## Abstract

This work is a review of current trends in the stray flux signal processing techniques applied to the diagnosis of electrical machines. Initially, a review of the most commonly used standard methods is performed in the diagnosis of failures in induction machines and using stray flux; and then specifically it is treated and performed the algorithms based on statistical analysis using cumulants and polyspectra. In addition, the theoretical foundations of the analyzed algorithms and examples applications are shown from the practical point of view where the benefits that processing can have using HOSA and its relationship with stray flux signal analysis, are illustrated.

## Abstract

A new approach to achieve fault diagnosis and prognosis of bearing based on hidden Markov model (HMM) with multi-features is proposed. Firstly, the time domain, frequency domain, and wavelet packet decomposition are utilized to extract the condition features of bearing vibration signals, and the PCA method is merged into multi-features to reduce their dimensionality. Then the low-dimensional features are processed to obtain the scalar probabilities of each bearing condition, which are multiplied to generate the observed values of HMM. The results reveal that the established approach can well diagnose fault conditions and achieve the remaining life estimation of bearing.

## Abstract

In this article, the study of qualitative properties of a special type of non-autonomous nonlinear second order ordinary differential equations containing Rayleigh damping and generalized Duffing functions is considered. General conditions for the stability and periodicity of solutions are deduced via fixed point theorems and the Lyapunov function method. A gyro dynamic application represented by the motion of axi-symmetric gyro mounted on a sinusoidal vibrating base is analyzed by the interpretation of its dynamical motion in terms of Euler’s angles via the deduced theoretical results. Moreover, the existence of homoclinic bifurcation and the transition to chaotic behaviour of the gyro motion in terms of main gyro parameters are proved. Numerical verifications of theoretical results are also considered.

## Abstract

In recent years, China’s environmental pollution is serious, manufacturing industry has become one of the main targets of government environmental regulation. This paper uses the SBM model to calculate efficiency value of 29 manufacturing industries from 2008 to 2017. The results show that the overall performance of environmental regulation in manufacturing industry is high (the average efficiency value is 0.7806), but it shows a declining trend. The efficiency of environmental regulation also varies widely. The government should consider focusing on the 11 industries with low SBM value in the next step to improve the performance of environmental regulation.

## Summary

Preliminary studies which may be of significance for research against coronaviruses, including SARS-CoV-2, which has caused an epidemic in China, are presented. An analysis was made of publicly available data that contain information about important metabolites neutralizing coronaviruses. Preliminary studies show that especially Ficus, barley, thistle and sundew should be additionally tested with the aim of producing medicines for coronavirus.

## Abstract

In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes 15 ordinary multiplications, 6 trivial multiplications by 2 (left-shifts), 21 additions, and 4 squarings of real numbers, while the proposed algorithm can compute the same result in only 14 real multiplications (or multipliers—in a hardware implementation case), 43 additions, 4 right-shifts (multiplications by 1/4), and 3 left-shifts (multiplications by 2).

## Abstract

A class of Clifford-valued high-order Hopfield neural networks (HHNNs) with state-dependent and leakage delays is considered. First, by using a continuation theorem of coincidence degree theory and the Wirtinger inequality, we obtain the existence of anti-periodic solutions of the networks considered. Then, by using the proof by contradiction, we obtain the global exponential stability of the anti-periodic solutions. Finally, two numerical examples are given to illustrate the feasibility of our results.

## Abstract

We propose a skeletonization algorithm that is based on an iterative points contraction. We make an observation that the local center that is obtained via optimizing the sum of the distance to *k* nearest neighbors possesses good properties of robustness to noise and incomplete data. Based on such an observation, we devise a skeletonization algorithm that mainly consists of two stages: points contraction and skeleton nodes connection. Extensive experiments show that our method can work on raw scans of real-world objects and exhibits better robustness than the previous results in terms of extracting topology-preserving curve skeletons.

## Abstract

The classic interval has precise borders *μ*-cuts, which the authors aim to do.

## Abstract

The paper concerns the properties of linear dynamical systems described by linear differential equations, excited by the Dirac delta function. A differential equation of the form a_{n}*x*(* ^{n}*)(

*t*)+···+a

_{1}

*x*′ (

*t*)+a

_{0}

*x*(

*t*)=

*b*

_{m}*u*(

*)(*

^{m}*t*)+···+

*b*

_{1}

*u′*(

*t*)+

*b*

_{0}

*u*(

*t*) is considered with

*a*

_{i}, b*0. In the paper we assume that the polynomials*

_{j}>*M*

*(*

_{n}*s*)=

*a*

_{n}*s*

*+ ··· +*

^{n}*a*

_{1}

*s*+

*a*

_{0}and

*L*

*(*

_{m}*s*)=

*b*

_{m}*s*

*+ ··· +*

^{m}*b*

_{1}

*s*+

*b*

_{0}partly interlace. The solution of the above equation is denoted by

*x*(

*t, L*

*,*

_{m}*M*

*). It is proved that the function*

_{n}*x*(

*t, L*

*,*

_{m}*M*

*) is nonnegative for*

_{n}*t*∈ (0, ∞), and does not have more than one local extremum in the interval (0, ∞) (Theorems 1, 3 and 4). Besides, certain relationships are proved which occur between local extrema of the function

*x*(

*t, L*

*,*

_{m}*M*

*), depending on the degree of the polynomial*

_{n}*M*

*(*

_{n}*s*) or

*L*

*(*

_{m}*s*) (Theorems 5 and 6).