The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,w...The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,which has significant applications in heat exchangers and engineering devices.To optimize heat transfer,a liquid film of Cu and TiO_(2)hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its importance.The nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid film.The solution of the problem is acquired using the homotopy analysis method HAM,and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve analysis.HAM data is utilized to train the ANN in this study,which uses Cu and TiO_(2)hybrid nanofluids in a variable porous space for unsteady thin film flow,and it is used to train the ANN.The results indicate that Cu and TiO_(2)play a greater role in boosting the rate.展开更多
In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Mo...In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular ...Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems,heat transfer and thermal management systems improve efficiency using porous materials with variable porosity.Keeping these important applications in view,in current study blood-based hybrid nanofluid flow has considered on a convectively heated sheet.The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions.Blood has used as base fluid in which the nanoparticles of Cu and Cu O have been mixed.Thermal radiation,space-dependent,and thermal-dependent heat sources have been incorporated into the energy equation,while magnetic effects have been integrated into the momentum equations.Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach.It has concluded in this study that,both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio,Casson,magnetic,and slip factors along x-and y-axes.Thermal distribution has grown up with upsurge in Casson factor,magnetic factor,thermal Biot number,and thermal/space-dependent heat sources while has retarded with growth in variable porous and stretching ratio factors.The findings of this investigation have been compared with the existing literature,revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.展开更多
An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive f...An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.展开更多
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley...In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.展开更多
Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.展开更多
In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable expo...In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.展开更多
In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditio...In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1.展开更多
A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid ...A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.展开更多
Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task ow...Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.展开更多
Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positiv...Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).展开更多
We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the auth...We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.展开更多
In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,th...In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.展开更多
In this paper,by applying the extension of Rubio de Francia’s extrapolation theorem in Lebesgue spaces with variable exponent,the boundedness of theθ-type Calderon-Zygmund operator Tθis bounded in variable exponent...In this paper,by applying the extension of Rubio de Francia’s extrapolation theorem in Lebesgue spaces with variable exponent,the boundedness of theθ-type Calderon-Zygmund operator Tθis bounded in variable exponent Lebesgue spaces.In addition,the commutators generated by Tθand Besov,BMO and Lipschitz functions are respectively obtained in L^(p)^((·))(R^(n)).展开更多
Taking the three-riser group arranged in tandem as the research subject,an experimental study was carried out on the risers arranged in tandem.The purpose is to explore the sensitivity of the dynamic response of each ...Taking the three-riser group arranged in tandem as the research subject,an experimental study was carried out on the risers arranged in tandem.The purpose is to explore the sensitivity of the dynamic response of each riser to spacing ratio and reveal the physical mechanism of riser groups under the interference effect.The spacing ratios of the adj acent risers are 4.0,5.0,6.0,and 8.0.At the spacing between the risers of 4.0D,the strong feedback effect increases the cross-flow(CF) displacement amplitude of the upstream riser.The shielding effect is the key factor affecting the interference effect on the midstream and downstream risers.At low reduced velocities,the shielding area initially appears,the displacement amplitude of the midstream and downstream risers varies greatly,the vibration of the two risers is still dominated by the first-order mode,and the transition between adjacent vibration modes is restrained.The multi-frequency superposition phenomenon is very significant at high reduced velocities.The most sensitive interference spacing under the test conditions is obtained.Due to the separation of the incoming flow and the double shielding effect of the upstream and midstream risers,the regular vortex-induced vibration in the wake area of the downstream riser is broken,and the vibration in the two directions is weakened.In general,the interference effect is more significant for the CF vibration of the three-riser groups than the in-line(IL) vibration.展开更多
This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprg...This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,which has significant applications in heat exchangers and engineering devices.To optimize heat transfer,a liquid film of Cu and TiO_(2)hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its importance.The nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid film.The solution of the problem is acquired using the homotopy analysis method HAM,and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve analysis.HAM data is utilized to train the ANN in this study,which uses Cu and TiO_(2)hybrid nanofluids in a variable porous space for unsteady thin film flow,and it is used to train the ANN.The results indicate that Cu and TiO_(2)play a greater role in boosting the rate.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)。
文摘In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
基金supported via funding from Prince Sattam bin Abdulaziz University(Grant No.PSAU/2024/R/1446)。
文摘Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems,heat transfer and thermal management systems improve efficiency using porous materials with variable porosity.Keeping these important applications in view,in current study blood-based hybrid nanofluid flow has considered on a convectively heated sheet.The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions.Blood has used as base fluid in which the nanoparticles of Cu and Cu O have been mixed.Thermal radiation,space-dependent,and thermal-dependent heat sources have been incorporated into the energy equation,while magnetic effects have been integrated into the momentum equations.Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach.It has concluded in this study that,both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio,Casson,magnetic,and slip factors along x-and y-axes.Thermal distribution has grown up with upsurge in Casson factor,magnetic factor,thermal Biot number,and thermal/space-dependent heat sources while has retarded with growth in variable porous and stretching ratio factors.The findings of this investigation have been compared with the existing literature,revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.
基金co-supported by National Natural Science Foundation of China (Nos. 91116017, 60974106 and 11102080)Funding for Outstanding Doctoral Dissertation in NUAA (No. BCXJ10-04)
文摘An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
文摘In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
基金supported by NSFC (No. 11101001 and No. 11201003)Education Committee of Anhui Province (No. KJ2011A138 and No. KJ2012A133)
文摘Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
基金Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
基金supported by NSFC(11471251)supported by NSFC(11271293)
文摘In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.
基金Supported by the NSF of Zhejiang Province (Y6090681)the Education Dept.of Zhejiang Province(Y201120509)
文摘In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
文摘In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1.
基金Supported by the National Natural Science Foundation of China(90920304)
文摘A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.
文摘Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.
基金supported by the National Natural Science Foundation of China(11801555 and 11971058)the Fundamental Research Funds for the Central Universities(2020YQLX02)supported by the National Natural Science Foundation of China(11971058,11761131002 and 11671185)。
文摘Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).
文摘We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
基金Supported by the Guangdong Natural Science foundation(2023A1515012044)Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities(2023ZDZX4069)+1 种基金the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College’s Characteristic Research Projects(2024HSTS09)。
文摘In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.
基金supported by National Natural Science Foundation of China(Grant No.12361018)Key Laboratory of Computational Science and Application of Hainan Province(Grant No.JSKX 202304).
文摘In this paper,by applying the extension of Rubio de Francia’s extrapolation theorem in Lebesgue spaces with variable exponent,the boundedness of theθ-type Calderon-Zygmund operator Tθis bounded in variable exponent Lebesgue spaces.In addition,the commutators generated by Tθand Besov,BMO and Lipschitz functions are respectively obtained in L^(p)^((·))(R^(n)).
基金financially supported by the National Natural Science Foundation of China (Grant No. 42177167)the Natural Science Foundation of Shandong Province (Grant No. ZR2019QEE008)。
文摘Taking the three-riser group arranged in tandem as the research subject,an experimental study was carried out on the risers arranged in tandem.The purpose is to explore the sensitivity of the dynamic response of each riser to spacing ratio and reveal the physical mechanism of riser groups under the interference effect.The spacing ratios of the adj acent risers are 4.0,5.0,6.0,and 8.0.At the spacing between the risers of 4.0D,the strong feedback effect increases the cross-flow(CF) displacement amplitude of the upstream riser.The shielding effect is the key factor affecting the interference effect on the midstream and downstream risers.At low reduced velocities,the shielding area initially appears,the displacement amplitude of the midstream and downstream risers varies greatly,the vibration of the two risers is still dominated by the first-order mode,and the transition between adjacent vibration modes is restrained.The multi-frequency superposition phenomenon is very significant at high reduced velocities.The most sensitive interference spacing under the test conditions is obtained.Due to the separation of the incoming flow and the double shielding effect of the upstream and midstream risers,the regular vortex-induced vibration in the wake area of the downstream riser is broken,and the vibration in the two directions is weakened.In general,the interference effect is more significant for the CF vibration of the three-riser groups than the in-line(IL) vibration.
基金Supported by the National Natrual Science Foun dation of ChiYla(10071058)
文摘This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
