Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump

This paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely unknown. Based on calculating the weak infinitesimal generator and combining Poincare inequality and Green formula, a stochastic stability criterion is given in terms of a set of linear matrix inequalities (LMIs) by the Schur complement lemma. Because of the existence of the neutral term, we need to construct Lyapunov functionals showing more complexity to handle the cross terms involving the Laplace operator. Finally, a numerical example is provided to support the validity of the mathematical results.

Pattern recognition of head movement based on mechanomyography and its application

The first part of this study investigated pattern recognition of head movements based on mechanomyography (MMG) signals. Four channel MMG signals were collected from the sternocleidomastoid (SCM) muscles and the splenius capitis (SPL) muscles in the subjects’ neck when they bowed the head, raised the head, side-bent to left, side-bent to right, turned to left and turned to right. The MMG signals were then filtered, normalized and divided using an unequal length segmentation algorithm into a single action frame. After extracting the energy features of the wavelet packet coefficients and the feature of the principal diagonal slices of the bispectrum, the dimension of the energy features were reduced by the Fisher linear discriminant analysis (FLDA). Finally, all the features were classified through the support vector machine (SVM) classifier. The recognition rate was up to 95.92%. On this basis, the second part of this study used the head movements to control a car model for simulating the control of a wheelchair, and the success rate was 85.74%.

Criteria for H-Matrices Based on γ−Diagonally Dominant Matrix

In this paper, we present a new practical criteria for H-matrix based on γ-diagonally dominant matrix. In order to make the judgment conditions convenient and effective, we give two new definitions, one is called strong and weak diagonally dominant degree, the other is called the sum of non-principal diagonal element for the matrix. Further, we obtain a new practical method for the determination of the H-matrix by combining the properties of γ-diagonally dominant matrix, constructing positive diagonal matrix, and adding the appropriate parameters. Finally, we offer numerical examples to verify the validity of the judgment conditions, corresponding numerical examples compared the new criteria and the existing results are presented to verify the advantages of the new determination method.

Optimized Electrode Locations for Wearable Single-Lead ECG Monitoring Devices: A Case Study Using WFEES Modules based on the LANS Method

Body surface potential mapping (BSPM) is a valuable tool for research regarding electrocardiograms (ECG). However, the BSPM system is limited by its large number of electrodes and wires, long installation time, and high computational complexity. In this paper, we designed a wearable four-electrode electrocardiogram-sensor (WFEES) module that measures six-channel ECGs simultaneously for ECG investigation. To reduce the testing lead number and the measurement complexity, we further proposed a method, the layered (A, N) square-based (LANS) method, to optimize the ECG acquisition and analysis process using WFEES modules for different applications. Moreover, we presented a case study of electrode location optimization for wearable single-lead ECG monitoring devices using WFEES modules with the LANS method. In this study, 102 sets of single-lead ECG data from 19 healthy subjects were analyzed. The signal-to-noise ratio of ECG, as well as the mean and coefficient of variation of QRS amplitude, was derived among different channels to determine the optimal electrode locations. The results showed that a single-lead electrode pair should be placed on the left chest above the electrode location of standard precordial leads V1 to V4. Additionally, the best orientation was the principal diagonal as the direction of the heart’s electrical axis.

A research on the time-varying stiffness of the ball bearing considering the time-varying number of laden balls and load distribution

In response to the fact that not all rolling balls are laden when the angular contact ball bearing working under the condition with certain combined loads especially when the axial preload is not large enough, an analytical method for the determination of the time-varying stiffness of angular contact ball bearing considering the effect of time-varying number of laden balls and load distribution is proposed in this paper. According to the definition of the stiffness, the time-varying stiffness under different sets of combined loads is obtained by the implicit function derivation method. Only the principal diagonal elements of the stiffness matrix are studied for the sake of simplicity. Several numerical examples are simulated and the simulation results indicate that the time-varying number of laden balls and load distribution have a significant effect on the stiffness. The period of the time-varying stiffness is consistent with the time required for the cage to rotate the angle between the adjacent rolling balls. The calculation of the ball bearing quasi-static model and the analytical method for the determination of the stiffness is verified by the existing references.

Honeybee navigation: critically examining the role of the polarization compass

Although it is widely accepted that honeybees use the polarized-light pattern of the sky as a compass for navigation, there is little direct evidence that this information is actually sensed during flight. Here, we ask whether flying bees can obtain compass cues derived purely from polarized light, and communicate this information to their nest-mates through the ‘waggle dance’. Bees, from an observation hive with vertically oriented honeycombs, were trained to fly to a food source at the end of a tunnel, which provided overhead illumination that was polarized either parallel to the axis of the tunnel, or perpendicular to it. When the illumination was transversely polarized, bees danced in a predominantly vertical direction with waggles occurring equally frequently in the upward or the downward direction. They were thus using the polarized-light information to signal the two possible directions in which they could have flown in natural outdoor flight: either directly towards the sun, or directly away from it. When the illumination was axially polarized, the bees danced in a predominantly horizontal direction with waggles directed either to the left or the right, indicating that they could have flown in an azimuthal direction that was 90° to the right or to the left of the sun, respectively. When the first half of the tunnel provided axial illumination and the second half transverse illumination, bees danced along all of the four principal diagonal directions, which represent four equally likely locations of the food source based on the polarized-light information that they had acquired during their journey. We conclude that flying bees are capable of obtaining and signalling compass information that is derived purely from polarized light. Furthermore, they deal with the directional ambiguity that is inherent in polarized light by signalling all of the possible locations of the food source in their dances, thus maximizing the chances of recruitment to it.

Method of Controlling the Inversion Quality of NMR T2 Spectrum

In order to improve the application effect of the NMR in Petroleum exploration and development, the quality of T2 spectrum inversion need to be controlled. Echo resolution matrix,T2 spectrum resolution matrix are deduced, the quality control index of T2 spectrum inversion is provided: the stretch coefficient, maximum, minimum, average and range of principal diagonal elements of resolution matrix. Calculating the inversion quality control index under different observation modes and choosing the observation mode of resolution matrix approximate to unit matrix for data acquisition can improve T2 spectrum inversion quality. Numerical experimentation indicate there is very good consistency between inversion quality and control index. Hence, it may direct the design before NMR data acquisition, control inversion quality of T2 spectrum

Structural Damage Detection Depending on Curvature Matrix of Change in Flexibility

Flexibility is more sensitive to structural damage than frequency or mode. Curvature matrix of change in flexibility is presented as a new index of nondestructive damage detection, which is derived from change in structural flexibilities calculated from before damaging and after damaging by means of difference calculation twice, firstly to columns, and then to rows. Therefore a new indicator called as δ Flexibility Curvature Matrix Diagonal (δFCMD) is constructed from the principal diagonal elements based on curvature matrix of change in flexibility. The numerical simulation examples indicate that the damage location and severity in structures, with single damage, multiple ones, slight ones and ones at the supports, can be detected efficiently for a cantilever beam, a fixed supported beam, a simply supported beams and so on by the indicator of δFCMD depending on only a few of lower order modes.

On absolute summability for double triangle matrices

A lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a double triangle T to be a bounded operator on ; i.e., T ∈ B () for the sequence space defined below. As special summability methods T we consider weighted mean and double Cesàro, (C, 1, 1), methods. As a corollary we obtain necessary and sufficient conditions for a double triangle T to be a bounded operator on the space of double sequences of bounded variation.

Eigenproblem for Jacobi matrices: hypergeometric series solution

We study the perturbative power series expansions of the eigenvalues and eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d . The (small) expansion parameters are the entries of the two diagonals of length d −1 sandwiching the principal diagonal that gives the unperturbed spectrum. The solution is found explicitly in terms of multivariable (Horn-type) hypergeometric series in 3 d −5 variables in the generic case. To derive the result, we first rewrite the spectral problem for the Jacobi matrix as an equivalent system of algebraic equations, which are then solved by the application of the multivariable Lagrange inversion formula. The corresponding Jacobi determinant is calculated explicitly. Explicit formulae are also found for any monomial composed of eigenvector's components.