Fingerprint singular points extraction based on orientation tensor field and Laurent series

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.

Computing Numerical Singular Points of Plane Algebraic Curves

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.

SOME NEW RESULTS ON THE CHORD METHOD AT SINGULAR POINTS

In this paper, we prove that the chord method and the modified chord method are also convergent to the solution x? of F（x）=0 if the dimension of the null space of F’(x?) is】1.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

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(φ)=(1+k)sinφ/ 1+kcosφ.

BIFURCATION OF SINGULAR POINTS NEAR A DOUBLE FOLD POINT INZ_2 -SYMMETRIC NONLINEAR EQUATIONS

We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.

TRAVELLING FRONT SOLUTION FOR A CLASS OF COMPETITION-DIFFUSION SYSTEM WITH HIGH-ORDER SINGULAR POINT

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 herecis 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.

To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point

In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three arbitrary constants, two arbitrary constants, one constant and may have unique solution. In the case when general solution of integral equation contains arbitrary constants, we stand and investigate different boundary value problems, when conditions are given in singular point. Besides for considered integral equation, the solution found cane represented in generalized power series. Some results obtained in the general model case.

Learning Dynamics of the Complex-Valued Neural Network in the Neighborhood of Singular Points

In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.

A FORMULA FOR INDEX OF A SINGULAR POINT OF POLYNOMIAL DIFFERENTIAL SYSTEMS IN THE PLANE

By discussing the relation between the method of Poincare’s transformation and the method of Bendixsion’s transformation which are used to analyse the behavior of singular points at infinity, a formula for index of a singular point of polynomial differential system in the plane is deduced. It is convenient to use the formula in this paper to calculate the index of a singular point with higher order.

Some New Results on Indices of Singular Points of a Polynomial Vector Field

Several new results on the indices of singular points in a polynomial vector field areproved in this paper(see Theorems 1-5).

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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.

THEORY OF VALUES OF SINGULAR POINT IN COMPLEX AUTONOMOUS DIFFERENTIAL SYSTEMS

Consider the complex autonomous differential system (E). The main results of this paper are as follows: (i) The concept of values of singular point has been defined. It can realize the unity between the saddle values and the focal values in real systems, (ii) By defining the concept of the Lie-invariant, the constructive theorem of values of singular point and the extended symmetric principle can be obtained. (iii) All the 120 elementary Lie-invariants of (E3) have been computed. The constructive theorem being used, formulas of values of singular point and the integrability conditions of (E2) and (E(3)3) have been derived.

Fingerprint singular points extraction based on the properties of orientation model

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.

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η∈ (0, 1), α∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ∈ (0, λ*) under certain conditions on the nonlinear term f.

Precise integration method for a class of singular two-point boundary value problems

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.

Existence of Positive Solution for Superlinear Semipositone Singular Second-order m-point Boundary Value Problem

由使用固定的点定理，积极答案的存在为 superlinear semipositone 被认为单个m点边界价值问题--(n)(x)= f ( x ，(x))+ g (x)， 0 < x < 1 ，( 0 ) =0 ，( 1 )= m-2i=1 ai (i)，吗在哪儿(L)(x)=( p (x)“(x))”+ q (x)(x)和 i ( 0 ， 1 )与 0 < 1 < 2 << m-2 < 1 ， ai R+， f C [( 0,1 )???嘠???畭瑬杩楲???????牥業整？？

FORMULAS OF VALUES OF SINGULAR POINT AND THE INTEGRABILITY CONDITIONS FOR A CLASS OF CUBIC SYSTEM, M(3)≥7

The values of the singular point in complex autonomous differential systems have been introduced and discussed in [1] in order that the focal values and the saddle values in real plane autonomous differential systems can be treated in the same way. One problem unsloved up to now is that for any second order autonomous differential system with a cubic polynomial on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is(M(3)=?). Inequality M(3)≥5 can be obtained from the results in[2] and[3].

The Values of Singular Point of E_n and Some Kinds of Problems of Bifurcation

In this paper, by discussing 2π-periodical solutions under the polar coordinates for the complex system E_n~*(ε, λ), the research for the real planar Hopf bifurcation, center point bifurcation and a class of homoclinic bifurcation are all reduced to calculating the formulas of the values of the singular point and to extracting the roots of an algebraic equation. Therefore, the general criteria for the existence of several limit cycles appearing in these bifurcations are obtained. The examples of quadratic systems with three limit cycles appearing in both a homoclinic loop bifurcation and a center point bifurcation are obtained. For the cubic system, the functions on the right-hand side have no quadraticterms, the examples about 10 and 5 limit cycles appearing in a double homoclinic loop bifurcation and a center point bifurcation are also obtained.

STUDY ON STRUCTURE OF SINGULARPOINTS OF LAMINAR FLAME SYSTEM

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.