In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modul...In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.展开更多
The urgent requirement of electronic skin conformably attached to nonplanar surfaces to provide sta-ble monitoring in areas of healthcare,prosthetics,and robotics promotes the development of strain-insensitive/unpertu...The urgent requirement of electronic skin conformably attached to nonplanar surfaces to provide sta-ble monitoring in areas of healthcare,prosthetics,and robotics promotes the development of strain-insensitive/unperturbed pressure sensors.The main challenges lie in:(1)stretchability and conduc-tive stability of flexible electrodes and(2)mechanical stability of heterogeneous interfaces.This study presents a highly stable strain-insensitive pressure sensor achieved by in-plane strain modulation and quasi-homogenous interfacial design.Strain modulation of stretchable electrodes by both periodic mi-crostructured engineering and pre-stretching strategies(called“island-ripple”)was employed to suppress microcracks propagation.The improvement in stretchability and cyclic conductive stability of electrodes was identified by finite element analysis and experimental verification.The pre-stretched microconed stretchable electrode with a low sheet resistance of 0.546sq^(−1) shows a maximum deformation of up to 80%and excellent cyclic conductive stability over 10000 times under 30%strain.Quasi-homogenous interface strategy by the CNTs/PDMS system was employed to enhance the mechanical and electrical sta-bility of the electrode-active materials interface,demonstrating a strong peel strength and shear strength of>40.9 N/m and>124.8 kPa,respectively.The as-prepared strain-insensitive pressure sensor provides constant sensing performance over 5000 stretching-releasing cycles within 20%stretching.In addition,a 4×4 pixel strain-insensitive pressure sensor array with reduced cross-talk circuit design was further integrated to identify the shape and weight of different objects under strains.The stretchability and sta-bility of our sensor enable it to be applied in stretchable electronics with great potential.展开更多
A simple model for reconstructing the paleomagnetic field intensity with (10)~Be production rate was used for the first time in Loess (10)~Be studies of Luochuan profile. Using the LGM (Last Glacial Maxmium) method, t...A simple model for reconstructing the paleomagnetic field intensity with (10)~Be production rate was used for the first time in Loess (10)~Be studies of Luochuan profile. Using the LGM (Last Glacial Maxmium) method, the climatic effects and geomagnetic modulation effects on loess (10)~Be was separated and in turn the 80 ka geomagnetic excursion sequence reconstructed, of which the globally remarkable geomagnetic excursion events such as the Laschamp (42 ka), Mono Lake (32 ka) during the Last Glacial period were revealed and the paleo-geomagnetic intensity curve from Loess (10)~Be over the past 80 ka was quantitatively reconstructed. The reconstructed paleo-intensity fits well with the paleo-intensity curves (SINT200 and NAPIS75), which indicates the significance of global criterion of the (10)~Be paleo- intensity curve and the future direction of loess (10)~Be tracing studies. Results show the irregular vari-ability of the East Asian monsoon precipitation in Loess Plateau is the main cause that has resulted in the ambiguity of the geomagnetic modulation of the (10)~Be record in the loess, and the intrinsic source component of the loess (10)~Be and inherited fraction of magnetic susceptibility (SUS) are characterized by the 'quasi-homogeneous distribution' manner.展开更多
We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhard...We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.展开更多
The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular...The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.展开更多
When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concent...When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.展开更多
To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for...To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for risk assessment, because there emerge many high-intensity pollutant areas in the instantaneous concentration field. In this study, we tried to estimate the frequency of appearance of the high concentration areas in a turbulent flow based on the Probability Density Function (PDF) of concentration. The high concentration area was recognized by two conditions based on the concentration and the concentration gradient values. We considered that the estimation equation for the frequency of appearance of the recognized areas consisted of two terms based on each condition. In order to represent the two terms with physical quantities of velocity and concentration fields, simultaneous PIV (Particle Image Velocimetry) and PLIF (Planar Laser-Induced Fluorescence) measurement and PLIF time-serial measurement were performed in a quasi-homogeneous turbulent flow. According to the experimental results, one of the terms, related to the condition of the concentration, was found to be represented by the concentration PDF, while the other term, by the streamwise mean velocity and the integral length scale of the turbulent flow. Based on the results, we developed an estimation equation including the concentration PDF and the flow features of mean velocity and integral scale of turbulence. In the area where the concentration PDF was a Gaussian one, the difference between the frequencies of appearance estimated by the equation and calculated from the experimental data was within 25%, which showed good accuracy of our proposed estimation equation. Therefore, our proposed equation is feasible for estimating the frequency of appearance of high concentration areas in a limited area in turbulent mass diffusion.展开更多
In this paper, we characterize the essential normality of quasi-homogeneous quotient Hardy modules over the polydisc by giving a complete criterion in terms of partially maximal ideals. Then we generalize this result ...In this paper, we characterize the essential normality of quasi-homogeneous quotient Hardy modules over the polydisc by giving a complete criterion in terms of partially maximal ideals. Then we generalize this result to the weighted Bergman modules.展开更多
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\...By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite展开更多
In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields w...In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields which generalize the so–called degenerate infinityvector fields are also integrable.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101240and10831007)Laboratory of Mathematics for Nonlinear Science of Fudan UniversityIndependent Innovation Foundation of Shandong University
文摘In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.
基金the National Key R&D Program of China(No.2018YFA0702100)the Zhejiang Provincial Key R&D Program of China(Nos.2021C05002 and 2021C01026)+3 种基金the National Natural Science Foundation of China(No.U21A2079)the Beijing Natural Science Foundation(No.2182032)the Basic R&D Program of Zhejiang(No.LGC22B050044)the Leading In-novative and Entrepreneur Team Introduction Program of Zhejiang(No.2020R01007).
文摘The urgent requirement of electronic skin conformably attached to nonplanar surfaces to provide sta-ble monitoring in areas of healthcare,prosthetics,and robotics promotes the development of strain-insensitive/unperturbed pressure sensors.The main challenges lie in:(1)stretchability and conduc-tive stability of flexible electrodes and(2)mechanical stability of heterogeneous interfaces.This study presents a highly stable strain-insensitive pressure sensor achieved by in-plane strain modulation and quasi-homogenous interfacial design.Strain modulation of stretchable electrodes by both periodic mi-crostructured engineering and pre-stretching strategies(called“island-ripple”)was employed to suppress microcracks propagation.The improvement in stretchability and cyclic conductive stability of electrodes was identified by finite element analysis and experimental verification.The pre-stretched microconed stretchable electrode with a low sheet resistance of 0.546sq^(−1) shows a maximum deformation of up to 80%and excellent cyclic conductive stability over 10000 times under 30%strain.Quasi-homogenous interface strategy by the CNTs/PDMS system was employed to enhance the mechanical and electrical sta-bility of the electrode-active materials interface,demonstrating a strong peel strength and shear strength of>40.9 N/m and>124.8 kPa,respectively.The as-prepared strain-insensitive pressure sensor provides constant sensing performance over 5000 stretching-releasing cycles within 20%stretching.In addition,a 4×4 pixel strain-insensitive pressure sensor array with reduced cross-talk circuit design was further integrated to identify the shape and weight of different objects under strains.The stretchability and sta-bility of our sensor enable it to be applied in stretchable electronics with great potential.
基金the Key Innovation Project of the Chinese Academy of Sciences (Grant No. KZCX2-YW-118)the National Natural Science Foundation of China (Grant Nos: 40531003, 40121303, 40523002)State Key Laboratory of Loess and Qua-ternary Geology in the Institute of Earth Environment of Chinese Academy of Sci-ences (Grant No. SKLLQG0712)
文摘A simple model for reconstructing the paleomagnetic field intensity with (10)~Be production rate was used for the first time in Loess (10)~Be studies of Luochuan profile. Using the LGM (Last Glacial Maxmium) method, the climatic effects and geomagnetic modulation effects on loess (10)~Be was separated and in turn the 80 ka geomagnetic excursion sequence reconstructed, of which the globally remarkable geomagnetic excursion events such as the Laschamp (42 ka), Mono Lake (32 ka) during the Last Glacial period were revealed and the paleo-geomagnetic intensity curve from Loess (10)~Be over the past 80 ka was quantitatively reconstructed. The reconstructed paleo-intensity fits well with the paleo-intensity curves (SINT200 and NAPIS75), which indicates the significance of global criterion of the (10)~Be paleo- intensity curve and the future direction of loess (10)~Be tracing studies. Results show the irregular vari-ability of the East Asian monsoon precipitation in Loess Plateau is the main cause that has resulted in the ambiguity of the geomagnetic modulation of the (10)~Be record in the loess, and the intrinsic source component of the loess (10)~Be and inherited fraction of magnetic susceptibility (SUS) are characterized by the 'quasi-homogeneous distribution' manner.
基金supported by the National Natural Science Foundation of China(11371257)Colleges and Universities Science and Technology Research Foundation of Hebei Province(QN2016304)
文摘We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.
基金Supported by Ministerio de Ciencia y Tecnología,Plan Nacional I+D+I co-financed with FEDER funds,in the frame of the pro jects MTM2010-20907-C02-02by Consejería de Educación y Ciencia de la Junta de Andalucía(Grant Nos.FQM-276 and P08-FQM-03770)
文摘The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.
文摘When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.
文摘To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for risk assessment, because there emerge many high-intensity pollutant areas in the instantaneous concentration field. In this study, we tried to estimate the frequency of appearance of the high concentration areas in a turbulent flow based on the Probability Density Function (PDF) of concentration. The high concentration area was recognized by two conditions based on the concentration and the concentration gradient values. We considered that the estimation equation for the frequency of appearance of the recognized areas consisted of two terms based on each condition. In order to represent the two terms with physical quantities of velocity and concentration fields, simultaneous PIV (Particle Image Velocimetry) and PLIF (Planar Laser-Induced Fluorescence) measurement and PLIF time-serial measurement were performed in a quasi-homogeneous turbulent flow. According to the experimental results, one of the terms, related to the condition of the concentration, was found to be represented by the concentration PDF, while the other term, by the streamwise mean velocity and the integral length scale of the turbulent flow. Based on the results, we developed an estimation equation including the concentration PDF and the flow features of mean velocity and integral scale of turbulence. In the area where the concentration PDF was a Gaussian one, the difference between the frequencies of appearance estimated by the equation and calculated from the experimental data was within 25%, which showed good accuracy of our proposed estimation equation. Therefore, our proposed equation is feasible for estimating the frequency of appearance of high concentration areas in a limited area in turbulent mass diffusion.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471189 and 11501329)Shandong Province Natural Science Foundation (Grant No. ZR2014AQ009)the Fundamental Research Funds of Shandong University (Grant No. 2015GN017)
文摘In this paper, we characterize the essential normality of quasi-homogeneous quotient Hardy modules over the polydisc by giving a complete criterion in terms of partially maximal ideals. Then we generalize this result to the weighted Bergman modules.
基金the National Natural Science Foundation of China (Grnat No. 19971068) .
文摘By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite
基金supported by the Spanish MCYT,Grant Number BFM 2002-04236-C01-01
文摘In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields which generalize the so–called degenerate infinityvector fields are also integrable.
