In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with...In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.展开更多
Melanoma is the most lethal malignant tumour,and its prevalence is increasing.Early detection and diagnosis of skin cancer can alert patients to manage precautions and dramatically improve the lives of people.Recently...Melanoma is the most lethal malignant tumour,and its prevalence is increasing.Early detection and diagnosis of skin cancer can alert patients to manage precautions and dramatically improve the lives of people.Recently,deep learning has grown increasingly popular in the extraction and categorization of skin cancer features for effective prediction.A deep learning model learns and co-adapts representations and features from training data to the point where it fails to perform well on test data.As a result,overfitting and poor performance occur.To deal with this issue,we proposed a novel Consecutive Layerwise weight Con-straint MaxNorm model(CLCM-net)for constraining the norm of the weight vector that is scaled each time and bounding to a limit.This method uses deep convolutional neural networks and also custom layer-wise weight constraints that are set to the whole weight matrix directly to learn features efficiently.In this research,a detailed analysis of these weight norms is performed on two distinct datasets,International Skin Imaging Collaboration(ISIC)of 2018 and 2019,which are challenging for convolutional networks to handle.According to thefindings of this work,CLCM-net did a better job of raising the model’s performance by learning the features efficiently within the size limit of weights with appropriate weight constraint settings.The results proved that the proposed techniques achieved 94.42%accuracy on ISIC 2018,91.73%accuracy on ISIC 2019 datasets and 93%of accuracy on combined dataset.展开更多
In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
As the host country of the 26 th United Nations Climate Conference,the United Kingdom(UK)fully carried out climate diplomacy at the conference,and intended to promote the green concept in the international community t...As the host country of the 26 th United Nations Climate Conference,the United Kingdom(UK)fully carried out climate diplomacy at the conference,and intended to promote the green concept in the international community through diplomatic means,which shows its greater ambition in international climate governance.However,the UK,as the source of the Industrial Revolution,has not always followed the so-called green norms in history.In the interaction with the EU norms after joining the European Community,the UK gradually developed from an"opponent"of green norms to an"advocate"of green norms.After"Brexit",the British government did not stop at the previous green norms of the EU,and further gave the green norms a special brand of the UK on this basis.At present,during the term of Boris Johnson's government,the green norms shaped by the UK have been basically formed and disseminated within a certain mechanism.In this paper,based on the normative power theory and relevant historical facts,how the UK has shaped international norms and obtained normative power through a series of climate policy will be discussed,and some enlightenment to China's participation in the construction of international norms system today will be obtained.展开更多
Electrical and electronic waste(e-waste)is a growing challenge,matching the widespread boom in the use of information and communication technology.Opposite to an alarming increasing amount of e-waste,a low rate of con...Electrical and electronic waste(e-waste)is a growing challenge,matching the widespread boom in the use of information and communication technology.Opposite to an alarming increasing amount of e-waste,a low rate of consumer engagement in ensuring the proper disposal of such materials intensifies the pressure on the exist‐ing e-waste crisis.To deal with this thorny problem,it is of great interest to grasp consumers’disposal and re‐cycling behavioral intentions.Therefore,this study attempts to understand complementary perspectives around consumers’e-waste recycling intention based on the integration of the valence theory and the norm activation theory.Four data mining models using classification and prediction-based algorithms,namely Chi squared automatic interaction detector(CHAID),Neural network,Discriminant analysis,and Quick,unbiased,efficient statistical tree(QUEST),were employed to analyze a set of the 398 data collected in Vietnam.The re‐sults revealed that the social support value is by far the most critical predictor,followed by the utilitarian value,task difficulty,and monetary risk.It is also noteworthy that the awareness of consequences,education background,the ascription of responsibility,and age were also ranked as critical affecting factors.The lowest influential predictors found in this study were income and gender.In addition,a comparison was made in terms of the classification performance of the four utilized data mining techniques.Based on several evalua‐tion measurements(confusion matrix,accuracy,precision,recall,specificity,F-measure,ROC curve,and AUC),the aggregated results suggested that CHAID and Neural network performed the best.The findings of this research are expected to assist policymakers and future researchers in updating all information surround‐ing consumer behavioral intention-related topics focusing on e-waste.Furthermore,the adoption of data min‐ing algorithms for prediction is another insight of this study,which may shed the light on data mining applica‐tions in such environmental studies in the future.展开更多
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金supported by the Natural Science Foundation of China (12271402)the Natural Science Foundation of Tianjin City (22JCYBJC00420)。
文摘In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.
文摘Melanoma is the most lethal malignant tumour,and its prevalence is increasing.Early detection and diagnosis of skin cancer can alert patients to manage precautions and dramatically improve the lives of people.Recently,deep learning has grown increasingly popular in the extraction and categorization of skin cancer features for effective prediction.A deep learning model learns and co-adapts representations and features from training data to the point where it fails to perform well on test data.As a result,overfitting and poor performance occur.To deal with this issue,we proposed a novel Consecutive Layerwise weight Con-straint MaxNorm model(CLCM-net)for constraining the norm of the weight vector that is scaled each time and bounding to a limit.This method uses deep convolutional neural networks and also custom layer-wise weight constraints that are set to the whole weight matrix directly to learn features efficiently.In this research,a detailed analysis of these weight norms is performed on two distinct datasets,International Skin Imaging Collaboration(ISIC)of 2018 and 2019,which are challenging for convolutional networks to handle.According to thefindings of this work,CLCM-net did a better job of raising the model’s performance by learning the features efficiently within the size limit of weights with appropriate weight constraint settings.The results proved that the proposed techniques achieved 94.42%accuracy on ISIC 2018,91.73%accuracy on ISIC 2019 datasets and 93%of accuracy on combined dataset.
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
文摘As the host country of the 26 th United Nations Climate Conference,the United Kingdom(UK)fully carried out climate diplomacy at the conference,and intended to promote the green concept in the international community through diplomatic means,which shows its greater ambition in international climate governance.However,the UK,as the source of the Industrial Revolution,has not always followed the so-called green norms in history.In the interaction with the EU norms after joining the European Community,the UK gradually developed from an"opponent"of green norms to an"advocate"of green norms.After"Brexit",the British government did not stop at the previous green norms of the EU,and further gave the green norms a special brand of the UK on this basis.At present,during the term of Boris Johnson's government,the green norms shaped by the UK have been basically formed and disseminated within a certain mechanism.In this paper,based on the normative power theory and relevant historical facts,how the UK has shaped international norms and obtained normative power through a series of climate policy will be discussed,and some enlightenment to China's participation in the construction of international norms system today will be obtained.
文摘Electrical and electronic waste(e-waste)is a growing challenge,matching the widespread boom in the use of information and communication technology.Opposite to an alarming increasing amount of e-waste,a low rate of consumer engagement in ensuring the proper disposal of such materials intensifies the pressure on the exist‐ing e-waste crisis.To deal with this thorny problem,it is of great interest to grasp consumers’disposal and re‐cycling behavioral intentions.Therefore,this study attempts to understand complementary perspectives around consumers’e-waste recycling intention based on the integration of the valence theory and the norm activation theory.Four data mining models using classification and prediction-based algorithms,namely Chi squared automatic interaction detector(CHAID),Neural network,Discriminant analysis,and Quick,unbiased,efficient statistical tree(QUEST),were employed to analyze a set of the 398 data collected in Vietnam.The re‐sults revealed that the social support value is by far the most critical predictor,followed by the utilitarian value,task difficulty,and monetary risk.It is also noteworthy that the awareness of consequences,education background,the ascription of responsibility,and age were also ranked as critical affecting factors.The lowest influential predictors found in this study were income and gender.In addition,a comparison was made in terms of the classification performance of the four utilized data mining techniques.Based on several evalua‐tion measurements(confusion matrix,accuracy,precision,recall,specificity,F-measure,ROC curve,and AUC),the aggregated results suggested that CHAID and Neural network performed the best.The findings of this research are expected to assist policymakers and future researchers in updating all information surround‐ing consumer behavioral intention-related topics focusing on e-waste.Furthermore,the adoption of data min‐ing algorithms for prediction is another insight of this study,which may shed the light on data mining applica‐tions in such environmental studies in the future.
