2017 No. 3
Display Method:
2017, (3): 1-19.
doi: 10.3969/j.issn.1000-5641.2017.03.001
Abstract(
HTML
PDF 287KB
Abstract:
In this paper, we studied representations of finite-dimensional Lie superalgebras over an algebraically closed field\begin{document} $\mathbb{F}$ \end{document} \begin{document} $\mathbb{F}$ \end{document} \begin{document} ${\mathfrak{g}}$ \end{document} \begin{document} ${\mathfrak{g}}$ \end{document}
In this paper, we studied representations of finite-dimensional Lie superalgebras over an algebraically closed field
2017, (3): 20-28.
doi: 10.3969/j.issn.1000-5641.2017.03.002
Abstract:
Differential equations are playing more and more important role in modern science and technologies, engineering. On solving and integrability analysis of differential equations, our research group developed a dozen different off-line related software based on Maple. On the basis of these Maple packages, Maple and some open-source technologies, an online automated computing platform for equations called Emathema was proposed and implemented. Emathema can provide convenient and efficient online computing and graphing services for users. On this platform, users can not only solve nonlinear algebraic and differential equations using external Maple packages, but also execute almost all simple symbolic computations related to equations in the interactive mode. For each input, Emathema outputs the computing result visually.
Differential equations are playing more and more important role in modern science and technologies, engineering. On solving and integrability analysis of differential equations, our research group developed a dozen different off-line related software based on Maple. On the basis of these Maple packages, Maple and some open-source technologies, an online automated computing platform for equations called Emathema was proposed and implemented. Emathema can provide convenient and efficient online computing and graphing services for users. On this platform, users can not only solve nonlinear algebraic and differential equations using external Maple packages, but also execute almost all simple symbolic computations related to equations in the interactive mode. For each input, Emathema outputs the computing result visually.
2017, (3): 29-38.
doi: 10.3969/j.issn.1000-5641.2017.03.003
Abstract:
This paper mainly studied the geometric average Asian option pricing on the condition that the underlying asset followed mixed jump-fraction process. The general Itô's lemma and the self-financing dynamic strategy were obtained by using the partial differential equation of such option pricing in the mixed fractional environment with jump. With the combination of boundary condition, an analytic formula for the geometric average Asian option was derived by solving the partial differential equation. The numerical experiments were showed to discuss the influence of different parameters on the option value. The results were the generalization of some existing results which was closer to the real financial market.
This paper mainly studied the geometric average Asian option pricing on the condition that the underlying asset followed mixed jump-fraction process. The general Itô's lemma and the self-financing dynamic strategy were obtained by using the partial differential equation of such option pricing in the mixed fractional environment with jump. With the combination of boundary condition, an analytic formula for the geometric average Asian option was derived by solving the partial differential equation. The numerical experiments were showed to discuss the influence of different parameters on the option value. The results were the generalization of some existing results which was closer to the real financial market.
2017, (3): 39-47.
doi: 10.3969/j.issn.1000-5641.2017.03.004
Abstract:
A class of singularly perturbed system for the hyperbolic nonlinear integral-differential system is considered. Firstly, the outer solution to system is obtained by employing the Fredholm type integral equation. Then the boundary layer corrective term is constructed using the variables of multiple scales method. And the initial layer corrective term is found via the stretched variable method. Finally, from the fixed point theory, the uniformly valid behavior for the composed asymptotic expansion of singular perturbation solution is proved.
A class of singularly perturbed system for the hyperbolic nonlinear integral-differential system is considered. Firstly, the outer solution to system is obtained by employing the Fredholm type integral equation. Then the boundary layer corrective term is constructed using the variables of multiple scales method. And the initial layer corrective term is found via the stretched variable method. Finally, from the fixed point theory, the uniformly valid behavior for the composed asymptotic expansion of singular perturbation solution is proved.
2017, (3): 48-53.
doi: 10.3969/j.issn.1000-5641.2017.03.005
Abstract:
This paper investigates the oscillation of third-order half linear neutral functional differential equations with damping. By introducing parameter function and the generalized Riccati transformation and using integral averaging technique and some necessary technique, some new sufficient conditions which ensure that any solution of such equation oscillates or converges to zero were proposed. The corresponding results in literature are extended and improved.
This paper investigates the oscillation of third-order half linear neutral functional differential equations with damping. By introducing parameter function and the generalized Riccati transformation and using integral averaging technique and some necessary technique, some new sufficient conditions which ensure that any solution of such equation oscillates or converges to zero were proposed. The corresponding results in literature are extended and improved.
2017, (3): 54-63.
doi: 10.3969/j.issn.1000-5641.2017.03.006
Abstract:
This paper is concerned with oscillatory behavior of the following second-order nonlinear neutral variable delay functional dynamic equations[A(t)Φ([x(t)+B(t)g(x(τ(t)))]Δ)]Δ+ƒ(t, x(δ(t)))=0on a time scale T, where Φ(u)=|u|λ-1u (hereλ> 0 is an arbitrary constant). By using a couple of Riccati substitutions, the time scales theory and inequality technique, we establish two new oscillation criteria for the equations, these results deal with some cases not covered by existing results in the literature. Finally, two examples are presented to illustrate the importance of our theorems.
This paper is concerned with oscillatory behavior of the following second-order nonlinear neutral variable delay functional dynamic equations[A(t)Φ([x(t)+B(t)g(x(τ(t)))]Δ)]Δ+ƒ(t, x(δ(t)))=0on a time scale T, where Φ(u)=|u|λ-1u (hereλ> 0 is an arbitrary constant). By using a couple of Riccati substitutions, the time scales theory and inequality technique, we establish two new oscillation criteria for the equations, these results deal with some cases not covered by existing results in the literature. Finally, two examples are presented to illustrate the importance of our theorems.
2017, (3): 64-77, 86.
doi: 10.3969/j.issn.1000-5641.2017.03.007
Abstract:
A lot of images are usually photographed in the sports of track and field, and manual operation is a general method to retrieve image containing certain athletes. In order to quickly retrieve images containing a particular player, a method based on the number to identify a player is proposed. It firstly applied DPM (Deformable Part Model) algorithm to narrow the search scope of number plate. Secondly, according to the prior knowledge, the position of number plate can be located by considering two different ways to ensure the reliability. Thirdly, the characters of number plate are segmented by connected component analysis method. Finally, feature-based BP (Back Propagation) neural network is adopted to recognize the number plate. Experimental results show that the proposed method is efficient to identify the number plate of the players. The number plate recognition method provides a guideline of retrieving a specific player's images.
A lot of images are usually photographed in the sports of track and field, and manual operation is a general method to retrieve image containing certain athletes. In order to quickly retrieve images containing a particular player, a method based on the number to identify a player is proposed. It firstly applied DPM (Deformable Part Model) algorithm to narrow the search scope of number plate. Secondly, according to the prior knowledge, the position of number plate can be located by considering two different ways to ensure the reliability. Thirdly, the characters of number plate are segmented by connected component analysis method. Finally, feature-based BP (Back Propagation) neural network is adopted to recognize the number plate. Experimental results show that the proposed method is efficient to identify the number plate of the players. The number plate recognition method provides a guideline of retrieving a specific player's images.
2017, (3): 78-86.
doi: 10.3969/j.issn.1000-5641.2017.03.008
Abstract:
Due to the shortcomings that wolf pack algorithm is not high solving precision and easy to fall into the local convergence region, adaptive grouping difference variation wolf pack algorithm is proposed based on the excellent characteristics of cloud model transformation between qualitative and quantitative. Individual wolves are initialized by good-point set. Individual hunting behavior is accomplished through the cloud model theory and the self energy of the wolf is considered in the siege behavior. Finally, the differential evolution algorithm and the chaos theory are used to complete the individual variation to explore the global optimal location. The simulation results show that the proposed algorithm has fine capability of finding global optimum, especially for multi peak function.
Due to the shortcomings that wolf pack algorithm is not high solving precision and easy to fall into the local convergence region, adaptive grouping difference variation wolf pack algorithm is proposed based on the excellent characteristics of cloud model transformation between qualitative and quantitative. Individual wolves are initialized by good-point set. Individual hunting behavior is accomplished through the cloud model theory and the self energy of the wolf is considered in the siege behavior. Finally, the differential evolution algorithm and the chaos theory are used to complete the individual variation to explore the global optimal location. The simulation results show that the proposed algorithm has fine capability of finding global optimum, especially for multi peak function.
2017, (3): 87-93, 132.
doi: 10.3969/j.issn.1000-5641.2017.03.009
Abstract:
Based on our former theoretical analysis [Yaling Yin, et al, Opt. Commun. 281(22), 5511 (2008)], we experimentally design a simple optical device to generate a neat semi-Gaussian laser beam (SGB) without diffraction fringes by using a coherence attenuator and a thin sharp blade. The coherence attenuator is composed of two organic glasses and a piece of plastic film rotated by a motor, which can efficiently decrease the coherence of the laser field. In the experiment, we use He-Ne laser as light source and obtain a 632.8 nm neat SGB without diffraction fringes with a quality factor QSGB=1:16.42 at the propagating position z=0.5 cm. The experimental results show that the generated SGB's quality factor decreases with the increasing of the propagating distance. The ascent border width of the generated SGB is independent on the waist radius and wavelength of the incident Gaussian beam, which corresponds well with the theoretical analysis. Our generated SGB can be widely used in modern optics for its asymmetric intensity profile and good propagating properties.
Based on our former theoretical analysis [Yaling Yin, et al, Opt. Commun. 281(22), 5511 (2008)], we experimentally design a simple optical device to generate a neat semi-Gaussian laser beam (SGB) without diffraction fringes by using a coherence attenuator and a thin sharp blade. The coherence attenuator is composed of two organic glasses and a piece of plastic film rotated by a motor, which can efficiently decrease the coherence of the laser field. In the experiment, we use He-Ne laser as light source and obtain a 632.8 nm neat SGB without diffraction fringes with a quality factor QSGB=1:16.42 at the propagating position z=0.5 cm. The experimental results show that the generated SGB's quality factor decreases with the increasing of the propagating distance. The ascent border width of the generated SGB is independent on the waist radius and wavelength of the incident Gaussian beam, which corresponds well with the theoretical analysis. Our generated SGB can be widely used in modern optics for its asymmetric intensity profile and good propagating properties.
2017, (3): 94-98.
doi: 10.3969/j.issn.1000-5641.2017.03.010
Abstract:
In order to study the integration and the stability of autonomous Birkhoffian systems, we propose four kinds of gradient systems to represent the autonomous Birkhoffian systems. By analysing the relationship between the gradient systems and the Birkhoffian systems, we obtain the conditions that the Birkhoffian systems can be transformed into a kind of four gradient systems. Then, we use the properties of gradient system to investigate the problems of integration and stability of the Birkhoffian systems. Finally, we give some examples to illustrate the application of the theory.
In order to study the integration and the stability of autonomous Birkhoffian systems, we propose four kinds of gradient systems to represent the autonomous Birkhoffian systems. By analysing the relationship between the gradient systems and the Birkhoffian systems, we obtain the conditions that the Birkhoffian systems can be transformed into a kind of four gradient systems. Then, we use the properties of gradient system to investigate the problems of integration and stability of the Birkhoffian systems. Finally, we give some examples to illustrate the application of the theory.
2017, (3): 99-106.
doi: 10.3969/j.issn.1000-5641.2017.03.011
Abstract:
A Poisson bracket method to obtain the first order approximate conserved quantities of two-dimensional perturbed mechanical system is proposed. We consider the perturbed Hamiltonian function as the combination of Hamiltonian function of unperturbed system and the perturbed term. First, according to the peculiarity of unperturbed system, we select a suitable method to obtain the exact conserved quantities of unperturbed system. Second, we calculate the first order perturbed terms of conserved quantities by using Poisson bracket and the character of partial differential equations. Finally, according to the characters of Noether symmetries, Lie symmetries and Mei symmetries, the first order approximate Noether symmetries, approximate Lie symmetries and approximate Mei symmetries of the first order approximate conserved quantities can be obtained. A perturbed two-dimensional isotropic harmonic oscillator is studied in this paper, and three first order approximate conserved quantities are obtained by using Poisson bracket method, and the first order approximate symmetries of three first order approximate conserved quantities are either approximate Noether symmetries or approximate Lie symmetries and Mei symmetries.
A Poisson bracket method to obtain the first order approximate conserved quantities of two-dimensional perturbed mechanical system is proposed. We consider the perturbed Hamiltonian function as the combination of Hamiltonian function of unperturbed system and the perturbed term. First, according to the peculiarity of unperturbed system, we select a suitable method to obtain the exact conserved quantities of unperturbed system. Second, we calculate the first order perturbed terms of conserved quantities by using Poisson bracket and the character of partial differential equations. Finally, according to the characters of Noether symmetries, Lie symmetries and Mei symmetries, the first order approximate Noether symmetries, approximate Lie symmetries and approximate Mei symmetries of the first order approximate conserved quantities can be obtained. A perturbed two-dimensional isotropic harmonic oscillator is studied in this paper, and three first order approximate conserved quantities are obtained by using Poisson bracket method, and the first order approximate symmetries of three first order approximate conserved quantities are either approximate Noether symmetries or approximate Lie symmetries and Mei symmetries.
2017, (3): 107-113.
doi: 10.3969/j.issn.1000-5641.2017.03.012
Abstract:
This paper investigates the transmission of terahertz pulse in the ultrathin film with terahertz time-domain spectroscopy and the terahertz pulse produced by the interaction between femtosecond laser pulse and Fe/Pt heterostructure. The thickness of the Fe/Pt film ranges from 2 nm to 8 nm. The terahertz wave exponentially decays in Fe and Pt ultrathin films, but it decays much faster in the bulk Fe and Pt. Due to the limitation in the thickness, electrons have much longer free path in the film plane, which increases the conductivity in the film plane. We also find that the laser pulse with 800 nm wavelength also decays faster in the ultrathin film.
This paper investigates the transmission of terahertz pulse in the ultrathin film with terahertz time-domain spectroscopy and the terahertz pulse produced by the interaction between femtosecond laser pulse and Fe/Pt heterostructure. The thickness of the Fe/Pt film ranges from 2 nm to 8 nm. The terahertz wave exponentially decays in Fe and Pt ultrathin films, but it decays much faster in the bulk Fe and Pt. Due to the limitation in the thickness, electrons have much longer free path in the film plane, which increases the conductivity in the film plane. We also find that the laser pulse with 800 nm wavelength also decays faster in the ultrathin film.
2017, (3): 114-119.
doi: 10.3969/j.issn.1000-5641.2017.03.013
Abstract:
Amorphous Fe73.5Cu1.0Nb3.0Si13.5B9 microwires are prepared by the Taylor-Ulitovsky method. Then, the as-prepared microwires are annealed by cuurent annealing. The best performance microwires are obtained at annealing current density of 4.2×107 A/m2 because of the suitable volume ratio between nanocrystalline and amorphous phases. Influence of length on giant magnetoimpedance effect and magnetic properties for microwires is then investigated. The results show that anisotropy field increases and the GMI ratio descreases with decreased length of the wire. Demagnetizing field model gives a reasonable explanation.
Amorphous Fe73.5Cu1.0Nb3.0Si13.5B9 microwires are prepared by the Taylor-Ulitovsky method. Then, the as-prepared microwires are annealed by cuurent annealing. The best performance microwires are obtained at annealing current density of 4.2×107 A/m2 because of the suitable volume ratio between nanocrystalline and amorphous phases. Influence of length on giant magnetoimpedance effect and magnetic properties for microwires is then investigated. The results show that anisotropy field increases and the GMI ratio descreases with decreased length of the wire. Demagnetizing field model gives a reasonable explanation.
2017, (3): 120-132.
doi: 10.3969/j.issn.1000-5641.2017.03.014
Abstract:
Because the conventional CFAR (Constant False-Alarm Rate) detectors have poor detection performance in non-homogeneous environments, an automatic censoring switching-CFAR detector based on sorting (ACS-CFAR) is proposed. The middle cell of the reference window acts as a cell under test; other cells are sorted into the ranked reference cells by ascending order according to their magnitudes. According to the location parameters of the two boundary points which can effectively discriminate between thermal noise, clutter edge or interferences plus thermal noise and interferences immersed in the clutter plus thermal noise region, the detection algorithm can effectively select a suitable cell set from the ranked reference cells to estimate the unknown background level. Combined with the number of the selecting reference cells and the desired probability of false alarm, the corresponding scaling factor can be calculated. Finally, the adaptive detection threshold will be obtained according to background noise level estimated value and the calculated scaling factor. The performances of the ACS-CFAR detector is simulated and evaluated in different simulation environments and compared to the performance of the CA-CFAR, VI-CFAR and ACCA-CFAR detectors, the detection probability of ACS-CFAR detector is up to 98.73%, 98.16% in homogeneous and non-homogeneous environments, respectively. The ACS-CFAR detector performs like the CA-CFAR detector in homogeneous environments and better than the VI-CFAR and ACCA-CFAR detector in non-homogeneous environments, false alarm rate errors are controlled within $\pm $ 0.10%. The simulation results show that the proposed ACS-CFAR detector has better detection performance in homogenous and the presence of interfering targets and clutter edge environments.
Because the conventional CFAR (Constant False-Alarm Rate) detectors have poor detection performance in non-homogeneous environments, an automatic censoring switching-CFAR detector based on sorting (ACS-CFAR) is proposed. The middle cell of the reference window acts as a cell under test; other cells are sorted into the ranked reference cells by ascending order according to their magnitudes. According to the location parameters of the two boundary points which can effectively discriminate between thermal noise, clutter edge or interferences plus thermal noise and interferences immersed in the clutter plus thermal noise region, the detection algorithm can effectively select a suitable cell set from the ranked reference cells to estimate the unknown background level. Combined with the number of the selecting reference cells and the desired probability of false alarm, the corresponding scaling factor can be calculated. Finally, the adaptive detection threshold will be obtained according to background noise level estimated value and the calculated scaling factor. The performances of the ACS-CFAR detector is simulated and evaluated in different simulation environments and compared to the performance of the CA-CFAR, VI-CFAR and ACCA-CFAR detectors, the detection probability of ACS-CFAR detector is up to 98.73%, 98.16% in homogeneous and non-homogeneous environments, respectively. The ACS-CFAR detector performs like the CA-CFAR detector in homogeneous environments and better than the VI-CFAR and ACCA-CFAR detector in non-homogeneous environments, false alarm rate errors are controlled within $\pm $ 0.10%. The simulation results show that the proposed ACS-CFAR detector has better detection performance in homogenous and the presence of interfering targets and clutter edge environments.
2017, (3): 133-144.
doi: 10.3969/j.issn.1000-5641.2017.03.015
Abstract:
In order to better understand the travel behavior of taxies and evaluate taxi operation efficiency, this paper proposed a taxi-operation-and-management-oriented work flow for processing big floating car data (FCD); calculated a set of taxi operation indicators; and analysed taxi operation characteristics on weekdays, weekends as well as public holidays based on GPS data during one month collected by taxies in Shanghai. It is found that daily average idle taxi ratio reaches 39.1%, close to the upper bound of the critical interval. The idle taxi ratio varies significantly across space and time within one day. When compared with a normal weekday, sunday and public holiday are characterized by relatively low operation time and travelling time with passengers, and hence relatively low taxi operation efficiency. More countermeasures should be conducted to improve the capability of taxi management.
In order to better understand the travel behavior of taxies and evaluate taxi operation efficiency, this paper proposed a taxi-operation-and-management-oriented work flow for processing big floating car data (FCD); calculated a set of taxi operation indicators; and analysed taxi operation characteristics on weekdays, weekends as well as public holidays based on GPS data during one month collected by taxies in Shanghai. It is found that daily average idle taxi ratio reaches 39.1%, close to the upper bound of the critical interval. The idle taxi ratio varies significantly across space and time within one day. When compared with a normal weekday, sunday and public holiday are characterized by relatively low operation time and travelling time with passengers, and hence relatively low taxi operation efficiency. More countermeasures should be conducted to improve the capability of taxi management.
2017, (3): 145-152.
doi: 10.3969/j.issn.1000-5641.2017.03.016
Abstract:
This paper introduced the spatio-temporal association rules based on clustering minging to find out the spatio-temporal crime patterns of bus pickpocketing. It can be carried out through three steps. Firstly, extract time, places and other information from the case information by text extraction. Then, confirm the boarding stations and getting off stations of victims using the geocoding service and POI search capability of Amap API. Divide the bus routes into sections according to the bus stops and merge the crime time into time interval. Thirdly, the analysis of association rules based on clustering is carried out to discover the patterns of bus pickpocketing. The results prove that the proposed mining model has the following characteristics: ① This method can reduce the database scanning times, the candidate item sets amount and improve time efficiency of the searching. ② After clustering, the data in a cluster is similar and the characteristics are more obvious. On this basis, the association rules of high confidence are extracted. ③ When the analysis was carried out, the temporal and spatial characteristics of the bus pickpocketing crime were also considered.
This paper introduced the spatio-temporal association rules based on clustering minging to find out the spatio-temporal crime patterns of bus pickpocketing. It can be carried out through three steps. Firstly, extract time, places and other information from the case information by text extraction. Then, confirm the boarding stations and getting off stations of victims using the geocoding service and POI search capability of Amap API. Divide the bus routes into sections according to the bus stops and merge the crime time into time interval. Thirdly, the analysis of association rules based on clustering is carried out to discover the patterns of bus pickpocketing. The results prove that the proposed mining model has the following characteristics: ① This method can reduce the database scanning times, the candidate item sets amount and improve time efficiency of the searching. ② After clustering, the data in a cluster is similar and the characteristics are more obvious. On this basis, the association rules of high confidence are extracted. ③ When the analysis was carried out, the temporal and spatial characteristics of the bus pickpocketing crime were also considered.
