Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatm...Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatment and detecting relapse.Here,a highly enhanced plasmonic biosensor that can overcome this challenge is developed using atomically thin two-dimensional phase change nanomaterial.By precisely engineering the configuration with atomically thin materials,the phase singularity has been successfully achieved with a significantly enhanced lateral position shift effect.Based on our knowledge,it is the first experimental demonstration of a lateral position signal change>340μm at a sensing interface from all optical techniques.With this enhanced plasmonic effect,the detection limit has been experimentally demonstrated to be 10^(-15) mol L^(−1) for TNF-α cancer marker,which has been found in various human diseases including inflammatory diseases and different kinds of cancer.The as-reported novel integration of atomically thin Ge_(2)Sb_(2)Te_(5) with plasmonic substrate, which results in a phase singularity and thus a giant lateral position shift, enables the detection of cancer markers with low molecular weight at femtomolar level. These results will definitely hold promising potential in biomedical application and clinical diagnostics.展开更多
Acoustic-vortex(AV)tweezers ensure stable particle trapping at a zero-pressure center,while particle assembly between two vortex cores is still prevented by the high-potential barrier.Although a one-dimensional low-pr...Acoustic-vortex(AV)tweezers ensure stable particle trapping at a zero-pressure center,while particle assembly between two vortex cores is still prevented by the high-potential barrier.Although a one-dimensional low-pressure attractive path of particle assembly can be constructed by the interference between two independent cylindrical Bessel beams,it remains challenging to create two-dimensional(2D)neighboring vortexes using a source array in practical applications.In this paper,a three-step phase-reversal strategy of 2D particle assembly based on the synchronized evolution of a centrosymmetric array of M off-axis acoustic vortexes(OA-AVs)with a preset radial offset is proposed based on a ring array of planar sources.By introducing initial vortex phase differences of-2π/M and+2π/M to the vortex array,low-pressure patterns of an M-sided regular polygon and M-branched star are formed by connecting the vortex cores and the field center before and after the tangent state of adjacent OA-AVs.Center-oriented particle assembly is finally realized by a central AV constructed by coincident in-phase OA-AVs.The capability of particle manipulation in the lateral and radial directions is demonstrated by low-pressure patterns with acoustic radiation forces pointing to the field center during a synchronized central approach.The field evolution is certified by experimental field measurements for OA-AVs with different vo rtex numbers,initial vortex phase differences,and radial offsets using a ring array of 16 planar sources.The feasibility of particle assembly in two dimensions is also verified by the accurate manipulation of four particles using the low-pressure patterns of a four-sided polygon,a four-branched star,and a central AV in experiments.The three-step strategy paves a new way for 2D particle assembly based on the synchronize d evolution of centrosymmetric OA-AVs using a simplified single-sided source array,exhibiting excellent potential for the precise navigation and manipulation of cells and particles in biomedical applications.展开更多
Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experi...Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experimental and theoretical investigations of an ultrasensitive and multiplexed phase-sensitive sensor utilizing dual topological PSs in the visible and near-infrared regions.This sensor uses a simple structure,which consists of an ultra-thin highly absorbing film deposited on a metal substrate.We demonstrate the achievement of dual-polarization darkness points for s-and p-polarizations at different incident angles.Furthermore,we theoretically explain the double topological PSs accompanied by a perfect±π-jump near a zero-reflection point,based on the temporal coupled-mode formalism.To validate its multifunctional capabilities,humidity sensing tests were carried out.The results demonstrate that the sensor has a detection limit reaching the level of 0.12‰.These findings go beyond the scope of conventional interference optical coatings and highlight the potential applications of this technology in gas sensing and biosensing domains.展开更多
By using the generalized Debye diffraction integral, this paper studies the spatial correlation properties and phase singularity annihilation of apertured Gaussian Schell-model （GSM） beams in the focal region. It is...By using the generalized Debye diffraction integral, this paper studies the spatial correlation properties and phase singularity annihilation of apertured Gaussian Schell-model （GSM） beams in the focal region. It is shown that the width of the spectral degree of coherence can be larger, less than or equal to the corresponding width of spectral density, which depends not only on the scalar coherence length of the beams, but also on the truncation parameter. With a gradual increase of the truncation parameter, a pair of phase singularities of the spectral degree of coherence in the focal plane approaches each other, resulting in subwavelength structures. Finally, the annihilation of pairs of phase singularities takes place at a certain value of the truncation parameter. With increasing scalar coherence length, the annihilation occurs at the larger truncation parameter. However, the creation process of phase singularities outside the focal plane is not found for GSM beams.展开更多
In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.
Within the framework of Einstein-Cartan theory,we obtain a general condition leading to singularity and inflation for all Bianchi cosmological models.If the spin energy is smaller than anisotropic energy density(i.e.S...Within the framework of Einstein-Cartan theory,we obtain a general condition leading to singularity and inflation for all Bianchi cosmological models.If the spin energy is smaller than anisotropic energy density(i.e.S^(2)σ^(2)<0),the Universe can not avoid singularity.If S^(2)-σ^(2)>-pv/^(2)(pv is vacuum energy density),the Universe can undergo an inflation phase.Examples of Bianchi type-IX,I and V cosmological models are discussed.展开更多
In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the to...In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the topological currentform of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum ofthe linking and self-linking numbers of the knotted RS vortices.Furthermore,the conservation of the Hopf invariant inthe splitting,the mergence and the intersection processes of knotted RS vortices is also discussed.展开更多
Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Wi...Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Within the framework of a statistical approach,the authors have investigated values and ranges for changes of statistical moments of thefirst to the fourth orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by blood plasma with various pathologies.In the framework of the fractal approach,determined are the dimensions of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of hominal mammary gland pathologies.展开更多
We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positiv...We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positive, energy minimizing solutions.展开更多
Photonic devices that exhibit both sensitivity and robustness have long been sought;yet,these characteristics are thought to be mutually exclusive;through sensitivity,a sensor responds to external stimuli,whereas robu...Photonic devices that exhibit both sensitivity and robustness have long been sought;yet,these characteristics are thought to be mutually exclusive;through sensitivity,a sensor responds to external stimuli,whereas robustness embodies the inherent ability of a device to withstand weathering by these same stimuli.This challenge stems from the inherent contradiction between robustness and sensitivity in wave dynamics,which require the coexistence of noise-immune sensitive states and modulation-sensitive transitions between these states.We report and experimentally demonstrate a subwavelength phase singularity in a chiral medium that is resilient to fabrication imperfections and disorder while remaining highly responsive to external stimuli.The combination of subwavelength light confinement and its robustness lays the foundation for the development of hitherto unexplored chip-scale photonics devices,enabling a simultaneous development of high-sensitivity and robust devices in both quantum and classical realms.展开更多
Recently,physical fields with topological configurations are evoking increasing attention due to their fascinating structures both in fundamental researches and practical applications.Therein,topological light fields,...Recently,physical fields with topological configurations are evoking increasing attention due to their fascinating structures both in fundamental researches and practical applications.Therein,topological light fields,because of their unique opportunity of combining experimental and analytical studies,are attracting more interest.Here,based on the Pancharatnam-Berry(PB)phase,we report the creation of Hopf linked and Trefoil knotted optical vortices by using phaseonly encoded liquid crystal(LC)holographic plates.Utilizing scanning measurement and the digital holographic interference method,we accurately locate the vortex singularities and map these topological nodal lines in three-dimensions.Compared with the common methods realized by the spatial light modulator(SLM),the phase-only LC plate is more efficient.Meanwhile,the smaller pixel size of the LC element reduces the imperfection induced by optical misalignment and pixellation.Moreover,we analyze the influence of the incident beam size on the topological configuration.展开更多
As a third generation light source, Shanghai Synchrotron Radiation Facility (SSRF) has up to 140 beam position monitors (BPM) installed to monitor the beam dynamics on its storage ring. Once the operation mode is chos...As a third generation light source, Shanghai Synchrotron Radiation Facility (SSRF) has up to 140 beam position monitors (BPM) installed to monitor the beam dynamics on its storage ring. Once the operation mode is chosen, the betatron functions are determined. Since the sinusoidal betatron oscillation is the dominant component of the transverse motion, these BPMs can be used to measure the motion to get the betatron functions. Three methods are compared to calculate the phase advance among the BPMs in this paper, aiming to find one or more feasible ways to check the beam optics in SSRF. Some experiments have also been made to verify the practicality of the phase information.展开更多
Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics...Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics theory and the corresponding conservative laws, was studied. With the aid of qualitative theory and method of ordinary differential equations, the location of singular points on the Rayleigh curves is determined, the qualitative structure and the stability of the singular points of the laminar flame system, which are located in the areas of deflagration and detonation, are given for different parameter values and uses of combustion. The phase portraits of the laminar flame system in the reaction-stagnation enthalpy and combustion velocity-stagnation enthalpy planes are shown in the corresponding figures.展开更多
In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under...In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.展开更多
In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to H...In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.展开更多
The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there e...The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.展开更多
In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is...In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is a nonnegative function with only two zeros α and β. We show that the limit of a sequence of minimizers {u ε} ε>0 (as ε→0) is a solution of another variational problem.展开更多
基金We thank Shiyue Liu from School of Life Sciences in The Chinese University of Hong Kong for helpful discussions.This work is supported under the PROCORE-France/Hong Kong Joint Research Scheme(F-CUHK402/19)the Research Grants Council,Hong Kong Special Administration Region(AoE/P-02/12,14210517,14207419,N_CUHK407/16)the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No.798916.Y.Wang is supported under the Hong Kong PhD Fellowship Scheme.
文摘Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatment and detecting relapse.Here,a highly enhanced plasmonic biosensor that can overcome this challenge is developed using atomically thin two-dimensional phase change nanomaterial.By precisely engineering the configuration with atomically thin materials,the phase singularity has been successfully achieved with a significantly enhanced lateral position shift effect.Based on our knowledge,it is the first experimental demonstration of a lateral position signal change>340μm at a sensing interface from all optical techniques.With this enhanced plasmonic effect,the detection limit has been experimentally demonstrated to be 10^(-15) mol L^(−1) for TNF-α cancer marker,which has been found in various human diseases including inflammatory diseases and different kinds of cancer.The as-reported novel integration of atomically thin Ge_(2)Sb_(2)Te_(5) with plasmonic substrate, which results in a phase singularity and thus a giant lateral position shift, enables the detection of cancer markers with low molecular weight at femtomolar level. These results will definitely hold promising potential in biomedical application and clinical diagnostics.
基金funded by the National Nature Science Foundation of China(11934009,12174198,and 12227808)the Natural Science Foundation of Jiangsu Province,China(BE2022814)+2 种基金the Universal Technology for Primary and Secondary Schoolsthe National Research Institute for Teaching Materialsthe Qing Lan Project of Jiangsu Province,China。
文摘Acoustic-vortex(AV)tweezers ensure stable particle trapping at a zero-pressure center,while particle assembly between two vortex cores is still prevented by the high-potential barrier.Although a one-dimensional low-pressure attractive path of particle assembly can be constructed by the interference between two independent cylindrical Bessel beams,it remains challenging to create two-dimensional(2D)neighboring vortexes using a source array in practical applications.In this paper,a three-step phase-reversal strategy of 2D particle assembly based on the synchronized evolution of a centrosymmetric array of M off-axis acoustic vortexes(OA-AVs)with a preset radial offset is proposed based on a ring array of planar sources.By introducing initial vortex phase differences of-2π/M and+2π/M to the vortex array,low-pressure patterns of an M-sided regular polygon and M-branched star are formed by connecting the vortex cores and the field center before and after the tangent state of adjacent OA-AVs.Center-oriented particle assembly is finally realized by a central AV constructed by coincident in-phase OA-AVs.The capability of particle manipulation in the lateral and radial directions is demonstrated by low-pressure patterns with acoustic radiation forces pointing to the field center during a synchronized central approach.The field evolution is certified by experimental field measurements for OA-AVs with different vo rtex numbers,initial vortex phase differences,and radial offsets using a ring array of 16 planar sources.The feasibility of particle assembly in two dimensions is also verified by the accurate manipulation of four particles using the low-pressure patterns of a four-sided polygon,a four-branched star,and a central AV in experiments.The three-step strategy paves a new way for 2D particle assembly based on the synchronize d evolution of centrosymmetric OA-AVs using a simplified single-sided source array,exhibiting excellent potential for the precise navigation and manipulation of cells and particles in biomedical applications.
基金supported by the National Key R&D Program of China(2022YFA1404701)Program of Shanghai Academic Research Leader under Grant(22XD1422100)+4 种基金National Natural Science Foundation of China(62075231,12141303,12073018)Shanghai Science and Technology Committee(20JC1414603,23dz2260100)Shanghai Pujiang Program(21PJ1411400)China Postdoctoral Science Foundation(2021M703335)Young Elite Scientists Sponsorship Program by CAST(YESS20220355).
文摘Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experimental and theoretical investigations of an ultrasensitive and multiplexed phase-sensitive sensor utilizing dual topological PSs in the visible and near-infrared regions.This sensor uses a simple structure,which consists of an ultra-thin highly absorbing film deposited on a metal substrate.We demonstrate the achievement of dual-polarization darkness points for s-and p-polarizations at different incident angles.Furthermore,we theoretically explain the double topological PSs accompanied by a perfect±π-jump near a zero-reflection point,based on the temporal coupled-mode formalism.To validate its multifunctional capabilities,humidity sensing tests were carried out.The results demonstrate that the sensor has a detection limit reaching the level of 0.12‰.These findings go beyond the scope of conventional interference optical coatings and highlight the potential applications of this technology in gas sensing and biosensing domains.
基金supported by the National Natural Science Foundation of China (Grant No 10574097)the Youth Foundation of University of Electronics Science and Technology of China
文摘By using the generalized Debye diffraction integral, this paper studies the spatial correlation properties and phase singularity annihilation of apertured Gaussian Schell-model （GSM） beams in the focal region. It is shown that the width of the spectral degree of coherence can be larger, less than or equal to the corresponding width of spectral density, which depends not only on the scalar coherence length of the beams, but also on the truncation parameter. With a gradual increase of the truncation parameter, a pair of phase singularities of the spectral degree of coherence in the focal plane approaches each other, resulting in subwavelength structures. Finally, the annihilation of pairs of phase singularities takes place at a certain value of the truncation parameter. With increasing scalar coherence length, the annihilation occurs at the larger truncation parameter. However, the creation process of phase singularities outside the focal plane is not found for GSM beams.
文摘In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.
基金Partially supported by the Natural Science Foundation of Jiangsu Province under Grant No 07KJD140011the National Natural Science Foundation of China under Grant No 10573012Shanghai Municipal Science and Technology Commission(No 04dz05905).
文摘Within the framework of Einstein-Cartan theory,we obtain a general condition leading to singularity and inflation for all Bianchi cosmological models.If the spin energy is smaller than anisotropic energy density(i.e.S^(2)σ^(2)<0),the Universe can not avoid singularity.If S^(2)-σ^(2)>-pv/^(2)(pv is vacuum energy density),the Universe can undergo an inflation phase.Examples of Bianchi type-IX,I and V cosmological models are discussed.
基金supported by National Natural Science Foundation of China and the Cuiying Programme of Lanzhou University
文摘In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the topological currentform of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum ofthe linking and self-linking numbers of the knotted RS vortices.Furthermore,the conservation of the Hopf invariant inthe splitting,the mergence and the intersection processes of knotted RS vortices is also discussed.
文摘Performed in this work are complex statistical,fractal and singular analyses of phase properties inherent to birefringence networks of protein crystals consisting of optically-thin layers prepared from blood plasma.Within the framework of a statistical approach,the authors have investigated values and ranges for changes of statistical moments of thefirst to the fourth orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by blood plasma with various pathologies.In the framework of the fractal approach,determined are the dimensions of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of hominal mammary gland pathologies.
基金supported by the NNSF of China (12071413, 12111530282)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 CONMECH。
文摘We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positive, energy minimizing solutions.
基金supported by the 2023 Beckman Young Investigator Award, from the Arnold and Mabel Beckman FoundationAir Force Office of Scientific Research MURI (Award No. FA9550-22-1-0312)+5 种基金PAIR-UP program sponsored by ASCBfunded in part by The Gordon Moore Foundation, with additional support from the Burroughs Wellcome Funds2022 Scialog: Advancing Bio ImagingKavli Innovation GrantSilicon Valley Community Foundation (Grant No. DAF2023331948)cZi Dynamic imaging via the Chan Zuckerberg Donor Advised Fund (DAF) through the Silicon Valley Community Foundation
文摘Photonic devices that exhibit both sensitivity and robustness have long been sought;yet,these characteristics are thought to be mutually exclusive;through sensitivity,a sensor responds to external stimuli,whereas robustness embodies the inherent ability of a device to withstand weathering by these same stimuli.This challenge stems from the inherent contradiction between robustness and sensitivity in wave dynamics,which require the coexistence of noise-immune sensitive states and modulation-sensitive transitions between these states.We report and experimentally demonstrate a subwavelength phase singularity in a chiral medium that is resilient to fabrication imperfections and disorder while remaining highly responsive to external stimuli.The combination of subwavelength light confinement and its robustness lays the foundation for the development of hitherto unexplored chip-scale photonics devices,enabling a simultaneous development of high-sensitivity and robust devices in both quantum and classical realms.
基金supported by National Natural Science Foundation of China(61273197,61503224)Applied Fundamental Research of Qingdao(14-2-4-19-jch)+2 种基金Huangdao District Science and Technology Project(2014-1-33)China Postdoctoral Science Foundation(2015M582115)"Taishan Scholarship"Construction Engineering
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11634010,91850118,11774289,61675168,and 11804277)the National Key Research and Development Program of China(Grant No.2017YFA0303800)+1 种基金the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics(Grant No.U1630125)the Fundamental Research Funds for the Central Universities,China(Grant Nos.3102018zy036,3102019JC008,and 310201911cx022)。
文摘Recently,physical fields with topological configurations are evoking increasing attention due to their fascinating structures both in fundamental researches and practical applications.Therein,topological light fields,because of their unique opportunity of combining experimental and analytical studies,are attracting more interest.Here,based on the Pancharatnam-Berry(PB)phase,we report the creation of Hopf linked and Trefoil knotted optical vortices by using phaseonly encoded liquid crystal(LC)holographic plates.Utilizing scanning measurement and the digital holographic interference method,we accurately locate the vortex singularities and map these topological nodal lines in three-dimensions.Compared with the common methods realized by the spatial light modulator(SLM),the phase-only LC plate is more efficient.Meanwhile,the smaller pixel size of the LC element reduces the imperfection induced by optical misalignment and pixellation.Moreover,we analyze the influence of the incident beam size on the topological configuration.
基金Supported by National Natural Science Foundation of China (No.11075198)
文摘As a third generation light source, Shanghai Synchrotron Radiation Facility (SSRF) has up to 140 beam position monitors (BPM) installed to monitor the beam dynamics on its storage ring. Once the operation mode is chosen, the betatron functions are determined. Since the sinusoidal betatron oscillation is the dominant component of the transverse motion, these BPMs can be used to measure the motion to get the betatron functions. Three methods are compared to calculate the phase advance among the BPMs in this paper, aiming to find one or more feasible ways to check the beam optics in SSRF. Some experiments have also been made to verify the practicality of the phase information.
基金theNaturalScienceFoundationofBeijingMunicipalGovernment (No .1 0 42 0 0 7)andtheScientificResearchFoundationfortheReturnedOverseasChineseScholars,StateEducationMinistry (No .Lxkyjj2 0 0 41 6)
文摘Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics theory and the corresponding conservative laws, was studied. With the aid of qualitative theory and method of ordinary differential equations, the location of singular points on the Rayleigh curves is determined, the qualitative structure and the stability of the singular points of the laminar flame system, which are located in the areas of deflagration and detonation, are given for different parameter values and uses of combustion. The phase portraits of the laminar flame system in the reaction-stagnation enthalpy and combustion velocity-stagnation enthalpy planes are shown in the corresponding figures.
基金Supported by the National Natural Science Foundation of China (11026104, 11201103, 11226108)
文摘In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.
基金Xu Jingshi is partially supported by the NSF of Hunan,China(01JJY3003)A project supported by Scientific Research Fund of Hunan Provincial Education Department(02C067)
文摘In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.
基金the National Natural Science Foundation of China (No.60473120)the Natural Science Foundation of Guangdong(No.6023190)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China.
文摘The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.
文摘In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is a nonnegative function with only two zeros α and β. We show that the limit of a sequence of minimizers {u ε} ε>0 (as ε→0) is a solution of another variational problem.
