A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma mode...A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma model of ITER physics guidelines and the two-point SOL-divertor model are applied, This CSD model is validated by the two dimensional divertor transport code （B2-EIRINE） and by the JT-60U divertor recycling database, and this model is applicable to the low- and high-recycling state of the divertor plasma. The CSD model is applied to the study of the EAST operational space with lower hybrid current drive under various kinds of trade-off for the basic plasma parameters, and the relationship between the operational space and the plasma discharge duration is also discussed.展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.展开更多
Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is...Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is shown that phi is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number lambda satisfying lambda(k-1) = 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - 1)-th power I.展开更多
In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak＊ dense in the corresponding completely bound mapping spaces.
Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(...Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.展开更多
We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital...We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N2 and O2 molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N2 and O2 molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of ／sigma and ／pi orbitals, the bonding orbital （π2pz）^2 of N2 determines the maximum of harmonic emission when the molecular axis of N2 is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O2 molecule the antibonding orbitals （π2pz）^1 and （π2pz）^1 contribute to the maximum of harmonic yield when O2 is aligned at 45° and bonding orbitals （π2pz）^2 and （π2pz）^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45°.展开更多
We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D）...We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D） =^∞∑k=0φkD^k.φk constant numbers an a power of D.Dn, meaning, is there a isomorphism X （from s onto s） such that Xφ（D） = D^nX？. We prove that if φ（D） is equivalent to Dn, then φ（D） is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n = 1.展开更多
In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the nor...In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.展开更多
基金supported in part by the JSPS-CAS Core-University Program in the field of Plasma and Nuclear Fusion
文摘A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma model of ITER physics guidelines and the two-point SOL-divertor model are applied, This CSD model is validated by the two dimensional divertor transport code （B2-EIRINE） and by the JT-60U divertor recycling database, and this model is applicable to the low- and high-recycling state of the divertor plasma. The CSD model is applied to the study of the EAST operational space with lower hybrid current drive under various kinds of trade-off for the basic plasma parameters, and the relationship between the operational space and the plasma discharge duration is also discussed.
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.
基金The project is partially supported by NNSFC and PNSFS
文摘Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is shown that phi is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number lambda satisfying lambda(k-1) = 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - 1)-th power I.
基金Project partially supported by the National Natural Science Foundation of China (10871174,10801119)
文摘In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak＊ dense in the corresponding completely bound mapping spaces.
基金the French ANR project(ANR-19-CE40-0002)the Natural Science Foundation of China(12031004).
文摘Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10774033, 60878018 and 10674036)the Program of Excellent Team in Harbin Institute of Technologythe Program for New Century Excellent Talents in University(NCET),China (Grant No. NCET-04-0319)
文摘We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N2 and O2 molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N2 and O2 molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of ／sigma and ／pi orbitals, the bonding orbital （π2pz）^2 of N2 determines the maximum of harmonic emission when the molecular axis of N2 is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O2 molecule the antibonding orbitals （π2pz）^1 and （π2pz）^1 contribute to the maximum of harmonic yield when O2 is aligned at 45° and bonding orbitals （π2pz）^2 and （π2pz）^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45°.
文摘We consider the space of rapidly decreasing sequences s and the derivative operator D defined on it. The object of this article is to study the equivalence of a differential operator of infinite order; that is φ（D） =^∞∑k=0φkD^k.φk constant numbers an a power of D.Dn, meaning, is there a isomorphism X （from s onto s） such that Xφ（D） = D^nX？. We prove that if φ（D） is equivalent to Dn, then φ（D） is of finite order, in fact a polynomial of degree n. The question of the equivalence of two differential operators of finite order in the space s is addressed too and solved completely when n = 1.
文摘In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.
