CHARACTERIZATION OF MULTIPLIER SPACES WITH DAUBECHIES WAVELETS

We characterize the multiplier spaces from Sobolev spaces to L2 with Daubechles wavelets without using capacity.

Using the Wavelet as the Private Key for Encrypting the Watermark

Watermarking is an effective approach to the copyright protection of digital media such as audio, image, and video. By inspiration from cryptography and considering the immensity of the set of all possible wavelets, it is presented that in wavelet domain watermarking, the associated wavelet can be considered as the private key for encrypting the watermark so as to enhance the security of the embedded mark. This idea is partly supported by the fact that from computational complexity viewpoint, it is very time-consuming to search over the immense set of all candidate wavelets for the right one if no a priori knowledge is known about it. To verify our proposal, the standard image 'Lena' is first watermarked in a specific wavelet domain, the watermark recovery experiments are then conducted in the wavelet domain for a set of wavelets with the one used for mark embedded in it,separately. It follows from the experimental results that the mark can be recovered only in the right wavelet domain, which justifies the suggestion.

Spectral Analysis and Validation of Parietal Signals for Different Arm Movements

Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique technique to identify an ideal region of the human brain that generates signals responsible for muscular movements;perform statistical analysis to provide an absolute characterization of the signal and validate the obtained results using a prototype arm.This can enhance the practical implementation of these frequency extractions for future neuro-prosthetic applications and the characterization of neurological diseases like Parkinson’s disease(PD).To play out this handling method,electroencepha-logram(EEG)signals are gained while the subject is performing different wrist and elbow movements.Then,the frontal brain signals and just the parietal signals are separated from the obtained EEG signal by utilizing a band pass filter.Then,feature extraction is carried out using Fast Fourier Transform(FFT).Subse-quently,the extraction process is done by Daubechies(db4)and Haar wavelet(db1)in MATLAB and classified using the Levenberg-Marquardt Algorithm.The results of the frequency changes that occurred during various wrist move-ments in the parietal region are compared with the frequency changes that occurred in frontal EEG signals.This proposed algorithm also uses the deep learn-ing pattern analysis network to evaluate the matching sequence for each action that takes place.Maximum accuracy of 97.2%and maximum error range of 0.6684%are achieved during the analysis.Results of this research confirm that the Levenberg-Marquardt algorithm,along with the newly developed deep learn-ing hybrid PatternNet,provides a more accurate range of frequency changes than any other classifier used in previous works of literature.Based on the analysis,the peak-to-peak value is used to define the threshold for the prototype arm,which performs all the intended degrees of freedom(DOF),verifying the results.These results would aid the specialists in their decision-making by facilitating the ana-lysis and interpretation of brain signals in the field of neuroscience,specifically in tremor analysis in PD.

Characteristics of Surface Water Quality Affected by Agricultural Non-point Sources in Guigang City

[Objectives]To analyze the influence characteristics of surface water quality by agricultural non-point sources in Guigang City of Guangxi.[Methods]The daily concentration series of water quality indicators at three state-controlled monitoring stations in Guigang City from^(2)019 to 2021 was analyzed by using Daubechies(db)wavelet,and Morlet wavelet was used to analyze the daily average concentration of water quality indicators.Continuous wavelet transform(CWT)was used to analyze the monthly concentration series of water quality indicators at three state-controlled monitoring stations in Guigang City from^(2)014 to 2021.[Results]The Daubechies(db)wavelet analysis showed that the concentrations of COD_(Mn),TP,and TN had the maximum values during June-July and October-November,and there were spatial differences among monitoring stations(COD_(Mn) concentration exceeding the standard was the most serious in Shizui,and DO concentration not up to standard was the most in Thermal Power Plant,and NH_(3)-N,TP and TN exceeding the standard was the most in Wulin Ferry).Morlet results showed that principal period of wavelet variance graphs of COD_(Mn),NH_(3)-N,and TP was 340 d,and there was the same sub-period of 140 d,and principal period of wavelet variance graph of DO was 260 d.CWT results showed that COD_(Cr) had similar resonance periods of about 1-2 and 5-7 months;BOD 5 and COD_(Mn) was dominant by the resonance period of 1-4 months(2014-2017);DO had a similar resonance period of about 1-3 months;NH_(3)-N was dominant by the resonance period of 1-5 months.[Conclusions]The surface water quality of Guigang City was mainly affected by the residual nitrogen and phosphorus nutrients and pesticide residues from agricultural production activities.

Non-classical Algorithm for Time Series Prediction of the Range of Economic Phenomena With Regard to the Interaction of Financial Market Indicators

The aim of the article is to present non-clasical copyrighted algorithm for prediction of time series, presenting macroeconomic indicators and stock market indices. The algorithm is based on artificial neural networks and multi-resolution analysis （the algorithm is based on Daubechies wavelet）. However, the main feature of the algorithm, which gives a good quality of the forecasts, is all included in the series analysis division into, a few partial under-series and prediction dependence on a number of other economic series. The algorithm used for the prediction, is copyrighted algorithm, labeled M.H-D in this article. Application of the algorithm was performed on a series presenting WIG 20. The forecast of WIG 20 was conditional on trading the Dow Jones, DAX, Nikkei, Hang Seng, taking into account the sliding time window. As an example application of copyrighted model, the forecast of WIG 20 for a period of two years, one year, six month was appointed. An empirical example is described. It shows that the proposed model can predict index with the scale of two years, one year, a half year and other intervals. Precision of prediction is satisfactory. An average absolute percentage error of each forecast was： 0.0099%---for two-year forecasts WIG 20; 0.0552%--for the annual forecast WIG 20; and 0.1788%---for the six-month forecasts WIG 20.

Continuity of a Class of Calderón-Zygmund Operators on Certain Besov Spaces

In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.

A CHARACTERIZATION OF N-DIMENSIONAL DAUBECHIES TYPE TENSOR PRODUCT WAVELET

In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form. We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form. This helps us to explicate the difficulty of constructing the non-separable variate wavlet basis and to hint how to construct non-separable variate wavlet basis.

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.

SEMG-based fighter pilot muscle fatigue analysis and operation performance research

Fatigue has a tremendously adverse impact on pilot performance.This study aims to explore the Biceps Brachii(BB),Rectus Femoris(RF),Flexor Carpi Radialis(FCR),and Tibialis Anterior(TA)activities of fighter pilots in the early and late combat stages,and the target hitting time.A total of 13 volunteers were recruited to conduct simulated combats inside a real fighter cockpit.The surface Electromyography(sEMG)was collected from all volunteers in the initial and final 20s of flight,and the target hitting time during three simulated combats was recorded.The root mean square(RMS)values of right BB and TA were significantly higher than the left side values(p<0.001),while insignificant differences were found in the RMS values between the bilateral RF and FCR.Compared to the early flight period,the median frequency(MF)values of BB and TA were significantly lower during the late flight period,and the RMS values were significantly higher(p<0.047).Contrastively,the RMS values of FCR and RF differed insignificantly during the late flight period.Regarding the target hitting time,a significant difference was noted between task 1 and rask3.Subjects exhibit varying levels of muscle fatigue for different muscle groups before and after the flight.The muscle fatigue levels are asymmetrical on the left and right sides.Muscle fatigue might reduce the pilots'operational ability.This study provides a reference for fighter pilot fatigue protection and treatment.