What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio

Generalized Futaki Invariant of Almost Fano Toric Varieties, Examples

The interpretation, due to T. Mabuchi, of the classical Futaki invariant of Fano toric manifolds is extended to the case of the Generalized Futaki invariant, introduced by W. Ding and G. Tian, of almost Fano toric varieties. As an application it is shown that the real part of the Generalized Futaki invariant is positive for all degenerations of the Fano manifold V_{38}, obtained by intersection of the Veronese embedding of ${\bf P}^3\times{\bf P}^2 \subset {\bf P}^{11}$ with codimension-two hyperplanes.Comment: 22 pages, LaTeX2

Single-index quantile regression

This is the post-print version of the final paper published in Journal of Multivariate Analysis. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the “curse of dimensionality”. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index function View the MathML sourceg0(xTγ0), where a univariate link function g0(⋅)g0(⋅) is applied to a linear combination of covariates View the MathML sourcexTγ0, often called the single-index. We introduce a practical algorithm where the unknown link function g0(⋅)g0(⋅) is estimated by local linear quantile regression and the parametric index is estimated through linear quantile regression. Large sample properties of estimators are studied, which facilitate further inference. Both the modeling and estimation approaches are demonstrated by simulation studies and real data applications

Dynamical Models of Extreme Rolling of Vessels in Head Waves

Rolling of a ship is a swinging motion around its length axis. In particular vessels transporting containers may show large amplitude roll when sailing in seas with large head waves. The dynamics of the ship is such that rolling interacts with heave being the motion of the mass point of the ship in vertical direction. Due to the shape of the hull of the vessel its heave is influenced considerably by the phase of the wave as it passes the ship. The interaction of heave and roll can be modeled by a mass-spring-pendulum system. The effect of waves is then included in the system by a periodic forcing term. In first instance the damping of the spring can be taken infinitely large making the system a pendulum with an in vertical direction periodically moving suspension. For a small angular deflection the roll motion is then described by the Mathieu equation containing a periodic forcing. If the period of the solution of the equation without forcing is about twice the period of the forcing then the oscillation gets unstable and the amplitude starts to grow. After describing this model we turn to situation that the ship is not anymore statically fixed at the fluctuating water level. It may move up and down showing a motion modeled by a damped spring. One step further we also allow for pitch, a swinging motion around a horizontal axis perpendicular to the ship. It is recommended to investigate the way waves may directly drive this mode and to determine the amount of energy that flows along this path towards the roll mode. Since at sea waves are a superposition of waves with different wavelengths, we also pay attention to the properties of such a type of forcing containing stochastic elements. It is recommended that as a measure for the occurrence of large deflections of the roll angle one should take the expected time for which a given large deflection may occur instead of the mean amplitude of the deflection

From Gas Sensors to Detection of Etanol Vapour to Sensor of Bacteria Detection

Introduction. Metal oxide semiconductor sensors have many advantages. But their working temperature is still high and their sensitivities are frequently low. In the current work, I present the results from investigation of sensing ability of new kind of potentiometric solid state gas sensor.Aim. The main goal of this work is investigation of the temperature dependence in the flow of air and in ethanol vapour mixture of the investigated junction structures. Also, we investigated at fixed temperature the dependence of the thermoelectric force from the ethanol vapour concentration at possible low operation temperature. For the structure, which shows the lowest operation temperature to ethanol vapour, we investigate the ability to detect Pseudomonas putida suspension.Materials and methods. In this work, the sensitivity to ethanol vapour and Pseudomonas putida suspension were investigated by measuring the thermoelectric force (the voltage) appearing of the structures by standart voltmeters.Results. Two experimental installations for sensors have been developed. The first one is for detection of ethanol vapour by ZnO/ZnO:Cu, ZnO/ZnO:CuO, ZnO/ZnO:Fe junction structures. The second installation was for Pseudomonas putida suspension detection in gas phase by ZnO/ZnO:Fe junction structure. We discovered that ZnO/ZnO:Fe structure, has the lowest operation temperature of 200 °C to ethanol vapour. For this structure, the potential difference has a negative value and decreases with increasing the amount of the pulverized bacteria.Conclusion. We discovered that ZnO/ZnO:Fe structure, has the lowest operation temperature of 200 °C. This operation temperature is a bit higher than operation temperature of at which some very novel sensing structures shows the maximum sensitivity.Introduction. Metal oxide semiconductor sensors have many advantages. But their working temperature is still high and their sensitivities are frequently low. In the current work, I present the results from investigation of sensing ability of new kind of potentiometric solid state gas sensor.Aim. The main goal of this work is investigation of the temperature dependence in the flow of air and in ethanol vapour mixture of the investigated junction structures. Also, we investigated at fixed temperature the dependence of the thermoelectric force from the ethanol vapour concentration at possible low operation temperature. For the structure, which shows the lowest operation temperature to ethanol vapour, we investigate the ability to detect Pseudomonas putida suspension.Materials and methods. In this work, the sensitivity to ethanol vapour and Pseudomonas putida suspension were investigated by measuring the thermoelectric force (the voltage) appearing of the structures by standart voltmeters.Results. Two experimental installations for sensors have been developed. The first one is for detection of ethanol vapour by ZnO/ZnO:Cu, ZnO/ZnO:CuO, ZnO/ZnO:Fe junction structures. The second installation was for Pseudomonas putida suspension detection in gas phase by ZnO/ZnO:Fe junction structure. We discovered that ZnO/ZnO:Fe structure, has the lowest operation temperature of 200 °C to ethanol vapour. For this structure, the potential difference has a negative value and decreases with increasing the amount of the pulverized bacteria.Conclusion. We discovered that ZnO/ZnO:Fe structure, has the lowest operation temperature of 200 °C. This operation temperature is a bit higher than operation temperature of at which some very novel sensing structures shows the maximum sensitivity

FUNCTIONAL MORPHОLOGY OF THYMIC EPITHELIAL CELLS

No abstrac