number of grid points is achieved. Based on this method, a convergence accelerating strategy is developed and the convergence rate is improved remarkably. Typically, quite accurate results can be obtained with a few tens of grid points. In order to demonstrate its suitability for the treatment of dynamos in other than spherical domains, the method is also applied to alpha^2 dynamos in rectangular boxes. The magnetic fields and the electric potentials for the first eigenvalues are visualized.

Abstract:
Using a spherical symmetric mean field alpha^2-dynamo model for Earth's magnetic field reversals, we show the coexistence of the noise-induced phenomena coherence resonance and stochastic resonance. Stochastic resonance has been recently invoked to explain the 100 kyr periodicity in the distribution of the residence time between reversals. The comparison of the resulting residence time distribution with the paleomagnetic one allows for some estimate of the effective diffusion time of the Earth's core which may be 100 kyr or slightly below rather than 200 kyr as it would result from the molecular resistivity.

Abstract:
The spectral branching behavior of the 2x2 operator matrix of the magneto-hydrodynamic alpha^2-dynamo is analyzed numerically. Some qualitative aspects of level crossings are briefly discussed with the help of a simple toy model which is based on a Z_2-graded-pseudo-Hermitian 2x2 matrix. The considered issues comprise: the underlying SU(1,1) symmetry and the Krein space structure of the system, exceptional points of branching type and diabolic points, as well as the algebraic and geometric multiplicity of corresponding degenerate eigenvalues.

Abstract:
The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial direction. The time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. Whereas the presence of an inner core with different magnetic diffusivity has remarkable little impact on the character of the dominating dynamo eigenmodes, the introduction of equatorial symmetry breaking considerably changes the geometric character of the solutions. Around the dynamo threshold the leading modes correspond to hemispherical dynamos even when the symmetry breaking is small. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios may occur in case of more realistic anisotropies of \alpha- and \beta-effect or through non-linearities caused by the back-reaction of the magnetic field (magnetic quenching).