A method for extracting human gait series from accelerometer signals based on the ensemble empirical mode decomposition

In this paper,the ensemble empirical mode decomposition(EEMD) is applied to analyse accelerometer signals collected during normal human walking.First,the self-adaptive feature of EEMD is utilised to decompose the accelerometer signals,thus sifting out several intrinsic mode functions(IMFs) at disparate scales.Then,gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity.Compared with the method based on the empirical mode decomposition(EMD),the EEMD-based method has the following advantages:it remarkably improves the detection rate of peak values hidden in the original accelerometer signal,even when the signal is severely contaminated by the intermittent noises;this method effectively prevents the phenomenon of mode mixing found in the process of EMD.And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method.Meanwhile,the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions.The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.     

Chaos based multiple image encryption using multiple canonical transforms

We propose a new method for multiple image encryption using linear canonical transforms and chaotic maps. Three linear canonical transforms and three chaotic maps are used in the proposed technique. The three linear canonical transforms that have been used are the fractional Fourier transform, the extended fractional Fourier transform and the Fresnel transform. The three chaotic maps that have been used are the tent map, the Kaplan-Yorke map and the Ikeda map. These chaotic maps are used to generate the random phase masks and these random phase masks are known as chaotic random phase masks. The mean square error and the signal to noise ratio have been calculated. Robustness of the proposed technique to blind decryption has been evaluated. Optical implementation of the technique has been proposed. Experimental and simulations results are presented to verify the validity of the proposed technique.     

On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four sub-tetrahedra that form a given pyramidal element.     

Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. PACS 21.60.Cs; 21.60.Fw; 21.60.-n; 03.65.Fd; 03.65.Ge; 03.65.-w     

The role of emitter quasi-bound state and scattering on intrinsic bistability in resonant tunneling diodes

Usually, numerical self-consistent calculations predict a much larger intrinsic bistability region than actually is measured in resonant tunneling diodes (RTDs). In addition, numerical calculations have shown that scattering in the well reduces bistability. We used a unified treatment of current flowing from continuum states and emitter quasi-bound states to show numerically and analytically that not only the scattering in the quantum well but also the scattering in the emitter reduces bistability. Moreover, within the Hartree approximation, bistability occurs by tunneling resonantly between emitter quasi-bound state and well quasi-bound state as a pitchfork bifurcation.     

Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models

Partition functions of critical 2D models on a torus can be derived from their microscopic formulation and their free field representation in the continuum limit. This is worked out explicitly for theO(n) andQ-state Potts model. Forn orQ integer we recover results obtained from conformal invariance, but our procedure also extends to nonintegral values. In the latter case the expansion on characters of the Virasoro algebra involves real coefficients of either sign. The operator content of both models is discussed in detail.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

The Weierstrass–Mandelbrot Process Revisited

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot–Weierstrass process is a complex fractional Brownian motion.     

红宝石Cr~(3+)∶Al_2O_3的电子云延伸效应及压力对电子云延伸效应影响(英文)

本文以 Cr3 +自由离子的 3 d电子径向波函数为基础 ,对 Cr3 +∶Al2 O3 中的电子云延伸效应进行了理论研究 ,引入了电子云延伸效应系数 κ,得到了 Cr3 +∶Al2 O3 中 Cr3 +离子的最优化 3 d电子径向波函数 .并研究了压力对电子云延伸效应系数κ的影响