Continuous quantum measurement of a Bose-Einstein condensate: a stochastic Gross-Pitaevskii equation

We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed within the Gross-Pitaevskii mean-field approach. Continuous weak measurements allow instead to replace, for timescales short enough, the exact problem with its mean-field approximation through a stochastic analogue of the Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark soliton undergoing a continuous imaging.Comment: 13 pages, 10 figure

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

The Sub-Surface Structure of a Large Sample of Active Regions

We employ ring-diagram analysis to study the sub-surface thermal structure of active regions. We present results using a large number of active regions over the course of Solar Cycle 23. We present both traditional inversions of ring-diagram frequency differences, with a total sample size of 264, and a statistical study using Principal Component Analysis. We confirm earlier results on smaller samples that sound speed and adiabatic index are changed below regions of strong magnetic field. We find that sound speed is decreased in the region between approximately r=0.99R_sun and r=0.995R_sun (depths of 3Mm to 7Mm), and increased in the region between r=0.97R_sun and r=0.985R_sun (depths of 11Mm to 21Mm). The adiabatic index is enhanced in the same deeper layers that sound-speed enhancement is seen. A weak decrease in adiabatic index is seen in the shallower layers in many active regions. We find that the magnitudes of these perturbations depend on the strength of the surface magnetic field, but we find a great deal of scatter in this relation, implying other factors may be relevant.Comment: 16 pages, 11 figures, accepted for publication in Solar Physic

mtDNA lineage analysis of mouse L-cell lines reveals the accumulation of multiple mtDNA mutants and intermolecular recombination

The role of mitochondrial DNA (mtDNA) mutations and mtDNA recombination in cancer cell proliferation and developmental biology remains controversial. While analyzing the mtDNAs of several mouse L cell lines, we discovered that every cell line harbored multiple mtDNA mutants. These included four missense mutations, two frameshift mutations, and one tRNA homopolymer expansion. The LA9 cell lines lacked wild-type mtDNAs but harbored a heteroplasmic mixture of mtDNAs, each with a different combination of these variants. We isolated each of the mtDNAs in a separate cybrid cell line. This permitted determination of the linkage phase of each mtDNA and its physiological characteristics. All of the polypeptide mutations inhibited their oxidative phosphorylation (OXPHOS) complexes. However, they also increased mitochondrial reactive oxygen species (ROS) production, and the level of ROS production was proportional to the cellular proliferation rate. By comparing the mtDNA haplotypes of the different cell lines, we were able to reconstruct the mtDNA mutational history of the L-L929 cell line. This revealed that every heteroplasmic L-cell line harbored a mtDNA that had been generated by intracellular mtDNA homologous recombination. Therefore, deleterious mtDNA mutations that increase ROS production can provide a proliferative advantage to cancer or stem cells, and optimal combinations of mutant loci can be generated through recombination

Optimal approximate fixed point results in locally convex spaces

Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate fixed point net. Next, it is shown that if $C$ is bounded but not totally bounded, then there is a uniformly continuous map $f\colon C\to C$ without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, it is constructed a affine sequentially continuous map from a compact convex set into itself without fixed points.Comment: 12 page

PHP61 The Financial Impacts of Pharmacist Intervention in Inpatient Department of a Local Hospital in Taiwan

Morphometric analysis of S. mortenseni. (DOC 44 kb

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

Intelligent tracking control of a DC motor driver using self-organizing TSK type fuzzy neural networks

[[abstract]]In this paper, a self-organizing Takagi–Sugeno–Kang (TSK) type fuzzy neural network (STFNN) is proposed. The self-organizing approach demonstrates the property of automatically generating and pruning the fuzzy rules of STFNN without the preliminary knowledge. The learning algorithms not only extract the fuzzy rule of STFNN but also adjust the parameters of STFNN. Then, an adaptive self-organizing TSK-type fuzzy network controller (ASTFNC) system which is composed of a neural controller and a robust compensator is proposed. The neural controller uses an STFNN to approximate an ideal controller, and the robust compensator is designed to eliminate the approximation error in the Lyapunov stability sense without occurring chattering phenomena. Moreover, a proportional-integral (PI) type parameter tuning mechanism is derived to speed up the convergence rates of the tracking error. Finally, the proposed ASTFNC system is applied to a DC motor driver on a field-programmable gate array chip for low-cost and high-performance industrial applications. The experimental results verify the system stabilization and favorable tracking performance, and no chattering phenomena can be achieved by the proposed ASTFNC scheme.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page