The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the re...The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the receiver. The receiver performs the unitary transformations and makes projective measurements on his particles to obtain the secret information. Using teleportation, the transmission of three-qubit secret information can be completed in each quantum channel展开更多
We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of t...We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.展开更多
The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent e...The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.展开更多
This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The max...This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The maximum entanglement property of these states is examined. It also demonstrates how to discriminate among these states in the ion-trap.展开更多
Paolo Facchi,et al.[Phys.Rev.A 77 (2008)060304(R)]presented a maximally multipartite entangledstate (MMES).Here,we give a criterion for the identification of maximally entangled four-qubit states.Using thiscriterion,w...Paolo Facchi,et al.[Phys.Rev.A 77 (2008)060304(R)]presented a maximally multipartite entangledstate (MMES).Here,we give a criterion for the identification of maximally entangled four-qubit states.Using thiscriterion,we not only identify some existing maximally entangled four-qubit states in the literature,but also find severalnew maximally entangled four-qubit states as well.展开更多
As surgeons formidably continue to forge into the twentytwenties,after a considerably coronavirus-induced rocky start,one can predict that the era of minimally invasive surgery(mIS),an era of robotics,telehealth,and e...As surgeons formidably continue to forge into the twentytwenties,after a considerably coronavirus-induced rocky start,one can predict that the era of minimally invasive surgery(mIS),an era of robotics,telehealth,and enhanced recovery after surgery(ERAS■),is not only here to stay but will continue to thrive,develop,and transform our practices.Critics of robotics platforms would be hard pressed not to indulge in this prediction.Will the satisfyingly large midline“stem to stern”,the impressing exposuregenerating Makuuchi or transverse abdominal,the Kocher,paramedian,McBurney,Chevron,and Pfannenstiel incisions begin to disappear and fade away into a scar minimizing future precluding trauma laparotomies?Most likely not.Understanding and developing the skill and technique for a minimally invasive“mIS”approach does not negate or abrogate the maximally invasive“MIS”ones.It is not one or the other;not a“to be or not to be”Shakespearean scenario.Hepatobiliary surgery is a qualified landscape upon which to illuminate and exemplify this declaration:the necessity and companionship of“mIS”and“MIS”–minimally and maximally invasive surgery.展开更多
We show how the two interacting electrons in a field-driven coupled quantum dot can be used to prepare maximally entangled Bell states. The time durations of the oscillatory electric field for producing and maintainin...We show how the two interacting electrons in a field-driven coupled quantum dot can be used to prepare maximally entangled Bell states. The time durations of the oscillatory electric field for producing and maintaining such highly entangled states are identified by both analytic and exact numerical solutions of the quantum dynamical equations.展开更多
Huber et al.[Phys.Rev.Lett.118(2017)200502]have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist.Here,we propose a method to build a maximally entangled state bas...Huber et al.[Phys.Rev.Lett.118(2017)200502]have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist.Here,we propose a method to build a maximally entangled state based on orthogonal arrays to construct maximally entangled seven-qubit states.Using this method,we not only determine that a seven-qubit state whose three-body marginals are all maximally mixed does not exist,but also find the condition for maximally entangled seven-qubit states.We consider thatπME=19/140 is a condition for maximally entangled seven-qubit states.Furthermore,we derive three forms of maximally entangled seven-qubit states via orthogonal arrays.展开更多
Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . W...Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.展开更多
Maximally localized Wannier functions(MLWFs)are widely used in electronic-structure calculations.We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-li...Maximally localized Wannier functions(MLWFs)are widely used in electronic-structure calculations.We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals;these describe accurately both the occupied states and the complementary unoccupied ones.For many applications,it is required to use MLWFs that describe instead certain target groups of bands:the valence or the conduction bands,or correlated manifolds.Here,we start from these tight-binding sets of MLWFs,and mix them using a combination of parallel transport and maximal localization to construct manifold-remixed Wannier functions(MRWFs):these are orthogonal sets of MLWFs that fully and only span desired target submanifolds.The algorithm is simple and robust,and is showcased here in reference applications(silicon,MoS_(2),and SrVO_(3))and in a mid-throughput study of 77 insulators.展开更多
A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S i...A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.展开更多
In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensi...In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions.Fan and Tian et al.have already obtained two satisfactory results for the generalized Bell states(GBSs)and the qudit lattice states when applied to prime or prime power dimensions.We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in[Phys.Rev.A 70,022304(2004)].Using this teleportation scheme,we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs,which include the GBSs and the qudit lattice states as special cases.Moreover,we present a generalized version of the results in[Phys.Rev.A 92,042320(2015)]for the arbitrary dimensional case.展开更多
Background:When recommending avoidance of static stretching prior to athletic performance,authors and practitioners commonly refer to available systematic reviews.However,effect sizes(ES)in previous reviews were extra...Background:When recommending avoidance of static stretching prior to athletic performance,authors and practitioners commonly refer to available systematic reviews.However,effect sizes(ES)in previous reviews were extracted in major part from studies lacking control conditions and/or prepost testing designs.Also,currently available reviews conducted calculations without accounting for multiple study outcomes,with ES:0.03 to 0.10,which would commonly be classified as trivial.Methods:Since new meta-analytical software and controlled research articles have appeared since 2013,we revisited the available literatures and performed a multilevel meta-analysis using robust variance estimation of controlled prepost trials to provide updated evidence.Furthermore,previous research described reduced electromyography activity—also attributable to fatiguing training routines—as being responsible for decreased subsequent performance.The second part of this study opposed stretching and alternative interventions sufficient to induce general fatigue to examine whether static stretching induces higher performance losses compared to other exercise routines.Results:Including 83 studies with more than 400 ES from 2012 participants,our results indicate a significant,small ES for a static stretch-induced maximal strength loss(ES=0.21,p=0.003),with high magnitude ES(ES=0.84,p=0.004)for stretching durations≥60 s per bout when compared to passive controls.When opposed to active controls,the maximal strength loss ranges between ES:0.17 to0.28,p<0.001 and 0.040 with mostly no to small heterogeneity.However,stretching did not negatively influence athletic performance in general(when compared to both passive and active controls);in fact,a positive effect on subsequent jumping performance(ES=0.15,p=0.006)was found in adults.Conclusion:Regarding strength testing of isolated muscles(e.g.,leg extensions or calf raises),our results confirm previous findings.Nevertheless,since no(or even positive)effects could be found for athletic performance,our results do not support previous recommendations to exclude static stretching from warm-up routines prior to,for example,jumping or sprinting.展开更多
For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle...For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.展开更多
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene...In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.展开更多
Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services ope...Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.展开更多
This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of...This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.展开更多
In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete mem...In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10704011the Research Programs of the Educational Office of Liaoning Province under Grant No.2008006
文摘The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the receiver. The receiver performs the unitary transformations and makes projective measurements on his particles to obtain the secret information. Using teleportation, the transmission of three-qubit secret information can be completed in each quantum channel
文摘We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.
文摘The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.
基金Project supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 10947017/A05)
文摘This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The maximum entanglement property of these states is examined. It also demonstrates how to discriminate among these states in the ion-trap.
基金Supported by the National Natural Science Foundation of China under Grant No. 10902083Shaanxi Natural Science Foundation under Grant No. 2009JM1007
文摘Paolo Facchi,et al.[Phys.Rev.A 77 (2008)060304(R)]presented a maximally multipartite entangledstate (MMES).Here,we give a criterion for the identification of maximally entangled four-qubit states.Using thiscriterion,we not only identify some existing maximally entangled four-qubit states in the literature,but also find severalnew maximally entangled four-qubit states as well.
文摘As surgeons formidably continue to forge into the twentytwenties,after a considerably coronavirus-induced rocky start,one can predict that the era of minimally invasive surgery(mIS),an era of robotics,telehealth,and enhanced recovery after surgery(ERAS■),is not only here to stay but will continue to thrive,develop,and transform our practices.Critics of robotics platforms would be hard pressed not to indulge in this prediction.Will the satisfyingly large midline“stem to stern”,the impressing exposuregenerating Makuuchi or transverse abdominal,the Kocher,paramedian,McBurney,Chevron,and Pfannenstiel incisions begin to disappear and fade away into a scar minimizing future precluding trauma laparotomies?Most likely not.Understanding and developing the skill and technique for a minimally invasive“mIS”approach does not negate or abrogate the maximally invasive“MIS”ones.It is not one or the other;not a“to be or not to be”Shakespearean scenario.Hepatobiliary surgery is a qualified landscape upon which to illuminate and exemplify this declaration:the necessity and companionship of“mIS”and“MIS”–minimally and maximally invasive surgery.
基金Supported in part by the National Natural Science Foundation of China under Grant No.19725417the China Academy of Engineering Physics.
文摘We show how the two interacting electrons in a field-driven coupled quantum dot can be used to prepare maximally entangled Bell states. The time durations of the oscillatory electric field for producing and maintaining such highly entangled states are identified by both analytic and exact numerical solutions of the quantum dynamical equations.
文摘Huber et al.[Phys.Rev.Lett.118(2017)200502]have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist.Here,we propose a method to build a maximally entangled state based on orthogonal arrays to construct maximally entangled seven-qubit states.Using this method,we not only determine that a seven-qubit state whose three-body marginals are all maximally mixed does not exist,but also find the condition for maximally entangled seven-qubit states.We consider thatπME=19/140 is a condition for maximally entangled seven-qubit states.Furthermore,we derive three forms of maximally entangled seven-qubit states via orthogonal arrays.
文摘Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.
基金We acknowledge financial support from the NCCR MARVEL(a National Centre of Competence in Research,funded by the Swiss National Science Foundation,grant No.205602)the Swiss National Science Foundation(SNSF)Project Funding(grant 200021E_206190“FISH4DIET”)The work is also supported by a pilot access grant from the Swiss National Supercomputing Centre(CSCS)on the Swiss share of the LUMI system under project ID“PILOT MC EPFL-NM 01”,a CHRONOS grant from the CSCS on the Swiss share of the LUMI system under project ID“REGULAR MC EPFL-NM 02”,and a grant from the CSCS under project ID s0178.
文摘Maximally localized Wannier functions(MLWFs)are widely used in electronic-structure calculations.We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals;these describe accurately both the occupied states and the complementary unoccupied ones.For many applications,it is required to use MLWFs that describe instead certain target groups of bands:the valence or the conduction bands,or correlated manifolds.Here,we start from these tight-binding sets of MLWFs,and mix them using a combination of parallel transport and maximal localization to construct manifold-remixed Wannier functions(MRWFs):these are orthogonal sets of MLWFs that fully and only span desired target submanifolds.The algorithm is simple and robust,and is showcased here in reference applications(silicon,MoS_(2),and SrVO_(3))and in a mid-throughput study of 77 insulators.
基金Supported by NSFC(Grant Nos.11801148 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。
文摘A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.
基金supported by the National Natural Science Foundation of China(Grant Nos.11675113,11871295,and 11901084)Beijing Municipal Commission of Education(Grant No.KM201810011009)+1 种基金Beijing Natural Science Foundation(Grant No.Z190005)the Research Startup Funds of Dongguan University of Technology(Grant No.GC300501-103)。
文摘In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions.Fan and Tian et al.have already obtained two satisfactory results for the generalized Bell states(GBSs)and the qudit lattice states when applied to prime or prime power dimensions.We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in[Phys.Rev.A 70,022304(2004)].Using this teleportation scheme,we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs,which include the GBSs and the qudit lattice states as special cases.Moreover,we present a generalized version of the results in[Phys.Rev.A 92,042320(2015)]for the arbitrary dimensional case.
文摘Background:When recommending avoidance of static stretching prior to athletic performance,authors and practitioners commonly refer to available systematic reviews.However,effect sizes(ES)in previous reviews were extracted in major part from studies lacking control conditions and/or prepost testing designs.Also,currently available reviews conducted calculations without accounting for multiple study outcomes,with ES:0.03 to 0.10,which would commonly be classified as trivial.Methods:Since new meta-analytical software and controlled research articles have appeared since 2013,we revisited the available literatures and performed a multilevel meta-analysis using robust variance estimation of controlled prepost trials to provide updated evidence.Furthermore,previous research described reduced electromyography activity—also attributable to fatiguing training routines—as being responsible for decreased subsequent performance.The second part of this study opposed stretching and alternative interventions sufficient to induce general fatigue to examine whether static stretching induces higher performance losses compared to other exercise routines.Results:Including 83 studies with more than 400 ES from 2012 participants,our results indicate a significant,small ES for a static stretch-induced maximal strength loss(ES=0.21,p=0.003),with high magnitude ES(ES=0.84,p=0.004)for stretching durations≥60 s per bout when compared to passive controls.When opposed to active controls,the maximal strength loss ranges between ES:0.17 to0.28,p<0.001 and 0.040 with mostly no to small heterogeneity.However,stretching did not negatively influence athletic performance in general(when compared to both passive and active controls);in fact,a positive effect on subsequent jumping performance(ES=0.15,p=0.006)was found in adults.Conclusion:Regarding strength testing of isolated muscles(e.g.,leg extensions or calf raises),our results confirm previous findings.Nevertheless,since no(or even positive)effects could be found for athletic performance,our results do not support previous recommendations to exclude static stretching from warm-up routines prior to,for example,jumping or sprinting.
基金supported by the National Natural Science Foundation of China(11201324)the Fok Ying Tuny Education Foundation(141114)the Sichuan Technology Program(2022ZYD0011,2022NFSC1852).
文摘For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.
基金supported by Ministry of Education and Training(Vietnam),under grant number B2023-SPS-01。
文摘In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.
基金sponsored by the National Natural Science Foundation of China Nos.62172353,62302114 and U20B2046Future Network Scientific Research Fund Project No.FNSRFP-2021-YB-48Innovation Fund Program of the Engineering Research Center for Integration and Application of Digital Learning Technology of Ministry of Education No.1221045。
文摘Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.
基金Supported by NSF of Zhejiang Province of China(LQ18A010002,LQ17A010002)。
文摘This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.
基金financially supported in part by National Key R&D Program of China(No.2018YFB1801402)in part by Huawei Technologies Co.,Ltd.
文摘In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.
