In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In 2021,EAST realized a steady-state long pulse with a duration over 100 s and a core electron temperature over 10 keV.This is an integrated operation that resolves several key issues,including active control of wall ...In 2021,EAST realized a steady-state long pulse with a duration over 100 s and a core electron temperature over 10 keV.This is an integrated operation that resolves several key issues,including active control of wall conditioning,long-lasting fully noninductive current and divertor heat/particle flux.The fully noninductive current is driven by pure radio frequency(RF)waves with a lower hybrid current drive power of 2.5 MW and electron cyclotron resonance heating of 1.4 MW.This is an excellent experimental platform on the timescale of hundreds of seconds for studying multiscale instabilities,electron-dominant transport and particle recycling(plasma-wall interactions)under weak collisionality.展开更多
We experimentally demonstrate an In P-based hybrid integration of a single-mode DFB laser emitting at around 1310 nm and a tunneling diode. The evident negative differential resistance regions are obtained in both ele...We experimentally demonstrate an In P-based hybrid integration of a single-mode DFB laser emitting at around 1310 nm and a tunneling diode. The evident negative differential resistance regions are obtained in both electrical and optical output characteristics. The electrical and optical bistabilities controlled by the voltage through the tunneling diode are also measured. When the voltage changes between 1.46 V and 1.66 V, a 200-mV-wide hysteresis loop and an optical power ON/OFF ratio of 17 dB are obtained. A side-mode suppression ratio of the integrated device in the ON state is up to 43 dB. The tunneling diode can switch on/off the laser within a very small voltage range compared with that directly controlled by a voltage source.展开更多
We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on ...We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).展开更多
Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^...Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t...To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.展开更多
Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits...Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.展开更多
In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objectiv...In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.展开更多
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ...It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).展开更多
In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, t...In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.展开更多
It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have ans...It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].展开更多
Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they ar...Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.展开更多
On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operat...On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.展开更多
In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS...It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.展开更多
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
基金the National Key R&D Program of China(No.2022YFE03010003)National Natural Science Foundation of China(No.12275309).
文摘In 2021,EAST realized a steady-state long pulse with a duration over 100 s and a core electron temperature over 10 keV.This is an integrated operation that resolves several key issues,including active control of wall conditioning,long-lasting fully noninductive current and divertor heat/particle flux.The fully noninductive current is driven by pure radio frequency(RF)waves with a lower hybrid current drive power of 2.5 MW and electron cyclotron resonance heating of 1.4 MW.This is an excellent experimental platform on the timescale of hundreds of seconds for studying multiscale instabilities,electron-dominant transport and particle recycling(plasma-wall interactions)under weak collisionality.
基金Supported by the National Key Research and Development Program of China under Grant No 2017YFB0405301the National Natural Science Foundation of China under Grant Nos 61604144 and 61504137
文摘We experimentally demonstrate an In P-based hybrid integration of a single-mode DFB laser emitting at around 1310 nm and a tunneling diode. The evident negative differential resistance regions are obtained in both electrical and optical output characteristics. The electrical and optical bistabilities controlled by the voltage through the tunneling diode are also measured. When the voltage changes between 1.46 V and 1.66 V, a 200-mV-wide hysteresis loop and an optical power ON/OFF ratio of 17 dB are obtained. A side-mode suppression ratio of the integrated device in the ON state is up to 43 dB. The tunneling diode can switch on/off the laser within a very small voltage range compared with that directly controlled by a voltage source.
基金partially supported by the Fundamental Research Funds for the Central Universities(GK202207018)of China。
文摘We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).
基金Supported by the National Natural Science Foundation of China(11801518)the Natural Science Foundation of Zhejiang Province(LQ18A010005)the Science Foundation of Zhejiang Education Department(Y201738640)。
文摘Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
基金Project supported by the Foundation for Young Talents in College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant Nos. 2022AH051580 and 2022AH051586)。
文摘To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.
文摘Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.
文摘In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.
文摘It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).
文摘In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.
文摘It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].
文摘Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.
基金Supported by the National Natural Science Foundation of China (10771049, 10801043)the Hebei Natural Science Foundation (A2007000225, A2010000346)
文摘On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.
基金Supported by the National Natural Science Foundation of China(11271330)
文摘In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
基金NNSFC(11771223,11501308)Natural science foundation of Inner Mongolia(2019MS01003).
文摘Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
文摘It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.
