In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
Introduction: Cranioencephalic trauma caused by bladed weapons is rare, and that caused by sharp objects is exceptional. The aim of our study was to describe the clinical, therapeutic and evolutionary aspects. Materia...Introduction: Cranioencephalic trauma caused by bladed weapons is rare, and that caused by sharp objects is exceptional. The aim of our study was to describe the clinical, therapeutic and evolutionary aspects. Materials and method: This was a descriptive and analytical study over a 48-month period at CHU la Renaissance from January 1, 2018 to December 31, 2021, concerning patients admitted for penetrating cranioencephalic trauma by pointed object. Results: Twelve cases, all male, of penetrating cranioencephalic sharp-force trauma were identified. The mean age was 34 ± 7 years, with extremes of 11 and 60 years. Farmers and herders accounted for 31% and 25% of cases respectively. The average admission time was 47 hours. Brawls were the circumstances of occurrence in 81.2% of cases. Knives (33%), arrows (25%) and iron bars (16.6%) were the objects used. Altered consciousness was present in 43.8% of cases, and focal deficit in 50%. Scannographic lesions were fracture and/or embarrhment (12 cases), intra-parenchymal haematomas (6 cases) and presence of object in place (4 cases). Surgery was performed in 11 patients. Postoperative outcome was favorable in 9 patients. After 12 months, 2 patients were declared unfit. Conclusion: Penetrating head injuries caused by sharp objects are common in Chad. Urgent surgery can prevent disabling after-effects.展开更多
Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in th...Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.展开更多
Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hie...Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this...Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d1,d2,...,dn+1 and r.展开更多
We consider Jackson inequality in L^2 (B^d×T, Wκ,μ^B (x)), where the weight function Wκ,μ^B (X) is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-...We consider Jackson inequality in L^2 (B^d×T, Wκ,μ^B (x)), where the weight function Wκ,μ^B (X) is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1(f)2≤κn,m(τ,r)ωr(f,t)2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ (cos θ)(n ∈ N).展开更多
We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interactio...We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.展开更多
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this pa...Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.展开更多
The authors regret to report some missing information in the authorship and associated changes of the paper.On page 1512,the author information reads:“Caiyun Liu a,Wei Guo a,Yang Wang b,Bisheng Fu a,Jaroslav Dolezel ...The authors regret to report some missing information in the authorship and associated changes of the paper.On page 1512,the author information reads:“Caiyun Liu a,Wei Guo a,Yang Wang b,Bisheng Fu a,Jaroslav Dolezel c,Ying Liu a,Wenling Zhai a,Mahmoud Said c,d,István Molnár c,d,e,Katerina Holušovác,Ruiqi Zhang b,*,Jizhong Wu a,f,g,*”.It should be changed to“Caiyun Liu a,1,Wei Guo a,1,Yang Wang b,Bisheng Fu a,Jaroslav Dolezel c,Ying Liu a,Wenling Zhai a,Mahmoud Said c,d,István Molnár c,d,e,Katerina Holušovác,Ruiqi Zhang b,*,Jizhong Wu a,f,g,*”.On page 1512 in the footnote,the following sentence should be added below the corresponding authors’information:1 These authors contributed equally to this work.The correction has been updated above.The authors would like to apologize for any inconvenience caused.展开更多
It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising...It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.展开更多
Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality...Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.展开更多
Fluid resonance within narrow gaps in multiple-box systems with sharp and round inlet configurations are investigated by using the potential flow and viscous fluid flow models in the OpenFOAM^(■)package.Evident discr...Fluid resonance within narrow gaps in multiple-box systems with sharp and round inlet configurations are investigated by using the potential flow and viscous fluid flow models in the OpenFOAM^(■)package.Evident discrepancy between two numerical models can be observed for sharp inlet configurations.In addition to the dramatical decrease of resonant amplitude in narrow gaps,some peak values at the higher resonant frequencies predicted by the potential flow model even disappear in the viscous fluid flow results.The decreased normalized resonant amplitudes with the increase of incident wave amplitude can be observed for sharp inlet configurations.However,the hydrodynamic behaviors of multiple-box system with round inlet configurations between potential flow and viscous fluid flow models are quite similar with each other.The normalized resonant amplitudes are nearly independent of incident wave amplitudes for multiple-box systems with round inlet configurations.This implies that the energy dissipation associated with fluid viscosity and flow rotation plays an important role in the gap resonance for sharp inlet configurations;while it is insignificant for round inlet configurations.展开更多
The electron injection and acceleration driven by a few-cycle laser with a sharp vacuum-plasma boundary have been investigated through three-dimensional(3D)particle-in-cell simulations.It is found that an isotropic bo...The electron injection and acceleration driven by a few-cycle laser with a sharp vacuum-plasma boundary have been investigated through three-dimensional(3D)particle-in-cell simulations.It is found that an isotropic boundary impact injection(BII)first occurs at the vacuum-plasma boundary,and then carrier-envelope-phase(CEP)shift causes the transverse oscillation of the plasma bubble,resulting in a periodic electron self-injection(SI)in the laser polarization direction.It shows that the electron charge of the BII only accounts for a small part of the total charge,and the CEP can effectively tune the quality of the injected electron beam.The dependences of laser intensity and electron density on the total charge and the ratio of BII charge to the total charge are studied.The results are beneficial to electron acceleration and its applications,such as betatron radiation source.展开更多
The necrotrophic fungus Rhizoctonia cerealis is the causal agent of devastating diseases of cereal crops including wheat(Triticum aestivum).We present a high-quality genome assembly of R.cerealis Rc207,a virulent stra...The necrotrophic fungus Rhizoctonia cerealis is the causal agent of devastating diseases of cereal crops including wheat(Triticum aestivum).We present a high-quality genome assembly of R.cerealis Rc207,a virulent strain causing wheat sharp eyespot.The assembly(56.36 Mb)is composed of 17.87%repeat sequences and 14,433 predicted protein-encoding genes.The Rc207 genome encodes a large and diverse set of genes involved in pathogenicity,especially rich in those encoding secreted proteins,carbohydrateactive enzymes(CAZymes),peptidases,nucleases,cytochrome P450,and secondary metabolismassociated enzymes.Most secretory protein-encoding genes,including CAZymes,peroxygenases,dehydrogenases,and cytochrome P450,were up-regulated during fungal infection of wheat.We identified 831 candidate secretory effectors and validated the functions of 10 up-regulated candidate effector proteins.Of them,nine were confirmed as necrotrophic pathogen’s effectors promoting fungal infection.Abundant potential mobile or plastic genomic regions rich in repeat sequences suggest their roles in fungal adaption and virulence-associated genomic evolution.This study provides valuable resources for further comparative and functional genomics on important fungal pathogens,and provides essential tools for development of effective disease control strategies.展开更多
In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1...In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.展开更多
As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* ...As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
文摘Introduction: Cranioencephalic trauma caused by bladed weapons is rare, and that caused by sharp objects is exceptional. The aim of our study was to describe the clinical, therapeutic and evolutionary aspects. Materials and method: This was a descriptive and analytical study over a 48-month period at CHU la Renaissance from January 1, 2018 to December 31, 2021, concerning patients admitted for penetrating cranioencephalic trauma by pointed object. Results: Twelve cases, all male, of penetrating cranioencephalic sharp-force trauma were identified. The mean age was 34 ± 7 years, with extremes of 11 and 60 years. Farmers and herders accounted for 31% and 25% of cases respectively. The average admission time was 47 hours. Brawls were the circumstances of occurrence in 81.2% of cases. Knives (33%), arrows (25%) and iron bars (16.6%) were the objects used. Altered consciousness was present in 43.8% of cases, and focal deficit in 50%. Scannographic lesions were fracture and/or embarrhment (12 cases), intra-parenchymal haematomas (6 cases) and presence of object in place (4 cases). Surgery was performed in 11 patients. Postoperative outcome was favorable in 9 patients. After 12 months, 2 patients were declared unfit. Conclusion: Penetrating head injuries caused by sharp objects are common in Chad. Urgent surgery can prevent disabling after-effects.
文摘Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.
文摘Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d1,d2,...,dn+1 and r.
基金supported by National Natural Science Foundation of China(11071019)Beijing Natural Science Foundation(1132001)
文摘We consider Jackson inequality in L^2 (B^d×T, Wκ,μ^B (x)), where the weight function Wκ,μ^B (X) is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1(f)2≤κn,m(τ,r)ωr(f,t)2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ (cos θ)(n ∈ N).
文摘We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.
基金Supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022)the University Natural Science Research Project of Anhui Province (2022AH040067)+1 种基金the Fundamental Research Funds for the Central Universities (3132023202)National Natural Science Foundation of China (12001080).
文摘Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.
文摘The authors regret to report some missing information in the authorship and associated changes of the paper.On page 1512,the author information reads:“Caiyun Liu a,Wei Guo a,Yang Wang b,Bisheng Fu a,Jaroslav Dolezel c,Ying Liu a,Wenling Zhai a,Mahmoud Said c,d,István Molnár c,d,e,Katerina Holušovác,Ruiqi Zhang b,*,Jizhong Wu a,f,g,*”.It should be changed to“Caiyun Liu a,1,Wei Guo a,1,Yang Wang b,Bisheng Fu a,Jaroslav Dolezel c,Ying Liu a,Wenling Zhai a,Mahmoud Said c,d,István Molnár c,d,e,Katerina Holušovác,Ruiqi Zhang b,*,Jizhong Wu a,f,g,*”.On page 1512 in the footnote,the following sentence should be added below the corresponding authors’information:1 These authors contributed equally to this work.The correction has been updated above.The authors would like to apologize for any inconvenience caused.
文摘It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.
文摘Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52171250,52061135107)。
文摘Fluid resonance within narrow gaps in multiple-box systems with sharp and round inlet configurations are investigated by using the potential flow and viscous fluid flow models in the OpenFOAM^(■)package.Evident discrepancy between two numerical models can be observed for sharp inlet configurations.In addition to the dramatical decrease of resonant amplitude in narrow gaps,some peak values at the higher resonant frequencies predicted by the potential flow model even disappear in the viscous fluid flow results.The decreased normalized resonant amplitudes with the increase of incident wave amplitude can be observed for sharp inlet configurations.However,the hydrodynamic behaviors of multiple-box system with round inlet configurations between potential flow and viscous fluid flow models are quite similar with each other.The normalized resonant amplitudes are nearly independent of incident wave amplitudes for multiple-box systems with round inlet configurations.This implies that the energy dissipation associated with fluid viscosity and flow rotation plays an important role in the gap resonance for sharp inlet configurations;while it is insignificant for round inlet configurations.
基金the National Natural Science Foundation of China(Grant Nos.12005297,12175309,12175310,11975308,and 12275356)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA25050200)+3 种基金the Research Project of NUDT(Grant No.ZK21-12)the Key Laboratory Foundation of Laser Plasma of Ministry of Educationthe financial support from the NUDT Young Innovator Awards(Grant No.20190102)Outstanding Young Talents。
文摘The electron injection and acceleration driven by a few-cycle laser with a sharp vacuum-plasma boundary have been investigated through three-dimensional(3D)particle-in-cell simulations.It is found that an isotropic boundary impact injection(BII)first occurs at the vacuum-plasma boundary,and then carrier-envelope-phase(CEP)shift causes the transverse oscillation of the plasma bubble,resulting in a periodic electron self-injection(SI)in the laser polarization direction.It shows that the electron charge of the BII only accounts for a small part of the total charge,and the CEP can effectively tune the quality of the injected electron beam.The dependences of laser intensity and electron density on the total charge and the ratio of BII charge to the total charge are studied.The results are beneficial to electron acceleration and its applications,such as betatron radiation source.
基金funded by the National Key Project for Research on Transgenic Biology,China(2016ZX08002001 to Zengyan Zhang)。
文摘The necrotrophic fungus Rhizoctonia cerealis is the causal agent of devastating diseases of cereal crops including wheat(Triticum aestivum).We present a high-quality genome assembly of R.cerealis Rc207,a virulent strain causing wheat sharp eyespot.The assembly(56.36 Mb)is composed of 17.87%repeat sequences and 14,433 predicted protein-encoding genes.The Rc207 genome encodes a large and diverse set of genes involved in pathogenicity,especially rich in those encoding secreted proteins,carbohydrateactive enzymes(CAZymes),peptidases,nucleases,cytochrome P450,and secondary metabolismassociated enzymes.Most secretory protein-encoding genes,including CAZymes,peroxygenases,dehydrogenases,and cytochrome P450,were up-regulated during fungal infection of wheat.We identified 831 candidate secretory effectors and validated the functions of 10 up-regulated candidate effector proteins.Of them,nine were confirmed as necrotrophic pathogen’s effectors promoting fungal infection.Abundant potential mobile or plastic genomic regions rich in repeat sequences suggest their roles in fungal adaption and virulence-associated genomic evolution.This study provides valuable resources for further comparative and functional genomics on important fungal pathogens,and provides essential tools for development of effective disease control strategies.
基金supported by the Shanghai Sailing Program (21YF1415300)the Natural Science Foundation of China (12101392)supported by the Natural Science Foundation of China (11871382,11771161).
文摘In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.
文摘As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.