The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec...The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.展开更多
The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets a...The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2（R, C^s×s） is constructed from the orthogonal multiple vector-valued wavelet packets.展开更多
In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar...In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.展开更多
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectra...Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.展开更多
In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly...In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly(effectively imposing a wavelet-spectrum weighting,often akin to an amplitude-squared bias).This redundancy degrades structural fidelity and amplitude balance yet is frequently overlooked.We(i)formalize the mechanism by which cross-correlation duplicates the source-wavelet amplitude effect in both migration and demigration,and(ii)introduce a source-equalized operator that removes the redundancy by deconvolving(or dividing by)the wavelet amplitude spectrum in the imaging condition and its demigration counterpart,while leaving phase/kinematics intact.Using a band-limited Ricker wavelet on a two-layer model and on Marmousi,we show that,if unmanaged,the redundant wavelet spectrum broadens main lobes,introduces ringing,and suppresses vertical resolution in migrated images,and inflates spectrum mismatches between demigrated and observed data even when peak times agree.With our correction,images recover observed-data-consistent bandwidth and sharpened interfaces,and demigrated data also exhibit improved spectrum conformity and reduced amplitude misfit.The results clarify when source amplitudes matter,why cross-correlation makes them redundantly matter,and how a lightweight spectral correction restores physically meaningful amplitude behavior in wave-equation migration/demigration.展开更多
In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the bo...In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.展开更多
In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector...In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.展开更多
Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)wi...Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)with another one's adjointC_(ψ)^(*)on the vector-valued Bergman spaceB_(1)(X)for formsC_(φ)C_(ψ)^(*)andC_(ψ)C_(φ)^(*).展开更多
Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain cri...Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.展开更多
If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we...If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.展开更多
Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-ban...Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-band spectra,hyperspectral technology has become a crucial tool to monitor crop diseases using remote sensing.However,existing continuous wavelet analysis(CWA)methods suffer from feature redundancy issues,while the continuous wavelet projection algorithm(CWPA),an optimization approach for feature selection,has not been fully validated to monitor plant diseases.This study utilized rice bacterial leaf blight(BLB)as an example by evaluating the performance of four wavelet basis functions-Gaussian2,Mexican hat,Meyer,andMorlet-within theCWAandCWPAframeworks.Additionally,the classification models were constructed using the k-nearest neighbors(KNN),randomforest(RF),and Naïve Bayes(NB)algorithms.The results showed the following:(1)Compared to traditional CWA,CWPA significantly reduced the number of required features.Under the CWPA framework,almost all the model combinations achieved maximum classification accuracy with only one feature.In contrast,the CWA framework required three to seven features.(2)Thechoice of wavelet basis functions markedly affected the performance of themodel.Of the four functions tested,the Meyer wavelet demonstrated the best overall performance in both the CWPA and CWA frameworks.(3)Under theCWPAframework,theMeyer-KNNandMeyer-NBcombinations achieved the highest overall accuracy of 93.75%using just one feature.In contrast,under the CWA framework,the CWA-RF combination achieved comparable accuracy(93.75%)but required six features.This study verified the technical advantages of CWPA for monitoring crop diseases,identified an optimal wavelet basis function selection scheme,and provided reliable technical support to precisely monitor BLB in rice(Oryza sativa).Moreover,the proposed methodological framework offers a scalable approach for the early diagnosis and assessment of plant stress,which can contribute to improved accuracy and timeliness when plant stress is monitored.展开更多
In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the ...In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the capacity of ViT to capture global features,it compromises the preservation of fine-grained local feature information.To address these challenges,we propose a spatial positional enhancement module and a wavelet transform enhancement module tailored for ViT models.These modules aim to reduce spatial positional information loss during the patch embedding process and enhance the model’s feature extraction capabilities.The spatial positional enhancement module reinforces spatial information in sequential data through convolutional operations and multi-scale feature extraction.Meanwhile,the wavelet transform enhancement module utilizes the multi-scale analysis and frequency decomposition to improve the ViT’s understanding of global and local image structures.This enhancement also improves the ViT’s ability to process complex structures and intricate image details.Experiments on CIFAR-10,CIFAR-100 and ImageNet-1k datasets are done to compare the proposed method with advanced classification methods.The results show that the proposed model achieves a higher classification accuracy,confirming its effectiveness and competitive advantage.展开更多
Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection...Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection.The laser radar echo signal is vulnerable to background light and electronic thermal noise.While single-photon LiDAR can effectively reduce background light interference,electronic thermal noise remains a significant challenge,especially at long distances and in environments with a low signal-to-noise ratio(SNR).However,conventional denoising methods cannot achieve satisfactory results in this case.In this paper,a novel adaptive continuous threshold wavelet denoising algorithm is proposed to filter out the noise.The algorithm features an adaptive threshold and a continuous threshold function.The adaptive threshold is dynamically adjusted according to the wavelet decomposition level,and the continuous threshold function ensures continuity with lower constant error,thus optimizing the denoising process.Simulation results show that the proposed algorithm has excellent performance in improving SNR and reducing root mean square error(RMSE)compared with other algorithms.Experimental results show that denoising of an actual LiDAR echo signal results in a 4.37 dB improvement in SNR and a 39.5%reduction in RMSE.The proposed method significantly enhances the ability of single-photon LiDAR to detect weak signals.展开更多
A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this wor...A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.展开更多
Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.展开更多
Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embe...Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.展开更多
Predicting the currency exchange rate is crucial for financial agents,risk managers,and policymakers.Traditional approaches use publicly announced news on macroeconomic and financial variables as predictors of currenc...Predicting the currency exchange rate is crucial for financial agents,risk managers,and policymakers.Traditional approaches use publicly announced news on macroeconomic and financial variables as predictors of currency exchange.However,the rise of social media may have changed the source of information.For instance,tweets can help investors make informed decisions about the foreign exchange(FX)market by reflecting market sentiment and opinion.From another aspect,changes in currency exchange may incite agents to post tweets.Are tweets good predictors of currency exchange?Is the relationship between tweets and currency exchange bidirectional?We investigate the comovement/causality between the number of#dolar(“enflasyon”resp.)tweets and USDTRY currency exchange using wavelet coherence and transfer entropy(TE)to answer these questions.Wavelet coherence allows us to determine the relationship between the number of tweets and the USDTRY rate by considering the time–frequency domain.TE enables us to quantify the net information flow between the number of tweets and USDTRY.Data from October 2020 to March 2022 were used.The obtained results remain robust regardless of the frequency of retained data(daily or hourly)and the methods used(wavelet or TE).Based on our results,USDTRY is correlated with the number of#dolar tweets(#inflation)mainly in the short run and a few times in the medium run.These relationships change through time and frequency(wavelet analysis results).However,the results from TE indicate a bidirectional relationship between the#dolar(#inflation)tweets number and the USDTRY exchange rate.The influence of the exchange rate on the number of tweets is highly pronounced.Financial agents,risk managers,policymakers,and investors should then pay moderate attention to the number of#dolar(#inflation)tweets in trading/forecasting the USD–TRY exchange rate.展开更多
In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-establis...In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-established Haar wavelet collocation method(HWCM)which has been much popular among researchers and has many applications in literature.Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM,depending on parameterλfor values 1 and 2,respectively.Several problems available in the literature of both,Volterra and Fredholm type of IDEs,are tested and compared with HWCM to illustrate the performance of our proposed method.展开更多
基金the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)the Items of Xi’an University of Architecture and Technology(RC0701JC0718)
文摘The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.
基金the National Natural Science Foundation of China (10371105).
文摘The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2（R, C^s×s） is constructed from the orthogonal multiple vector-valued wavelet packets.
基金Foundation item： Supported by the Natural Science Foundation of China（10571113）
文摘In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.
基金Supported by Natural Science Foundation of Henan Province（0511013500）
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
基金supported by the Henan Province Key R&D Project under Grant 241111210400the Henan Provincial Science and Technology Research Project under Grants 252102211047,252102211062,252102211055 and 232102210069+2 种基金the Jiangsu Provincial Scheme Double Initiative Plan JSS-CBS20230474,the XJTLU RDF-21-02-008the Science and Technology Innovation Project of Zhengzhou University of Light Industry under Grant 23XNKJTD0205the Higher Education Teaching Reform Research and Practice Project of Henan Province under Grant 2024SJGLX0126。
文摘Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.
基金supported by the National Natural Science Foundation of China(42430303)Strategy Priority Research Program(Category B)of the Chinese Academy of Sciences(XDB0710000)+2 种基金National Natural Science Foundation of China(42288201)the National Key R&D Program of China(2023YFF0803203)the IGGCAS start-up funding(Grant No.E251510101).
文摘In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly(effectively imposing a wavelet-spectrum weighting,often akin to an amplitude-squared bias).This redundancy degrades structural fidelity and amplitude balance yet is frequently overlooked.We(i)formalize the mechanism by which cross-correlation duplicates the source-wavelet amplitude effect in both migration and demigration,and(ii)introduce a source-equalized operator that removes the redundancy by deconvolving(or dividing by)the wavelet amplitude spectrum in the imaging condition and its demigration counterpart,while leaving phase/kinematics intact.Using a band-limited Ricker wavelet on a two-layer model and on Marmousi,we show that,if unmanaged,the redundant wavelet spectrum broadens main lobes,introduces ringing,and suppresses vertical resolution in migrated images,and inflates spectrum mismatches between demigrated and observed data even when peak times agree.With our correction,images recover observed-data-consistent bandwidth and sharpened interfaces,and demigrated data also exhibit improved spectrum conformity and reduced amplitude misfit.The results clarify when source amplitudes matter,why cross-correlation makes them redundantly matter,and how a lightweight spectral correction restores physically meaningful amplitude behavior in wave-equation migration/demigration.
基金Supported by the National Natural Science Foundation of China(11271330,11226104,11226108)the Jiangxi Natural Science Foundation of China(20114BAB211007)the Science Foundation of Jiangxi Education Department(GJJ13703)
文摘In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.
基金supported by the National Natural Science Foundation of China(10471107)RFDP of Higher Education(20060486001)
文摘In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.
基金Supported by the National Natural Science Foundation of China(19771063)
文摘Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)with another one's adjointC_(ψ)^(*)on the vector-valued Bergman spaceB_(1)(X)for formsC_(φ)C_(ψ)^(*)andC_(ψ)C_(φ)^(*).
文摘Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.
文摘If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.
基金supported by the‘Pioneer’and‘Leading Goose’R&D Program of Zhejiang(Grant No.2023C02018)Zhejiang Provincial Natural Science Foundation of China(Grant No.LTGN23D010002)+2 种基金National Natural Science Foundation of China(Grant No.42371385)Funds of the Natural Science Foundation of Hangzhou(Grant No.2024SZRYBD010001)Nanxun Scholars Program of ZJWEU(Grant No.RC2022010755).
文摘Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-band spectra,hyperspectral technology has become a crucial tool to monitor crop diseases using remote sensing.However,existing continuous wavelet analysis(CWA)methods suffer from feature redundancy issues,while the continuous wavelet projection algorithm(CWPA),an optimization approach for feature selection,has not been fully validated to monitor plant diseases.This study utilized rice bacterial leaf blight(BLB)as an example by evaluating the performance of four wavelet basis functions-Gaussian2,Mexican hat,Meyer,andMorlet-within theCWAandCWPAframeworks.Additionally,the classification models were constructed using the k-nearest neighbors(KNN),randomforest(RF),and Naïve Bayes(NB)algorithms.The results showed the following:(1)Compared to traditional CWA,CWPA significantly reduced the number of required features.Under the CWPA framework,almost all the model combinations achieved maximum classification accuracy with only one feature.In contrast,the CWA framework required three to seven features.(2)Thechoice of wavelet basis functions markedly affected the performance of themodel.Of the four functions tested,the Meyer wavelet demonstrated the best overall performance in both the CWPA and CWA frameworks.(3)Under theCWPAframework,theMeyer-KNNandMeyer-NBcombinations achieved the highest overall accuracy of 93.75%using just one feature.In contrast,under the CWA framework,the CWA-RF combination achieved comparable accuracy(93.75%)but required six features.This study verified the technical advantages of CWPA for monitoring crop diseases,identified an optimal wavelet basis function selection scheme,and provided reliable technical support to precisely monitor BLB in rice(Oryza sativa).Moreover,the proposed methodological framework offers a scalable approach for the early diagnosis and assessment of plant stress,which can contribute to improved accuracy and timeliness when plant stress is monitored.
基金National Natural Science Foundation of China(No.62176052)。
文摘In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the capacity of ViT to capture global features,it compromises the preservation of fine-grained local feature information.To address these challenges,we propose a spatial positional enhancement module and a wavelet transform enhancement module tailored for ViT models.These modules aim to reduce spatial positional information loss during the patch embedding process and enhance the model’s feature extraction capabilities.The spatial positional enhancement module reinforces spatial information in sequential data through convolutional operations and multi-scale feature extraction.Meanwhile,the wavelet transform enhancement module utilizes the multi-scale analysis and frequency decomposition to improve the ViT’s understanding of global and local image structures.This enhancement also improves the ViT’s ability to process complex structures and intricate image details.Experiments on CIFAR-10,CIFAR-100 and ImageNet-1k datasets are done to compare the proposed method with advanced classification methods.The results show that the proposed model achieves a higher classification accuracy,confirming its effectiveness and competitive advantage.
基金funded by the National Key R&D Program of China(Grant No.2022YFC3300705)the National Natural Science Foundation of China(Grant Nos.62203056,12202048,and 62201056).
文摘Atmospheric aerosols are the primary contributors to environmental pollution.As such aerosols are micro-to nanosized particles invisible to the naked eye,it is necessary to utilize LiDAR technology for their detection.The laser radar echo signal is vulnerable to background light and electronic thermal noise.While single-photon LiDAR can effectively reduce background light interference,electronic thermal noise remains a significant challenge,especially at long distances and in environments with a low signal-to-noise ratio(SNR).However,conventional denoising methods cannot achieve satisfactory results in this case.In this paper,a novel adaptive continuous threshold wavelet denoising algorithm is proposed to filter out the noise.The algorithm features an adaptive threshold and a continuous threshold function.The adaptive threshold is dynamically adjusted according to the wavelet decomposition level,and the continuous threshold function ensures continuity with lower constant error,thus optimizing the denoising process.Simulation results show that the proposed algorithm has excellent performance in improving SNR and reducing root mean square error(RMSE)compared with other algorithms.Experimental results show that denoising of an actual LiDAR echo signal results in a 4.37 dB improvement in SNR and a 39.5%reduction in RMSE.The proposed method significantly enhances the ability of single-photon LiDAR to detect weak signals.
文摘A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
基金supported by the researcher supporting Project number(RSPD2025R636),King Saud University,Riyadh,Saudi Arabia.
文摘Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.
文摘Predicting the currency exchange rate is crucial for financial agents,risk managers,and policymakers.Traditional approaches use publicly announced news on macroeconomic and financial variables as predictors of currency exchange.However,the rise of social media may have changed the source of information.For instance,tweets can help investors make informed decisions about the foreign exchange(FX)market by reflecting market sentiment and opinion.From another aspect,changes in currency exchange may incite agents to post tweets.Are tweets good predictors of currency exchange?Is the relationship between tweets and currency exchange bidirectional?We investigate the comovement/causality between the number of#dolar(“enflasyon”resp.)tweets and USDTRY currency exchange using wavelet coherence and transfer entropy(TE)to answer these questions.Wavelet coherence allows us to determine the relationship between the number of tweets and the USDTRY rate by considering the time–frequency domain.TE enables us to quantify the net information flow between the number of tweets and USDTRY.Data from October 2020 to March 2022 were used.The obtained results remain robust regardless of the frequency of retained data(daily or hourly)and the methods used(wavelet or TE).Based on our results,USDTRY is correlated with the number of#dolar tweets(#inflation)mainly in the short run and a few times in the medium run.These relationships change through time and frequency(wavelet analysis results).However,the results from TE indicate a bidirectional relationship between the#dolar(#inflation)tweets number and the USDTRY exchange rate.The influence of the exchange rate on the number of tweets is highly pronounced.Financial agents,risk managers,policymakers,and investors should then pay moderate attention to the number of#dolar(#inflation)tweets in trading/forecasting the USD–TRY exchange rate.
文摘In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-established Haar wavelet collocation method(HWCM)which has been much popular among researchers and has many applications in literature.Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM,depending on parameterλfor values 1 and 2,respectively.Several problems available in the literature of both,Volterra and Fredholm type of IDEs,are tested and compared with HWCM to illustrate the performance of our proposed method.
