Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent s...Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.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?.
Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular p...Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular points are ordinary. The numerical procedures rely on computing numerical solutions of polynomial systems by homotopy continuation method and a reliable method that calculates multiple roots of the univariate polynomials accurately using standard machine precision. It is completely different from the traditional symbolic computation and provides singular points and their related properties of some plane algebraic curves that the symbolic software Maple cannot work out. Without using multiprecision arithmetic, extensive numerical experiments show that our numerical procedures are accurate, efficient and robust, even if the coefficients of plane algebraic curves are inexact.展开更多
A novel method for fingerprint singular points extraction including location and orientation is proposed based on some properties of the orientation field models. Singular points are located by clustering the results ...A novel method for fingerprint singular points extraction including location and orientation is proposed based on some properties of the orientation field models. Singular points are located by clustering the results of corner detection. Then, through examining the sub-block orientation fields at a number of selected positions on concentric circles centered about the located singular point, an iterative method based on the orientation differences is proposed to compute the orientation of the core point. Experimental results on NIST4 and FVC2002 four databases demonstrate the proposed method can consistently locate singular points with the high accuracy. The location and orientation of the detected singular points can be used for alignment （translation and rotation） parameters in fingerprint matching.展开更多
In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet tr...In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.展开更多
IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, ever...IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows.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 consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an alg...In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .展开更多
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ...We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.展开更多
In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi>...In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.展开更多
We investigate the growth of solutions of the following complex linear di er-ential equation f″+A(z)f′+B(z)f=0,where A(z)and B(z)are analytic functions in -C-{z0},z0∈C.Some estimations of lower bounded of growth of...We investigate the growth of solutions of the following complex linear di er-ential equation f″+A(z)f′+B(z)f=0,where A(z)and B(z)are analytic functions in -C-{z0},z0∈C.Some estimations of lower bounded of growth of solutions of the di erential equation are obtained by using the concept of lower order.展开更多
Recently, some authors (Li, Yang and Wu, 2014) studied the parameterized preconditioned HSS (PPHSS) method for solving saddle point problems. In this short note, we further discuss the PPHSS method for solving singula...Recently, some authors (Li, Yang and Wu, 2014) studied the parameterized preconditioned HSS (PPHSS) method for solving saddle point problems. In this short note, we further discuss the PPHSS method for solving singular saddle point problems. We prove the semi-convergence of the PPHSS method under some conditions. Numerical experiments are given to illustrate the efficiency of the method with appropriate parameters.展开更多
In solving a response function by the boundary element method, the use of the singular valued method and the Laplace transform in a time domain makes the solving process be simplified and the result be accurate. The r...In solving a response function by the boundary element method, the use of the singular valued method and the Laplace transform in a time domain makes the solving process be simplified and the result be accurate. The restricted condition matrix formed by the response matrix method is much smaller than that by embedding method. In addition, the response function may realize directly the management decision making. So it is efficient for establishing and solving hydraulics management models.展开更多
To discover the characteristic of separated flows and mechanism of plasma flow control on a highly loaded compressor cascade, numerical investigation is conducted. The simulation method is validated by oil flow visual...To discover the characteristic of separated flows and mechanism of plasma flow control on a highly loaded compressor cascade, numerical investigation is conducted. The simulation method is validated by oil flow visualization and pressure distribution. The loss coefficients, streamline patterns, and topology structure as well as vortex structure are analyzed. Results show that the numbers of singular points increase and three pairs of additional singular points of topology structure on solid surface generate with the increase of angle of attack, and the total pressure loss increases greatly. There are several principal vortices inside the cascade passage. The pressure side leg of horse-shoe vortex coexists within a specific region together with passage vortex, but finally merges into the latter. Corner vortex exists independently and does not evolve from the suction side leg of horse-shoe vortex. One pair of radial coupling-vortex exists near blade trailing edge and becomes the main part of backflow on the suction surface. Passage vortex interacts with the concentrated shedding vortex and they evolve into a large-scale vortex rotating in the direction opposite to passage vortex. The singular points and separation lines represent the basic separation feature of cascade passage. Plasma actuation has better effect at low freestream velocity, and the relative reductions of pitch-averaged total pressure loss coefficient with different actuation layouts of five and two pairs of electrodes are up to 30.8% and 26.7% while the angle of attack is 2~. Plasma actuation changes the local topology structure, but does not change the number relation of singular points. One pair of additional singular point of topology structure generates with plasma actuation and one more reattachment line appears, both of which break the separation line on the suction surface.展开更多
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitut...The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.展开更多
In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We ...In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].展开更多
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
基金Project(11JJ3080)supported by Natural Science Foundation of Hunan Province,ChinaProject(11CY012)supported by Cultivation in Hunan Colleges and Universities,ChinaProject(ET51007)supported by Youth Talent in Hunan University,China
文摘Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.
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The NSF (61033012,10801023,11171052,10771028) of China
文摘Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular points are ordinary. The numerical procedures rely on computing numerical solutions of polynomial systems by homotopy continuation method and a reliable method that calculates multiple roots of the univariate polynomials accurately using standard machine precision. It is completely different from the traditional symbolic computation and provides singular points and their related properties of some plane algebraic curves that the symbolic software Maple cannot work out. Without using multiprecision arithmetic, extensive numerical experiments show that our numerical procedures are accurate, efficient and robust, even if the coefficients of plane algebraic curves are inexact.
基金supported by the National Key R&D Program of China(No.2024YFA1014400)the NSF Research Grants(Nos.DMS-1801851,DMS-1952522)the Grant from Simons Foundation(No.256202).
文摘The number of singular points on a klt Fano surface X is less than or equal to 2ρ(X)+2.
基金supported by the Key Project of The Ministry of Education of China (108012)the National Natural Science Foundation of China (90920001, 60772114)
文摘A novel method for fingerprint singular points extraction including location and orientation is proposed based on some properties of the orientation field models. Singular points are located by clustering the results of corner detection. Then, through examining the sub-block orientation fields at a number of selected positions on concentric circles centered about the located singular point, an iterative method based on the orientation differences is proposed to compute the orientation of the core point. Experimental results on NIST4 and FVC2002 four databases demonstrate the proposed method can consistently locate singular points with the high accuracy. The location and orientation of the detected singular points can be used for alignment （translation and rotation） parameters in fingerprint matching.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.
文摘IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows.
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.
文摘In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金Supported by the Scientific Research Funds for the Ningxia Universities(Grant No.NGY2015141)
文摘We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.
文摘In thispaper,theexistence oftravelling frontsolution fora classofcom petition-diffu- sion system w ith high-order singular point w it = diw ixx - w αii fi(w ),x ∈R,t> 0,i= 1,2 (Ⅰ) is studied,w here di,αi> 0 (i= 1,2) and w = (w 1(x,t),w 2(x,t)).Under the certain assum ptions on f,itis show ed thatifαi< 1 for som e i,then (Ⅰ) has no travelling frontsolution,ifαi≥1 for i= 1,2,then there isa c0,c:c0≥c> 0,w herecis called the m inim alwavespeed of(Ⅰ),such thatifc≥c0 orc= c,then (Ⅰ) has a travelling frontsolution,ifc< c,then (Ⅰ) hasno travel- ling frontsolution by using the shooting m ethod in com bination w ith a com pactness argum ent.
基金National Natural Science Foundation of China(11861023)the Foundation of Science and Technology project of Guizhou Province of China([2018]5769-05)。
文摘We investigate the growth of solutions of the following complex linear di er-ential equation f″+A(z)f′+B(z)f=0,where A(z)and B(z)are analytic functions in -C-{z0},z0∈C.Some estimations of lower bounded of growth of solutions of the di erential equation are obtained by using the concept of lower order.
文摘Recently, some authors (Li, Yang and Wu, 2014) studied the parameterized preconditioned HSS (PPHSS) method for solving saddle point problems. In this short note, we further discuss the PPHSS method for solving singular saddle point problems. We prove the semi-convergence of the PPHSS method under some conditions. Numerical experiments are given to illustrate the efficiency of the method with appropriate parameters.
文摘In solving a response function by the boundary element method, the use of the singular valued method and the Laplace transform in a time domain makes the solving process be simplified and the result be accurate. The restricted condition matrix formed by the response matrix method is much smaller than that by embedding method. In addition, the response function may realize directly the management decision making. So it is efficient for establishing and solving hydraulics management models.
基金National Natural Science Foundation of China(50906100, 10972236)Foundation for the Author of National Excellent Doctoral Dissertation of PR China (201172)Postgraduate Technology Innovation Foundation of Air Force Engineering University(DX2010103)
文摘To discover the characteristic of separated flows and mechanism of plasma flow control on a highly loaded compressor cascade, numerical investigation is conducted. The simulation method is validated by oil flow visualization and pressure distribution. The loss coefficients, streamline patterns, and topology structure as well as vortex structure are analyzed. Results show that the numbers of singular points increase and three pairs of additional singular points of topology structure on solid surface generate with the increase of angle of attack, and the total pressure loss increases greatly. There are several principal vortices inside the cascade passage. The pressure side leg of horse-shoe vortex coexists within a specific region together with passage vortex, but finally merges into the latter. Corner vortex exists independently and does not evolve from the suction side leg of horse-shoe vortex. One pair of radial coupling-vortex exists near blade trailing edge and becomes the main part of backflow on the suction surface. Passage vortex interacts with the concentrated shedding vortex and they evolve into a large-scale vortex rotating in the direction opposite to passage vortex. The singular points and separation lines represent the basic separation feature of cascade passage. Plasma actuation has better effect at low freestream velocity, and the relative reductions of pitch-averaged total pressure loss coefficient with different actuation layouts of five and two pairs of electrodes are up to 30.8% and 26.7% while the angle of attack is 2~. Plasma actuation changes the local topology structure, but does not change the number relation of singular points. One pair of additional singular point of topology structure generates with plasma actuation and one more reattachment line appears, both of which break the separation line on the suction surface.
基金Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
文摘The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
基金Partially supported by NSFC(11571233)NSF DMS-1405175+1 种基金NSF of Shanghai16ZR1402100China Scholarship Council
文摘In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].
