Radio and EUV signatures of a solar flare-CME event on November 28, 1998

Using the observational data of the solar radio spectrometer with a broad bandwidth of the Chinese National Astronomical Observatories (CNAO), the Nobeyama Radio Heliograph (NoRH) and Polarimeters (NoRP), YOHKOH and SOHO satellites, it is found that there are two characteristics in an X3.3 flare event associated with coronal mass ejection (CME). (ⅰ) X-ray and EUV loop interaction and evolution appeared evidently in corona, followed by the formation of a twisted loop structure, which is consistent with the theoretical calculations of Amari et al. (1999a,b) for the origin of flare-CME events. (ⅱ) The slow frequency drift was shown in the radio observations, corresponding to the relevant movement of the radio source observed by NoRH, at a speed of several tens kilometers per second, which may be associated with the speed of the shock waves resulting from the CME.     

An improved efficiency of fuzzy logic control of PMBLDC for PV pumping system

This paper presents an analysis by which the dynamic performances of a permanent magnet brushless DC (PMBLDC) motor is controlled through a hysteresis current loop and an outer speed loop with different controllers. The dynamics of the photovoltaic pumping drive system with (PI) and a fuzzy logic (FL) speed controllers are presented. In order to optimize the overall system efficiency, a maximum power point tracker is also used. Simulation is carried out by formatting the mathematical model for photovoltaic source, MPPT, motor and pump load. The results for such complicated and nonlinear system, with FL speed controller show improvement in transient response of PMBLDC drive over conventional PI. The effectiveness of the FL controller is also demonstrated.     

On compact vector formats in the solution of the chemical master equation with backward differentiation

A stochastic chemical system with multiple types of molecules interacting through reaction channels can be modeled as a continuous‐time Markov chain with a countably infinite multidimensional state space. Starting from an initial probability distribution, the time evolution of the probability distribution associated with this continuous‐time Markov chain is described by a system of ordinary differential equations, known as the chemical master equation (CME). This paper shows how one can solve the CME using backward differentiation. In doing this, a novel approach to truncate the state space at each time step using a prediction vector is proposed. The infinitesimal generator matrix associated with the truncated state space is represented compactly, and exactly, using a sum of Kronecker products of matrices associated with molecules. This exact representation is already compact and does not require a low‐rank approximation in the hierarchical Tucker decomposition (HTD) format. During transient analysis, compact solution vectors in HTD format are employed with the exact, compact, and truncated generated matrices in Kronecker form, and the linear systems are solved with the Jacobi method using fixed or adaptive rank control strategies on the compact vectors. Results of simulation on benchmark models are compared with those of the proposed solver and another version, which works with compact vectors and highly accurate low‐rank approximations of the truncated generator matrices in quantized tensor train format and solves the linear systems with the density matrix renormalization group method. Results indicate that there is a reason to solve the CME numerically, and adaptive rank control strategies on compact vectors in HTD format improve time and memory requirements significantly.     

A solar radio moving type IV burst of expanding arches type involving multi-sources

A complex solar radio moving type IV burst was observed on 23 September 1998 with the broadband (1.0–2.0 GHz and 2.6–3.8 GHz) spectrometers with high temporal and spectral resolutions at National Astronomical Observatories of China (NAOC). Comparing to the high spatial resolution data of Siberian Solar Radio Telescope (SSRT), we find that this burst is a rare type of moving type IV burst which is caused by the expanding arches, and the spatial structure oscillations of the radio sources are related with the time structure pulsations of the radio emission. Furthermore, the burst is associated with the multiple quasi-periodic long-term pulsations, and this suggests the existence of multi-scale magnetic structures in a large expanding coronal arch. We think the moving type IV burst is due to the synchrotron emission of the energetic electrons trapped in the expanding arch, and the multiple quasi-periodic pulsations are due to the second harmonic plasma emission.     

A solar radio moving type Ⅳ burst of expanding arches type involving multi-sources

A complex solar radio moving type IV burst was observed on 23 September 1998 with the broadband (1.0-2.0 GHz and 2.6-3.8 GHz) spectrometers with high temporal and spectral resolutions at National Astronomical Observatories of China (NAOC). Comparing to the high spatial resolution data of Siberian Solar Radio Telescope (SSRT), we find that this burst is a rare type of moving type IV burst which is caused by the expanding arches, and the spatial structure oscillations of the radio sources are related with the time structure pulsations of the radio emission. Furthermore, the burst is associated with the multiple quasi-periodic long-term pulsations, and this suggests the existence of multi-scale magnetic structures in a large expanding coronal arch. We think the moving type IV burst is due to the synchrotron emission of the energetic electrons trapped in the expanding arch, and the multiple quasi-periodic pulsations are due to the second harmonic plasma emission.     

Augmented lagrangian nonlinear programming algorithm that uses SQP and trust region techniques

An augmented Lagrangian nonlinear programming algorithm has been developed. Its goals are to achieve robust global convergence and fast local convergence. Several unique strategies help the algorithm achieve these dual goals. The algorithm consists of three nested loops. The outer loop estimates the Kuhn-Tucker multipliers at a rapid linear rate of convergence. The middle loop minimizes the augmented Lagrangian functions for fixed multipliers. This loop uses the sequential quadratic programming technique with a box trust region stepsize restriction. The inner loop solves a single quadratic program. Slack variables and a constrained form of the fixed-multiplier middleloop problem work together with curved line searches in the inner-loop problem to allow large penalty wieghts for rapid outer-loop convergence. The inner-loop quadratic programs include quadratic onstraint terms, which complicate the inner loop, but speed the middle-loop progress when the constraint curvature is large.The new algorithm compares favorably with a commercial sequential quadratic programming algorithm on five low-order test problems. Its convergence is more robust, and its speed is not much slower.This research was supported in part by the National Aeronautics and Space Administration under Grant No. NAG-1-1009.     

Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade

Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime than the usual QSSA. Here, we extend the tQSSA to the Mitogen-Activated Protein Kinase Cascade, an important signaling system in cell biochemistry. These approximations were first developed in a deterministic setting, but here we also describe how to incorporate this approximation into the discrete and stochastic framework of the Chemical Master Equation (CME). The CME gives rise to a large-scale matrix exponential that can be solved by Krylov methods in combination with operator splitting and the tQSSA.      

Synchronization of permanent magnet electric motors: New nonlinear advanced results

The nonlinear learning control techniques, based on Fourier approximation theory and used by Verrelli (2011) [2] to solve the synchronization problem for uncertain permanent magnet synchronous motors (performing repetitive tasks of uncertain repetition period), are considered in this paper. We show that, if the exogenous rotor position reference signal (which is to be globally tracked without assuming its foreknowledge) is restricted to the class of sinusoidal signals with uncertain bias, amplitude, frequency and phase, a stronger result can be derived by resorting to nonlinear advanced identification techniques. In contrast to Verrelli (2011) [2], neither availability of the rotor speed reference signal is required nor infinite memory identification schemes are used. The application to the problem of synchronizing a drumming robotic arm with a drumming human arm is presented: simulation results show satisfactory closed loop performances and confirm the effectiveness of the proposed solution.     

点时滞系统的反馈镇定

求解特征矩阵是镇定时滞系统的关键问题，本文给出了系统的特征根的代数重复度与几何重复度均为一般值的情况下特征矩阵的求法，即把它归结为求一组线性代数方程的问题，并得到了该方程组有组及对应于同一特征值的解向量组线性独立的充分条件。本文还提出了一种算法来处理系统对应于不同特征值的左行征向量线性相关情况下系统的镇定问题最后，举例说明了设计步骤。     

关于均值KIRCHHOFF板非线性边界镇定问题的几点注记

对于均值K IRCHHOFF板非线性边界镇定问题给出几点注记.首先应用G reen公式对具有非线性边界反馈控制的均值K IRCHHOFF板所决定的非线性系统的能量衰减速度进行了重新推导,从而修正了前人的结果.然后应用极大单调函数的定义和分部积分技巧,对均值K IRCHHOFF板非线性边界镇定问题所决定的非线性算子A的极大单调性给出了重新证明,进而更正了已有文献中相应证明的欠妥之处.     

Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations usefully contributes to the localization of good candidates for the role of global minimizer, a stochastic model of the function can be built to conduct a sequential choice of evaluation points. Based on Gaussian processes and Kriging, the authors have recently introduced the informational approach to global optimization (IAGO) which provides a one-step optimal choice of evaluation points in terms of reduction of uncertainty on the location of the minimizers. To do so, the probability density of the minimizers is approximated using conditional simulations of the Gaussian process model behind Kriging. In this paper, an empirical comparison between the underlying sampling criterion called conditional minimizer entropy (CME) and the standard expected improvement sampling criterion (EI) is presented. Classical test functions are used as well as sample paths of the Gaussian model and an industrial application. They show the interest of the CME sampling criterion in terms of evaluation savings.     

Loop coproducts in string topology and triviality of higher genus TQFT operations

Cohen and Godin constructed a positive boundary topological quantum field theory (TQFT) structure on the homology of free loop spaces of oriented closed smooth manifolds by associating certain operations called string operations to orientable surfaces with parametrized boundaries. We show that all TQFT string operations associated to surfaces of genus at least one vanish identically. This is a simple consequence of properties of the loop coproduct which will be discussed in detail. One interesting property is that the loop coproduct is nontrivial only on the degree d homology group of the connected component of LM consisting of contractible loops, where d=dimM, with values in the degree 0 homology group of constant loops. Thus the loop coproduct behaves in a dramatically simpler way than the loop product.     

Reliability-Based Optimization Using Differential Evolution and Inverse Reliability Analysis for Engineering System Design

In this contribution, a new methodology based on a double-loop iteration process is proposed for the treatment of uncertainties in engineering system design. The inner optimization loop is used to find the solution associated with the highest probability value (inverse reliability analysis), and the outer loop is the regular optimization loop used to solve the considered reliability problem through differential evolution and multi-objective optimization differential evolution algorithms. The proposed methodology is applied to mathematical functions and to the design of classical engineering systems according to both mono- and multi-objective contexts. The obtained results are compared with those obtained by classical approaches and demonstrate that the proposed strategy represents an interesting alternative to reliability design of engineering systems.     

Existence of Dirac eigenvalues of higher multiplicity

In this article, we prove that on any compact spin manifold of dimension \(m \equiv 0,6,7 \mod 8\), there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by “catching” the desired metric in a subspace of Riemannian metrics with a loop that is not homotopically trivial. We show how this can be done on the sphere with a loop of metrics induced by a family of rotations. Finally, we transport this loop to an arbitrary manifold (of suitable dimension) by extending some known results about surgery theory on spin manifolds.     

On left conjugacy closed loops with a nucleus of index two

A loop Q is said to be left conjugacy closed (LCC) if the left translations form a set of permutations that is closed under conjugation. Loops in which the left and middle nuclei coincide and are of index 2 are necesarilly LCC, and they are constructed in the paper explicitly. LCC loops Q with the right nucleus G of index 2 offer a larger diversity, but that is associated with the level of commutativity of G (amongst others, the centre of G has to be nontrivial). On the other hand, for each m ≥ 2 one can construct an LCC loop Q of order 2m in such a way that its left nucleus is trivial, and the right nucleus if of order m. If Q is involutorial, then it is a Bol loop. Work supported by institutional grant MSM 113200007 and by Grant Agency of Czech Republic, Grant 201/02/0594. The paper was written while the author was visiting Universitaet Hamburg in January 2004.     

Sparse grids and hybrid methods for the chemical master equation

The direct numerical solution of the chemical master equation (CME) is usually impossible due to the high dimension of the computational domain. The standard method for solution of the equation is to generate realizations of the chemical system by the stochastic simulation algorithm (SSA) by Gillespie and then taking averages over the trajectories. Two alternatives are described here using sparse grids and a hybrid method. Sparse grids, implemented as a combination of aggregated grids are used to address the curse of dimensionality of the CME. The aggregated components are selected using an adaptive procedure. In the hybrid method, some of the chemical species are represented macroscopically while the remaining species are simulated with SSA. The convergence of variants of the method is investigated for a growing number of trajectories. Two signaling cascades in molecular biology are simulated with the methods and compared to SSA results. AMS subject classification (2000)  65C20, 60J25, 92C45     

(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations

We consider the nonlinear Dirac equation (NLD) with time dependent external electro-magnetic potentials, involving a dimensionless parameter $ε\in(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime $ε\ll1$ (speed of light tends to infinity), we decompose the solution into the eigenspaces associated with the 'free Dirac operator' and construct an approximation to the NLD with $O(ε^2)$ error. The NLD converges (with a phase factor) to a coupled nonlinear Schrödinger system (NLS) with external electric potential in the nonrelativistic limit as $ε\to0^+$, and the error of the NLS approximation is first order $O(ε)$. The constructed $O(ε^2)$ approximation is well-suited for numerical purposes.     

Nocturnal absorption of radio waves due to the ionisation produced by X-rays from Sco X-1 and Tau X-1 in the lower ionosphere

The night-time attenuation of LF radio waves of frequency 164 kHz transmitted from Tashkent and received at Ahmedabad has been found to have a sidereal time variation which is associated with the transits of the X-ray stars Sco X-1 and Tau X-1. Using the full-wave admittance method of Barron and Budden for calculating the intensity and polarisation of LF radio waves reflected from ionosphere during night-time when the atmosphere is irradiated by X-rays from Sco X-1 and Tau X-1, the attenuation of 164 kHz waves transmitted from Tashkent and received at Ahmedabad, has been calculated and compared with the observed results. The agreement is reasonably satisfactory.     

A study of leveraged ETF based on geometric return

Leveraged (inverse) exchange-traded funds (LETFs) seek to deliver multiples (opposite) of the performance of the index or benchmark they track. LETFs typically are designed to achieve their stated performance objectives on a daily basis. Many real-life and hypothetical examples have been given to show that the performance of these ETFs over a period longer than one day can differ from their stated daily performance objectives. Formulae have been found using both continuous method and discrete method. A discrete method was used to find a formula linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance but the method needs to use some assumptions and statistical properties to create the volatility term. A CME report finds a very simple way to include volatility in their formula but fails to link to the return of the corresponding unleveraged product. In this paper, we find a natural way to link a leveraged fund with its corresponding unleveraged product and its realized variance in a discrete manner. Our derivation process is similar to that in the CME report, so we do not need to use assumptions and statistical properties to create the volatility term. Unlike the CME method, we use geometric return as opposed to arithmetic return. So, we are able to connect with the return of the corresponding unleveraged product.     

两个高维loop代数及应用

借助于循环数,构造了维数分别是5(s+1)和4(s+1)的两个高维loop代数．为了计算方便,本文只考虑s=1时的应用．利用第一个loop代数■_1~*得到了具有4-Hamilton结构的一个广义AKNS族,该方程族可约化为著名的AKNS族．利用第二个loop代数■_2~*,得到了具有4个分量位势函数的4-Hamilton结构方程族,该族可约化为一个非线性耦合Burgers方程和一个耦合的KdV方程．