In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
Effective fault identification is crucial for bearings, which are critical components of mechanical systems and play a pivotal role in ensuring overall safety and operational efficiency. Bearings operate under variabl...Effective fault identification is crucial for bearings, which are critical components of mechanical systems and play a pivotal role in ensuring overall safety and operational efficiency. Bearings operate under variable service conditions, and their diagnostic environments are complex and dynamic. In the process of bearing diagnosis, fault datasets are relatively scarce compared with datasets representing normal operating conditions. These challenges frequently cause the practicality of fault detection to decline, the extraction of fault features to be incomplete, and the diagnostic accuracy of many existing models to decrease. In this work, a transfer-learning framework, designated DSCNN-HA-TL, is introduced to address the enduring challenge of cross-condition diagnosis in rolling-bearing fault detection. The framework integrates a window global mixed attention mechanism with a deep separable convolutional network, thereby enabling adaptation to fault detection tasks under diverse operating conditions. First, a Convolutional Neural Network (CNN) is employed as the foundational architecture, where the original convolutional layers are enhanced through the incorporation of depthwise separable convolutions, resulting in a Depthwise Separable Convolutional Neural Network (DSCNN) architecture. Subsequently, the extraction of fault characteristics is further refined through a dual-branch network that integrates hybrid attention mechanisms, specifically windowed and global attention mechanisms. This approach enables the acquisition of multi-level feature fusion information, thereby enhancing the accuracy of fault classification. The integration of these features not only optimizes the characteristic extraction process but also yields improvements in accuracy, representational capacity, and robustness in fault feature recognition. In conclusion, the proposed method achieved average precisions of 99.93% and 99.55% in transfer learning tasks, as demonstrated by the experimental results obtained from the CWRU public dataset and the bearing fault detection platform dataset. The experimental findings further provided a detailed comparison between the diagnostic models before and after the enhancement, thereby substantiating the pronounced advantages of the DSCNN-HA-TL approach in accurately identifying faults in critical mechanical components under diverse operating conditions.展开更多
This study explores the aerodynamic performance and flow field characteristics of supercritical carbon dioxide(sCO_(2))centrifugal compressors under varying operating conditions.In particular,the Sandia main compresso...This study explores the aerodynamic performance and flow field characteristics of supercritical carbon dioxide(sCO_(2))centrifugal compressors under varying operating conditions.In particular,the Sandia main compressor impeller model is used as a reference system.Through three-dimensional numerical simulations,we examine the Mach number distribution,temperature field,blade pressure pulsation spectra,and velocity field evolution,and identify accordingly the operating boundaries ensuring stability and the mechanisms responsible for performance degradation.Findings indicate a stable operating range for mass flow rate between 0.74 and 3.74 kg/s.At the lower limit(0.74 kg/s),the maximum Mach number within the compressor decreases by 28%,while the temperature gradient sharpens,entropy rises notably,and fluid density varies significantly.The maximum pressure near the blades increases by 6%,yet flow velocity near the blades and outlet declines,with a 19%reduction in peak speed.Consequently,isentropic efficiency falls by 13%.Conversely,at 3.74 kg/s,the maximum Mach number increases by 23.7%,with diminished temperature gradients and minor fluid density variations.However,insufficient enthalpy gain and intensified pressure pulsations near the blades result in a 12%pressure drop.Peak velocity within the impeller channel surges by 23%,amplifying velocity gradients,inducing flow separation,and ultimately reducing the pressure ratio from 1.47 to 1.34.展开更多
This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that ...This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.展开更多
A control strategy of variable speed limits(VSL)was developed to reduce the travel time at freeway recurrent bottleneck areas.The proposed control strategy particularly focused on preventing the capacity drop and incr...A control strategy of variable speed limits(VSL)was developed to reduce the travel time at freeway recurrent bottleneck areas.The proposed control strategy particularly focused on preventing the capacity drop and increasing the discharge flow.A cell transmission model(CTM)was developed to evaluate the effects of the proposed VSL control strategy on the traffic operations.The results show that the total travel time is reduced by 25.5% and the delay is reduced by 56.1%.The average travel speed is increased by 34.3% and the queue length is reduced by 31.0%.The traffic operation is improved by the proposed VSL control strategy.The way to use the proposed VSL control strategy in different types of freeway bottlenecks was also discussed by considering different traffic flow characteristics.It is concluded that the VSL control strategy is effective for merge bottlenecks but is less effective for diverge bottlenecks.展开更多
It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered...It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution(CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source.It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.展开更多
We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receive...We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.展开更多
In the case of fault diagnosis for roller bearings, the conventional diagnosis approaches by using the time interval of energy impacts in time-frequency distribution or the pass-frequencies are based on the assumption...In the case of fault diagnosis for roller bearings, the conventional diagnosis approaches by using the time interval of energy impacts in time-frequency distribution or the pass-frequencies are based on the assumption that machinery operates under a constant rotational speed. However, when the rotational speed varies in the broader range, the pass-frequencies vary with the change of rotational speed and bearing faults cannot be identified by the interval of impacts. Researches related to automatic diagnosis for rotational machinery in variable operating conditions were quite few. A novel automatic feature extraction method is proposed based on a pseudo-Wigner-Ville distribution （PWVD） and an extraction of symptom parameter （SP）. An extraction method for instantaneous feature spectrum is presented using the relative crossing information （RCI） and sequential inference approach, by which the feature spectrum from time-frequency distribution can be automatically, sequentially extracted. The SPs are considered in the frequency domain using the extracted feature spectrum to identify among the conditions of a machine. A method to obtain the synthetic symptom parameter is also proposed by the least squares mapping （LSM） technique for increasing the diagnosis sensitivity of SP. Practical examples of diagnosis for bearings are given in order to verify the effectiveness of the proposed method. The verification results show that the features of bearing faults, such as the outer-race, inner-race and roller element defects have been effectively extracted, and the proposed method can be used for condition diagnosis of a machine under the variable rotational speed.展开更多
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley...In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.展开更多
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.展开更多
In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper...Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.展开更多
In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） an...In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.展开更多
In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-v...In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.展开更多
Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first charact...The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators.Immediately after,applying the characterizations of TriebelLizorkin space with variable exponent,we obtain that b∈∧βif and only if the commutator of Calderon-Zygmund singular integral operator is bounded,respectively,from L^p(·)(R^n)toF^β,∞p(·),fromL^p(·)(R^n)toL^q(·)(R^n)with1/p(·)-1/q(·)=β/n.Moreover,we prove that the commutator of Riesz potential operator also has corresponding results.展开更多
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
基金supported by the National Natural Science Foundation of China(12272259)the Key Research and Development Fund of Universities in Hebei Province(2510800601A).
文摘Effective fault identification is crucial for bearings, which are critical components of mechanical systems and play a pivotal role in ensuring overall safety and operational efficiency. Bearings operate under variable service conditions, and their diagnostic environments are complex and dynamic. In the process of bearing diagnosis, fault datasets are relatively scarce compared with datasets representing normal operating conditions. These challenges frequently cause the practicality of fault detection to decline, the extraction of fault features to be incomplete, and the diagnostic accuracy of many existing models to decrease. In this work, a transfer-learning framework, designated DSCNN-HA-TL, is introduced to address the enduring challenge of cross-condition diagnosis in rolling-bearing fault detection. The framework integrates a window global mixed attention mechanism with a deep separable convolutional network, thereby enabling adaptation to fault detection tasks under diverse operating conditions. First, a Convolutional Neural Network (CNN) is employed as the foundational architecture, where the original convolutional layers are enhanced through the incorporation of depthwise separable convolutions, resulting in a Depthwise Separable Convolutional Neural Network (DSCNN) architecture. Subsequently, the extraction of fault characteristics is further refined through a dual-branch network that integrates hybrid attention mechanisms, specifically windowed and global attention mechanisms. This approach enables the acquisition of multi-level feature fusion information, thereby enhancing the accuracy of fault classification. The integration of these features not only optimizes the characteristic extraction process but also yields improvements in accuracy, representational capacity, and robustness in fault feature recognition. In conclusion, the proposed method achieved average precisions of 99.93% and 99.55% in transfer learning tasks, as demonstrated by the experimental results obtained from the CWRU public dataset and the bearing fault detection platform dataset. The experimental findings further provided a detailed comparison between the diagnostic models before and after the enhancement, thereby substantiating the pronounced advantages of the DSCNN-HA-TL approach in accurately identifying faults in critical mechanical components under diverse operating conditions.
基金National Science Foundation of China(grant numbers 52366009 and 52130607)Doble First-Class Key Programof Gansu Provincial Department of Education(grant number GCJ2022-38)+1 种基金2022 Gansu Provincial University Industry Support Plan Project(grant number 2022CYZC-21)KeyR&DProgramofGansu Province of China(grant number 22YF7GA163).
文摘This study explores the aerodynamic performance and flow field characteristics of supercritical carbon dioxide(sCO_(2))centrifugal compressors under varying operating conditions.In particular,the Sandia main compressor impeller model is used as a reference system.Through three-dimensional numerical simulations,we examine the Mach number distribution,temperature field,blade pressure pulsation spectra,and velocity field evolution,and identify accordingly the operating boundaries ensuring stability and the mechanisms responsible for performance degradation.Findings indicate a stable operating range for mass flow rate between 0.74 and 3.74 kg/s.At the lower limit(0.74 kg/s),the maximum Mach number within the compressor decreases by 28%,while the temperature gradient sharpens,entropy rises notably,and fluid density varies significantly.The maximum pressure near the blades increases by 6%,yet flow velocity near the blades and outlet declines,with a 19%reduction in peak speed.Consequently,isentropic efficiency falls by 13%.Conversely,at 3.74 kg/s,the maximum Mach number increases by 23.7%,with diminished temperature gradients and minor fluid density variations.However,insufficient enthalpy gain and intensified pressure pulsations near the blades result in a 12%pressure drop.Peak velocity within the impeller channel surges by 23%,amplifying velocity gradients,inducing flow separation,and ultimately reducing the pressure ratio from 1.47 to 1.34.
基金Project supported by the Collaborative Research and Development Program of NSERC(Natural Sciences and Engineering Research Council of Canada) with Industrial Sponsorship from Vale,Teck Cominco,Xstrata Process Support,Agnico-Eagle,Shell Canada,Barrick Gold,COREM,SGS Lakefield Research and Flottec
文摘This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.
基金Project(2012CB725400)supported by the National Key Basic Research Program of ChinaProject(2011AA110303)supported by the National High Technology Research and Development Program of ChinaProject(YBPY1211)supported by the Scientific Research Foundation of the Graduate School of Southeast University,China
文摘A control strategy of variable speed limits(VSL)was developed to reduce the travel time at freeway recurrent bottleneck areas.The proposed control strategy particularly focused on preventing the capacity drop and increasing the discharge flow.A cell transmission model(CTM)was developed to evaluate the effects of the proposed VSL control strategy on the traffic operations.The results show that the total travel time is reduced by 25.5% and the delay is reduced by 56.1%.The average travel speed is increased by 34.3% and the queue length is reduced by 31.0%.The traffic operation is improved by the proposed VSL control strategy.The way to use the proposed VSL control strategy in different types of freeway bottlenecks was also discussed by considering different traffic flow characteristics.It is concluded that the VSL control strategy is effective for merge bottlenecks but is less effective for diverge bottlenecks.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11664017 and 11964013)the Training Program for Academic and Technical Leaders of Major Disciplines in Jiangxi Province,China (Grant No. 20204BCJL22053)。
文摘It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution(CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source.It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.
基金supported by the Natural Science Research Programme of the Education Department of Anhui Province under Grant No. KJ2009B039Zthe Municipal Level Research Project from Lu'an City directive entrusted to West Anhui University under Grant No. 2008lw004
文摘We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.
基金supported by National Natural Science Foundation of China (Grant No. 50875016, 51075023)Fundamental Research Funds for the Central Universities of China (Grant No. JD0903, JD0904)
文摘In the case of fault diagnosis for roller bearings, the conventional diagnosis approaches by using the time interval of energy impacts in time-frequency distribution or the pass-frequencies are based on the assumption that machinery operates under a constant rotational speed. However, when the rotational speed varies in the broader range, the pass-frequencies vary with the change of rotational speed and bearing faults cannot be identified by the interval of impacts. Researches related to automatic diagnosis for rotational machinery in variable operating conditions were quite few. A novel automatic feature extraction method is proposed based on a pseudo-Wigner-Ville distribution （PWVD） and an extraction of symptom parameter （SP）. An extraction method for instantaneous feature spectrum is presented using the relative crossing information （RCI） and sequential inference approach, by which the feature spectrum from time-frequency distribution can be automatically, sequentially extracted. The SPs are considered in the frequency domain using the extracted feature spectrum to identify among the conditions of a machine. A method to obtain the synthetic symptom parameter is also proposed by the least squares mapping （LSM） technique for increasing the diagnosis sensitivity of SP. Practical examples of diagnosis for bearings are given in order to verify the effectiveness of the proposed method. The verification results show that the features of bearing faults, such as the outer-race, inner-race and roller element defects have been effectively extracted, and the proposed method can be used for condition diagnosis of a machine under the variable rotational speed.
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
文摘In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
基金Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
基金supported by NSFC (No. 11201003)University NSR Project of Anhui Province (No. KJ2014A087)
文摘In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
基金supported by the National Natural Science Foundation of China(61402260,61473176)Taishan Scholar Project of Shandong Province(TSQN201812092)
文摘Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
基金The NSF(11361020)of Chinathe NSF(20151011)of Hainan Province
文摘In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.
文摘Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
基金Supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant Nos.2019D01C334,2016D01C381)the National Natural Science Foundation of China(Grant No.11661075)。
文摘The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators.Immediately after,applying the characterizations of TriebelLizorkin space with variable exponent,we obtain that b∈∧βif and only if the commutator of Calderon-Zygmund singular integral operator is bounded,respectively,from L^p(·)(R^n)toF^β,∞p(·),fromL^p(·)(R^n)toL^q(·)(R^n)with1/p(·)-1/q(·)=β/n.Moreover,we prove that the commutator of Riesz potential operator also has corresponding results.
