This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization p...We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.展开更多
We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking me...We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution,then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method.The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32~35 km,with an average thickness of 33 km,which is consistent with the crustal thickness results in South China from previous studies using the receiver function method.The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25,which is lower than the global value with a 0.27 average,indicating a predominantly intermediate-acidic or felsic crustal composition.There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas,suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination.The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces,with the first at a depth of approximately 1.5 km,the second at about 10~15 km,and the third being the Moho.The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κmethod,effectively reducing the standard deviation and dispersion of crustal thickness and vP/vSratio.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))...Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.展开更多
In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequa...In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequalities are established.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years...Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.展开更多
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S ...Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.展开更多
An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,...An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-con...In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-convex functions were derived.展开更多
In this paper,we obtain the convexity of new general integral operator on some classes of fc-uniformly p-valentα-convex functions of complex order.These results extend some known theorems.
In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Final...In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.展开更多
Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the opti...Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set which consists of different single kernel functions, endlessly finding the last two kernel functions on the performance in PPI extraction, using their optimal kernel function to replace them, until there is only one kernel function and it’s the final optimal kernel function. Finally, extracting PPI using the classified model made by this kernel function. This paper conducted the PPI extraction experiment on AIMed corpus, the experimental result shows that the optimal convex combination kernel function this paper presents can effectively improve the extraction performance than single kernel function, and it gets the best precision which reaches 65.0 among the similar PPI extraction systems.展开更多
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
基金supported in part by the Shanghai Natural Science Foundation under the Grant 22ZR1407000.
文摘We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.
基金supported by the Spark Program of Earthquake Technology of CEA,China(XH20032)open Research Project from the State Key Laboratory of Nuclear Resources and Environment,East China University of Technology(2022NRE17)+1 种基金open Research Project from the State Key Laboratory of Geological Processes,Mineral Resources,China University of Geosciences(GPMR202114)the Graduate Student Innovation Fund of East China University of Technology(YC2022-s628)。
文摘We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution,then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method.The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32~35 km,with an average thickness of 33 km,which is consistent with the crustal thickness results in South China from previous studies using the receiver function method.The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25,which is lower than the global value with a 0.27 average,indicating a predominantly intermediate-acidic or felsic crustal composition.There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas,suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination.The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces,with the first at a depth of approximately 1.5 km,the second at about 10~15 km,and the third being the Moho.The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κmethod,effectively reducing the standard deviation and dispersion of crustal thickness and vP/vSratio.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
文摘Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.
基金supported by NSFC (60850005)NSF of Zhejiang Province(D7080080, Y7080185, Y607128)
文摘In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequalities are established.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
文摘Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.
文摘In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
基金The NSF(11561001)of Chinathe NSF(2014MS0101)of Inner Mongolia Province+1 种基金the Higher School Foundation(NJZY19211)of Inner Mongolia of Chinathe NSF(KJ2018A0839,KJ2018A0833)of Anhui Provincial Department of Education
文摘Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.
文摘An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
基金Project supported by the National Natural Science Foundation of China(Grant No.10271071)
文摘In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-convex functions were derived.
基金Foundation item: Supported by the Natural Science Foundation of Inner Mongolia(2009MS0113) Sup- ported by the Higher School Research Foundation of Inner Mongolia(NJzy08150)
文摘In this paper,we obtain the convexity of new general integral operator on some classes of fc-uniformly p-valentα-convex functions of complex order.These results extend some known theorems.
基金The Doctoral Programs Foundation(20113401110009)of Education Ministry of ChinaNatural Science Research Project(2012kj11)of Hefei Normal University+1 种基金Universities Natural Science Foundation(KJ2013A220)of Anhui ProvinceResearch Project of Graduates Innovation Fund(2014yjs02)
文摘In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.
文摘Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set which consists of different single kernel functions, endlessly finding the last two kernel functions on the performance in PPI extraction, using their optimal kernel function to replace them, until there is only one kernel function and it’s the final optimal kernel function. Finally, extracting PPI using the classified model made by this kernel function. This paper conducted the PPI extraction experiment on AIMed corpus, the experimental result shows that the optimal convex combination kernel function this paper presents can effectively improve the extraction performance than single kernel function, and it gets the best precision which reaches 65.0 among the similar PPI extraction systems.