Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that th...Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l1 provided that the following two conditions are satisfied： （1） X＊ contains a subspace isomorphic to l1; and （2） X＊ contains a separable norming subspace.展开更多
The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but i...The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm.展开更多
Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small targe...Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.展开更多
In Morocco,hydrological and hydrobiological surveys of wadis,river and stream are rare.In this research,we plan to attempt to characterize the physico-chemistry of surface waters of sixteen stations sampled at the lev...In Morocco,hydrological and hydrobiological surveys of wadis,river and stream are rare.In this research,we plan to attempt to characterize the physico-chemistry of surface waters of sixteen stations sampled at the level of the Sebou basin during the period 2013-2023.The diagnosis showed that this natural watercourse is highly enriched in oce-anic salts.A large fluctuation in the chemical nature of the waters was recorded,as well as electrical conductivity(EC),which oscillates between 629 and 22,766μS/cm.Hydrogen Potential ranges from 8.01 to 8.79 while remaining basic.Nitrate(NO3-)concentrations range from a maximum of 886.9 mg/l to a minimum of 0.24 mg/l.Similarly,the am-monium concentration varies from 0.04 to 15.34 mg/l.It was also noted that the waters were very rich in chloride ions(860.27 to 145.55 mg/l),in sodium Na+ion(51 to 2,530 mg/l),in sulfate ions SO4--(441.4 to 37.62 mg/l),in calcium ions Ca2+(97.6 to 1,072.8 mg/l)and in magnesium ions Mg2+(631.2 to 17.28 mg/l)which explains the high hardness of these waters.The concentrations of potassium ions(K+)range from 2.54 to 17.55 mg/l.The high alkalinity is due to the high concentrations of bicarbonate ions(75.64 to 362.34 mg/l).Our study concludes that the waters of the Sebou re-main below the irrigation threshold authorized by Moroccan law when moving away from its Atlantic estuary.They are too degraded and we suggest that urban and industrial wastewater be pre-treated as a priority to reduce natural environment.展开更多
A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values.This method achieves...A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values.This method achieves precise adjustment of the network structure by constructing a preliminary random network model and introducing small-world network characteristics and combines L1 norm minimization regularization techniques to control model complexity and optimize the inference process of variable dependencies.In the experiment of game network reconstruction,when the success rate of the L1 norm minimization model’s existence connection reconstruction reaches 100%,the minimum data required is about 40%,while the minimum data required for a sparse Bayesian learning network is about 45%.In terms of operational efficiency,the running time for minimizing the L1 normis basically maintained at 1.0 s,while the success rate of connection reconstruction increases significantly with an increase in data volume,reaching a maximum of 13.2 s.Meanwhile,in the case of a signal-to-noise ratio of 10 dB,the L1 model achieves a 100% success rate in the reconstruction of existing connections,while the sparse Bayesian network had the highest success rate of 90% in the reconstruction of non-existent connections.In the analysis of actual cases,the maximum lift and drop track of the research method is 0.08 m.The mean square error is 5.74 cm^(2).The results indicate that this norm minimization-based method has good performance in data efficiency and model stability,effectively reducing the impact of outliers on the reconstruction results to more accurately reflect the actual situation.展开更多
The application of generative artificial intelligence(GAI)in the judicial domain represents an innovative approach to achieving digital justice.GAI’s functionalities are primarily exhibited in the enhancement of judi...The application of generative artificial intelligence(GAI)in the judicial domain represents an innovative approach to achieving digital justice.GAI’s functionalities are primarily exhibited in the enhancement of judicial efficiency,improving the accuracy and fairness of adjudications,promoting the uniform application of the law,and enhancing transparency and engagement in judicial processes.However,these advancements are accompanied by potential risks and challenges in technology,adjudication,and ethics.It is thus essential to strengthen privacy protection during the processing and transmission of data,ensure data security and confidentiality,and establish and refine clear legal norms regarding the roles,responsibilities,and legal obligations of GAI in judicial settings.In addition,ethical guidelines that delineate the behavioral boundaries and value orientations of GAI need to be formulated.Collectively,these elements can form a trinary model of technical controls,legal norms,and ethical constraints,to facilitate the modernization and intelligent development of the judicial system.展开更多
In the December 2025 issue of the Journal of Sport and Health Science,Tomkinson et al.^(1)present international norms for adult handgrip strength(HGS)developed from a systematic review of 100 studies with 2.4 million ...In the December 2025 issue of the Journal of Sport and Health Science,Tomkinson et al.^(1)present international norms for adult handgrip strength(HGS)developed from a systematic review of 100 studies with 2.4 million adults aged 20 to 100+years from 69 countries and regions.Twenty-eight interna-tional handGRIP Strength(iGRIPS)researchers contributed to the study.展开更多
Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain informat...Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain information.To address this challenge,this study presents a novel multi-criteria decision-making(MCDM)approach based on picture fuzzy hypersoft sets(PFHSS),integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators.The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties,such as idempotency,monotonicity,and boundedness.The decision-making model system-atically incorporates both benefit and cost-type criteria,enabling more nuanced evaluations in complex social or environmental decision problems.To enhance interpretability and practical relevance,the study conducts a sensitivity analysis on the Schweizer-Sklar parameter(Δ).The results show that varyingΔaffects the strictness of aggregation,thereby influencing the ranking stability of alternatives.A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness,expressiveness,and adaptability of the proposed approach.Notably,the use of picture fuzzy sets allows for the inclusion of positive,neutral,and negative memberships,offering a richer representation of expert opinions compared to traditional models.A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method.The analysis confirms that the approach yields consistent and interpretable results,even under varying degrees of decision uncertainty.Overall,this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes.展开更多
Lethal autonomous weapon systems(LAWS)have become a prominent issue in global security governance.However,significant divergences remain among the world's major countries regarding their regulation:some support re...Lethal autonomous weapon systems(LAWS)have become a prominent issue in global security governance.However,significant divergences remain among the world's major countries regarding their regulation:some support restrictions,while others oppose any binding rules,and there are also countries adopting a neutral stance,though their choices are subject to external pressure.In the foreseeable future,the deployment of LAWS will increase further,raising the risk of arms races,with international support for regulating these weapons gaining strength.Yet,establishing legally binding international rules within the United Nations(UN)framework remains a distant prospect.Given this backdrop,China should continue to actively participate in international norms setting concerning LAWS under UN auspices and deepen coordination and cooperation with other countries towards more applicable norms and global governance frameworks.展开更多
Table manners are important in manycultures.Inmost countries,youwait untileveryone has food before eating.Youalso don't put your elbows on the table.It's not polite to eat too fast.And youshouldn't talk wi...Table manners are important in manycultures.Inmost countries,youwait untileveryone has food before eating.Youalso don't put your elbows on the table.It's not polite to eat too fast.And youshouldn't talk with food in yourmouth orchew with your mouth open.展开更多
BACKGROUND Type 2 diabetes mellitus(T2DM)is increasing rapidly in Pakistan,especially among socioeconomically disadvantaged populations.While clinical care remains central,social determinants such as poverty,gender no...BACKGROUND Type 2 diabetes mellitus(T2DM)is increasing rapidly in Pakistan,especially among socioeconomically disadvantaged populations.While clinical care remains central,social determinants such as poverty,gender norms,and mistrust in healthcare critically shape disease outcomes.AIM To synthesize qualitative evidence on how these factors influence the experience and management of T2DM in Pakistan.METHODS Following PRISMA guidelines,a systematic review of qualitative studies published between 2000 and 2025 was conducted on February 25,2025 using PubMed,CINAHL,MEDLINE Plus,and PakMediNet.Eleven studies exploring socioeconomic influences on T2DM care and self-management in Pakistan were included.Thematic synthesis was used to identify key patterns.Quality was appraised using the Joanna Briggs Institute Checklist for Qualitative Research.RESULTS Three major themes were identified:(1)Economic insecurity.High cost of treatment,poor rural infrastructure,and food insecurity hinder access and adherence;(2)Sociocultural and gender norms.Restricted mobility of females,family control over health decisions,and fatalistic beliefs delay care;and(3)Knowledge gaps and mistrust.A lack of culturally appropriate education,reliance on traditional remedies,and distrust in public health systems reduce compliance.These intersecting barriers collectively impede effective diabetes management.CONCLUSION T2DM in Pakistan is driven by entrenched social and economic barriers.Addressing it requires culturally sensitive,equity-oriented strategies that go beyond biomedical models.Policy reforms should focus on affordability,rural outreach,and inclusive health education.Future research should engage marginalized voices through participatory methods.展开更多
To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the infl...To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.展开更多
Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this...Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.展开更多
This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere.By implementing the minimum norm tensor principle,we rigorously estimate the squared norm o...This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere.By implementing the minimum norm tensor principle,we rigorously estimate the squared norm of the quadratic gradient term associated with the Möbius second fundamental form.This analysis yields a critical inequality governing the geometric config-uration.Leveraging this inequality,we subsequently prove a Pinching theorem characterizing the eigenvalues of the Blaschke tensor.展开更多
文摘Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l1 provided that the following two conditions are satisfied： （1） X＊ contains a subspace isomorphic to l1; and （2） X＊ contains a separable norming subspace.
文摘The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm.
基金Supported by the Key Laboratory Fund for Equipment Pre-Research(6142207210202)。
文摘Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.
文摘In Morocco,hydrological and hydrobiological surveys of wadis,river and stream are rare.In this research,we plan to attempt to characterize the physico-chemistry of surface waters of sixteen stations sampled at the level of the Sebou basin during the period 2013-2023.The diagnosis showed that this natural watercourse is highly enriched in oce-anic salts.A large fluctuation in the chemical nature of the waters was recorded,as well as electrical conductivity(EC),which oscillates between 629 and 22,766μS/cm.Hydrogen Potential ranges from 8.01 to 8.79 while remaining basic.Nitrate(NO3-)concentrations range from a maximum of 886.9 mg/l to a minimum of 0.24 mg/l.Similarly,the am-monium concentration varies from 0.04 to 15.34 mg/l.It was also noted that the waters were very rich in chloride ions(860.27 to 145.55 mg/l),in sodium Na+ion(51 to 2,530 mg/l),in sulfate ions SO4--(441.4 to 37.62 mg/l),in calcium ions Ca2+(97.6 to 1,072.8 mg/l)and in magnesium ions Mg2+(631.2 to 17.28 mg/l)which explains the high hardness of these waters.The concentrations of potassium ions(K+)range from 2.54 to 17.55 mg/l.The high alkalinity is due to the high concentrations of bicarbonate ions(75.64 to 362.34 mg/l).Our study concludes that the waters of the Sebou re-main below the irrigation threshold authorized by Moroccan law when moving away from its Atlantic estuary.They are too degraded and we suggest that urban and industrial wastewater be pre-treated as a priority to reduce natural environment.
基金supported by the Scientific and Technological Developing Scheme of Jilin Province,China(No.20240101371JC)the National Natural Science Foundation of China(No.62107008).
文摘A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values.This method achieves precise adjustment of the network structure by constructing a preliminary random network model and introducing small-world network characteristics and combines L1 norm minimization regularization techniques to control model complexity and optimize the inference process of variable dependencies.In the experiment of game network reconstruction,when the success rate of the L1 norm minimization model’s existence connection reconstruction reaches 100%,the minimum data required is about 40%,while the minimum data required for a sparse Bayesian learning network is about 45%.In terms of operational efficiency,the running time for minimizing the L1 normis basically maintained at 1.0 s,while the success rate of connection reconstruction increases significantly with an increase in data volume,reaching a maximum of 13.2 s.Meanwhile,in the case of a signal-to-noise ratio of 10 dB,the L1 model achieves a 100% success rate in the reconstruction of existing connections,while the sparse Bayesian network had the highest success rate of 90% in the reconstruction of non-existent connections.In the analysis of actual cases,the maximum lift and drop track of the research method is 0.08 m.The mean square error is 5.74 cm^(2).The results indicate that this norm minimization-based method has good performance in data efficiency and model stability,effectively reducing the impact of outliers on the reconstruction results to more accurately reflect the actual situation.
文摘The application of generative artificial intelligence(GAI)in the judicial domain represents an innovative approach to achieving digital justice.GAI’s functionalities are primarily exhibited in the enhancement of judicial efficiency,improving the accuracy and fairness of adjudications,promoting the uniform application of the law,and enhancing transparency and engagement in judicial processes.However,these advancements are accompanied by potential risks and challenges in technology,adjudication,and ethics.It is thus essential to strengthen privacy protection during the processing and transmission of data,ensure data security and confidentiality,and establish and refine clear legal norms regarding the roles,responsibilities,and legal obligations of GAI in judicial settings.In addition,ethical guidelines that delineate the behavioral boundaries and value orientations of GAI need to be formulated.Collectively,these elements can form a trinary model of technical controls,legal norms,and ethical constraints,to facilitate the modernization and intelligent development of the judicial system.
文摘In the December 2025 issue of the Journal of Sport and Health Science,Tomkinson et al.^(1)present international norms for adult handgrip strength(HGS)developed from a systematic review of 100 studies with 2.4 million adults aged 20 to 100+years from 69 countries and regions.Twenty-eight interna-tional handGRIP Strength(iGRIPS)researchers contributed to the study.
基金supported by the National Natural Science Foundation of China(No.62172095).
文摘Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain information.To address this challenge,this study presents a novel multi-criteria decision-making(MCDM)approach based on picture fuzzy hypersoft sets(PFHSS),integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators.The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties,such as idempotency,monotonicity,and boundedness.The decision-making model system-atically incorporates both benefit and cost-type criteria,enabling more nuanced evaluations in complex social or environmental decision problems.To enhance interpretability and practical relevance,the study conducts a sensitivity analysis on the Schweizer-Sklar parameter(Δ).The results show that varyingΔaffects the strictness of aggregation,thereby influencing the ranking stability of alternatives.A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness,expressiveness,and adaptability of the proposed approach.Notably,the use of picture fuzzy sets allows for the inclusion of positive,neutral,and negative memberships,offering a richer representation of expert opinions compared to traditional models.A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method.The analysis confirms that the approach yields consistent and interpretable results,even under varying degrees of decision uncertainty.Overall,this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes.
文摘Lethal autonomous weapon systems(LAWS)have become a prominent issue in global security governance.However,significant divergences remain among the world's major countries regarding their regulation:some support restrictions,while others oppose any binding rules,and there are also countries adopting a neutral stance,though their choices are subject to external pressure.In the foreseeable future,the deployment of LAWS will increase further,raising the risk of arms races,with international support for regulating these weapons gaining strength.Yet,establishing legally binding international rules within the United Nations(UN)framework remains a distant prospect.Given this backdrop,China should continue to actively participate in international norms setting concerning LAWS under UN auspices and deepen coordination and cooperation with other countries towards more applicable norms and global governance frameworks.
文摘Table manners are important in manycultures.Inmost countries,youwait untileveryone has food before eating.Youalso don't put your elbows on the table.It's not polite to eat too fast.And youshouldn't talk with food in yourmouth orchew with your mouth open.
文摘BACKGROUND Type 2 diabetes mellitus(T2DM)is increasing rapidly in Pakistan,especially among socioeconomically disadvantaged populations.While clinical care remains central,social determinants such as poverty,gender norms,and mistrust in healthcare critically shape disease outcomes.AIM To synthesize qualitative evidence on how these factors influence the experience and management of T2DM in Pakistan.METHODS Following PRISMA guidelines,a systematic review of qualitative studies published between 2000 and 2025 was conducted on February 25,2025 using PubMed,CINAHL,MEDLINE Plus,and PakMediNet.Eleven studies exploring socioeconomic influences on T2DM care and self-management in Pakistan were included.Thematic synthesis was used to identify key patterns.Quality was appraised using the Joanna Briggs Institute Checklist for Qualitative Research.RESULTS Three major themes were identified:(1)Economic insecurity.High cost of treatment,poor rural infrastructure,and food insecurity hinder access and adherence;(2)Sociocultural and gender norms.Restricted mobility of females,family control over health decisions,and fatalistic beliefs delay care;and(3)Knowledge gaps and mistrust.A lack of culturally appropriate education,reliance on traditional remedies,and distrust in public health systems reduce compliance.These intersecting barriers collectively impede effective diabetes management.CONCLUSION T2DM in Pakistan is driven by entrenched social and economic barriers.Addressing it requires culturally sensitive,equity-oriented strategies that go beyond biomedical models.Policy reforms should focus on affordability,rural outreach,and inclusive health education.Future research should engage marginalized voices through participatory methods.
基金funded by National Nature Science Foundation of China,grant number 61302188.
文摘To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.
基金supported by the National Natural Science Foundation of China(Grant No.12474461)the Basic and Frontier Exploration Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.JCQY202402)the Goal-Oriented Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.MBDX202113).
文摘Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.
文摘This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere.By implementing the minimum norm tensor principle,we rigorously estimate the squared norm of the quadratic gradient term associated with the Möbius second fundamental form.This analysis yields a critical inequality governing the geometric config-uration.Leveraging this inequality,we subsequently prove a Pinching theorem characterizing the eigenvalues of the Blaschke tensor.
