Group Theoretical Description of the Periodic System

The group theoretical description of the periodic system of elements in the framework of the Rumer–Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract C*-algebra. It is shown that various concrete implementations of the operator algebra depend on the structure of the generators of the fundamental symmetry group attached to the energy operator. In the case of the generators of the complex shell of a group algebra of a conformal group, the spectrum of states of a single quantum system is given in the framework of the basic representation of the Rumer–Fet group, which leads to a group-theoretic interpretation of the Mendeleev’s periodic system of elements. A mass formula is introduced that allows giving the termwise mass splitting for the main multiplet of the Rumer–Fet group. The masses of elements of the Seaborg table (eight-periodic extension of the Mendeleev table) are calculated starting from the atomic number Z=3 and going to Z=220. The continuation of the Seaborg homology between lanthanides and actinides is established with the group of superactinides. A 10-periodic extension of the periodic table is introduced in the framework of the group-theoretic approach. The multiplet structure of the extended table’s periods is considered in detail. It is shown that the period lengths of the system of elements are determined by the structure of the basic representation of the Rumer–Fet group. The theoretical masses of the elements of 10th and 11th periods are calculated starting from Z=221 and going to to Z=364. The concept of hypertwistor is introduced.

A frequency-weighted energy operator and swarm decomposition for bearing fault diagnosis

The weak fault characteristics of rolling bearings are difficult to identify due to strong background noise. To address this issue, a bearing fault detection scheme combining swarm decomposition (SWD) and frequency-weighted energy operator (FWEO) is presented. First, SWD is applied to decompose the bearing fault signal into single mode components. Then, a new evaluation index termed LEP is constructed by combining the advantages of envelope entropy, Pearson correlation coefficient and L-kurtosis, and it is utilized to choose the sensitive component containing the richest bearing fault characteristics. Finally, FWEO is employed for extracting the bearing fault features from the sensitive component. Simulation and experimental analyses indicate that the LEP index has better performance than the L-kurtosis index in determining the sensitive component. The method has the effect of suppressing noise and enhancing impulse characteristics, which is superior to the SWD-based envelope demodulation method.

Weak Fault Feature Extraction of Rolling Bearing Based on SVMD and Improved MOMEDA

In order to solve the problem that it is very difficult to extract fault features directly from the weak impact component of early fault signal of rolling bearing, a method combining continuous variational mode decomposition (SVMD) with modified MOMEDA based on Teager energy operator is proposed. Firstly, the low resonance impulse component in the fault signal is separated from the harmonic component and noise by SVMD, and then the Teager energy operator is used to enhance the impulse feature in the low resonance component to ensure that the accurate fault period is selected by the MOMOEDA algorithm. After further noise reduction by MOMEDA, the envelope spectrum of the signal is analyzed, and finally the fault location is determined. The results of simulation and experimental data show that this method can accurately and effectively extract the characteristic frequency of rolling bearing weak fault.

Voltage Flicker Parameter Estimation Based On Improved Analytic Energy Operator And Novel K-B Mutual Convolution Window

<a></a>It is difficult to measure voltage flicker parameter accurately and in real time under a complex power grid environment, a voltage flicker envelope extraction algorithm based on multi-point differential improved analytic energy operator (IAEO) is proposed, which simplified formula for extracting flicker envelope and a novel K-B optimal mutual convolution window function is constructed. Then, the correction formula of flicker amplitude and frequency is derived based on the three-spectral line interpolation of the novel K-B optimized mutual convolution window, and the estimation algorithm of voltage flicker parameter is proposed based on the IAEO and the novel K-B mutual convolution window. Finally, a voltage-flicker-parameter-estimation platform based on virtual instrument is developed. The simulation and experimental results show that the proposed algorithm can effectively measure voltage flicker parameter under single frequency modulation, multi-frequency modulation and fundamental frequency fluctuation. In addition, it can effectively overcome harmonics, interharmonics and noise interference. Compared with the existing estimation algorithm, the flicker envelope extraction is simpler, the measurement result is more accurate, and it is easy to implement embedded.<br>

Voltage Flicker Parameter Estimation Based On Improved Analytic Energy Operator And Novel K-B Mutual Convolution Window

<a></a>It is difficult to measure voltage flicker parameter accurately and in real time under a complex power grid environment, a voltage flicker envelope extraction algorithm based on multi-point differential improved analytic energy operator (IAEO) is proposed, which simplified formula for extracting flicker envelope and a novel K-B optimal mutual convolution window function is constructed. Then, the correction formula of flicker amplitude and frequency is derived based on the three-spectral line interpolation of the novel K-B optimized mutual convolution window, and the estimation algorithm of voltage flicker parameter is proposed based on the IAEO and the novel K-B mutual convolution window. Finally, a voltage-flicker-parameter-estimation platform based on virtual instrument is developed. The simulation and experimental results show that the proposed algorithm can effectively measure voltage flicker parameter under single frequency modulation, multi-frequency modulation and fundamental frequency fluctuation. In addition, it can effectively overcome harmonics, interharmonics and noise interference. Compared with the existing estimation algorithm, the flicker envelope extraction is simpler, the measurement result is more accurate, and it is easy to implement embedded.<br>

A Low Power 1024-Channels Spike Detector Using Latch-Based RAM for Real-Time Brain Silicon Interfaces

High-density microelectrode arrays allow the neuroscientist to study a wider neurons population, however, this causes an increase of communication bandwidth. Given the limited resources available for an implantable silicon interface, an on-fly data reduction is mandatory to stay within the power/area constraints. This can be accomplished by implementing a spike detector aiming at sending only the useful information about spikes. We show that the novel non-linear energy operator called ASO in combination with a simple but robust noise estimate, achieves a good trade-off between performance and consumption. The features of the investigated technique make it a good candidate for implantable BMIs. Our proposal is tested both on synthetic and real datasets providing a good sensibility at low SNR. We also provide a 1024-channels VLSI implementation using a Random-Access Memory composed by latches to reduce as much as possible the power consumptions. The final architecture occupies an area of 2.3 mm2, dissipating 3.6 µW per channels. The comparison with the state of art shows that our proposal finds a place among other methods presented in literature, certifying its suitability for BMIs.

ON THE SPECTRUM OF THE TWO-PARTICLE SCHRÖDINGER OPERATOR WITH POINT POTENTIAL: ONE DIMENTIONAL CASE

In the paper a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schr\"{o}\-dinger operator (energy operator) $h_\varepsilon$ depending on $\varepsilon,$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The main results of the work are based to the study of the operator $h_\varepsilon.$ First the essential spectrum is described. The existence of unique negative eigenvalue of the Schr\"{o}dinger operator is proved. Further, this eigenvalue and corresponding eigenfunction are found.

Electromagnetic Reflection Field Detection Based on TEO

Active electromagnetic detection explores targets using electromagnetic reflection field of metal objects. In view of the detection of active electromagnetic by detecting target reflection field, a Teager energy operator(TEO) is adopted to improve the electromagnetic reflection amplitude and instantaneous frequency detection method, the method of theoretical description and simulation verification has also carried out in this paper. Results show that this method is able to track the change of the single frequency signal of electromagnetic reflection field with good effect. It is also able to provide full details of the judgment to confirm the target. This method is simple and convenient for real-time processing, and has good application value.

On the position-dependent mass Schrödinger equation for Mie-type potentials

The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.