Location Of Singular Points Research Articles

Singular Points Location Pattern Analysis based on Modes Interference

<p>Given the lack of research on the regularity of distribution of singular points, the singular points under different influence factors are analyzed. The location of singular points for adjacent modes group (AMG) generated by the interference modes is derived using normal modes theory in the far field of the ideal shallow waveguide. The singular points are verified by simulation, which compares the distribution of the acoustic field and singular points. Moreover, it is concluded that the number and distribution of singular points in the period of the interference structure of the field (PISF) has a relationship with order (lower order of AMG) and adjacent order (difference between two orders of AMG). The arrangement of upper-lower-two-points increases by 2 with each increase of order and is distributed at both ends of PISF. The arrangement of rhombic-four-points increases by 1 with each increase of adjacent order and increases alternately at both ends of PISF. Meanwhile, there is a periodic relationship between the depth of the source and the location of singular points.</p> <p> </p>

Location of singular points in orthorhombic media

The dependence of the location of singular points of orthorhombic (ORT) media on the stiffness coefficients , and phase velocity at the singularity point is studied under the assumption that are larger than and . In this case, singular points appear only at the intersection of slowness surfaces of S1- and S2-waves. To simplify the presentation of the results, the values , are fixed and changed within the limits at which the stiffness matrix remains positive definite. We define the parameters, , , , which result in 0, 1, or 2 singular points in the symmetry planes of the ORT medium. The types of these singular points and their location on the unit circle are described. It is shown that, by selecting parameters , any singular point in the symmetry plane 13 can be combined with the limiting position of the singularity point in-between the symmetry planes, or this point can be included in the singular curve of the degenerate ORT medium. We derive equations for the semi-axes of an ellipse of conical refraction, which is the image of a singular point from plane 13 in the group domain. Conditions for degeneration of the ellipse of conical refraction into a segment or a point are defined. It is shown that there exists only one ORT medium with a fixed phase velocity of S1- and S2-waves in a given singular direction n. If we present the ORT media as projections of these vectors n onto the plane 12 and mark the value of the Poincaré index of the S1- or S2-wave at the point n, we get 2 regions with indices 1/2 and –1/2 separated by projection of the singular curve in the form of an ellipse or hyperbola. We compute equations for of a degenerate ORT medium in terms of the values, , and velocity of S1-, S2-waves on a singular curve. The singular curve is defined by the intersection of a unit sphere with an elliptic cone. It is proved that a degenerate ORT medium for or is, respectively, a transversally isotropic medium with a vertical or horizontal axis of symmetry. The results are illustrated in several examples.

Combining multi-scale composite windows with hierarchical smoothing strategy for fingerprint orientation field computation

BackgroundOrientation field (OF) plays a very significant role in automatic fingerprint recognition systems. Many algorithms have been proposed for the estimation of fingerprints’ OF but it is hard to solve the dilemma of correcting spurious ridge structure and avoiding singularity location deviation, especially for poor images. So far, the following drawbacks still need to be solved for OF construction methods for practical application: (1) How to adaptively choose block scales to resolve the contradiction between accuracy and anti-noise, since small scale is beneficial to accuracy but is sensitive to noise, while large scale is more resistant to noise, but the accuracy is deteriorated. (2) How to construct the genuine OF in the areas close-by singular points and to evade singularity location deviation? Current block based methods give spurious OF estimates in the area near singular points because these areas have large curvature thus the detected singular points deviate from the genuine localizations. When these singular points are used as the anchor for referencing minutiae, it makes the average error of matching or recognition even larger. Therefore, it is essentials to construct the genuine OF in the areas close-by singular points and to evade singularity deviation.MethodsTo overcome the above-mentioned limitations, a novel method, combining a weighted multi-scale composite window (WMCM) with a hierarchical smoothing strategy has been proposed for the computation of fingerprint OF. This method mainly contains two procedures: the approximate OF estimation and the hierarchical OF smoothing. In the first procedure, a series of OFs are established under multiple scales of composite windows by using a gradient based method then a coarse OF is estimated using the weight of each scale determined by a squared gradient consistency. In the second procedure, the OF is first quantized into a two-digitized orientation zone and a two-orientation-zone filtering strategy is adapted to the OF blocks based on a filtering mask obtained after eliminating the isolated blocks. In the end a similar three-digitized orientation zone is performed to obtain an accurate and smooth OF. To validate the performance, the proposed method has been applied to OF computation using the FVC2004 databases and three experiments are designed. Experiment 1 aims to validate whether the weighted multi-scale composite window can balance the dilemma of accuracy and robustness more effectively than the previous works do. Experiment 2 is designed to examine whether the hierarchical smoothing method can correct the spurious ridge flow and preserve the genuine localization of singular points. The purpose of experiment 3 is to test the performance of the proposed method on OF reconstruction in low quality fingerprint images. The fingerprint databases FVC 2004 DB1–DB4 are employed in this study.ResultsThe results of experiment I shows that the proposed method is capable to extract the information of OF reliably and it is more robust against singularity localization deviation in comparison with the other three gradient based methods. The results of experiment II indicates that the proposed smoothing method can balance the contradiction in correcting spurious ridge structures and preserving genuine singularity localization. The results of experiment III illustrates that our approach combing WMCW with the hierarchical smoothing method is capable to extract the information of OF ridge reliably and it is more robust against singularity deviation in comparison with the other three gradient based methods. In a word, the experiment results demonstrate that the proposed method can correct spurious ridge structure and meanwhile avoid singularity deviation compared with the previous works.ConclusionsA novel gradient based algorithm has been proposed which is more reliable for the estimation of the ridge information for fingerprint OF and is more accurate in preserving the singularity localization. Compared with the previously proposed gradient based methods, the advantages of the proposed RBSF lie in three aspects. Firstly a weighted multi-scale composite window is put forward to replace the single window used by conventional gradient based methods and to adaptively choose the scales of the blocks. Secondly, a hierarchical smoothing strategy is proposed to enhance the OF by using the two-orientation-zone filtering and the three-orientation-zone filtering, aiming to correct the spurious ridges and preserving the genuine location of singular points. Finally, three experiments are designed to test the proposed algorithm together with other popular gradient based methods on real fingerprint images, which are selected from different categories and all are suffering from obvious noise effects. All the experiment results show that the proposed method is superior with respect to reliable OF construction and avoiding singularity localization deviation.

Green function, Painlevé VI equation, and Eisenstein series of weight one

The behavior and the location of singular points of a solution to Painlevé VI equation could encode important geometric properties. For example, Hitchin’s formula indicates that singular points of algebraic solutions are exactly the zeros of Eisenstein series of weight one. In this paper, we study the problem: How many singular points of a solution $\lambda (t)$ to the Painlevé VI equation with parameter $(\frac{1}{8}, \frac{-1}{8}, \frac{1}{8}, \frac{3}{8})$ might have in $\mathbb{C} \setminus \lbrace 0, 1\rbrace$? Here $t_0 \in \mathbb{C} \setminus \lbrace 0, 1\rbrace$ is called a singular point of $\lambda (t)$ if $\lambda (t_0) \in \lbrace 0, 1, t_0, \infty \rbrace$. Based on Hitchin’s formula, we explore the connection of this problem with Green function and the Eisenstein series of weight one. Among other things, we prove: (i) There are only three solutions which have no singular points in $\mathbb{C} \setminus \lbrace 0, 1\rbrace$. (ii) For a special type of solutions (called real solutions here), any branch of a solution has at most two singular points (in particular, at most one pole) in $\mathbb{C} \setminus \lbrace 0, 1\rbrace$}. (iii) Any Riccati solution has singular points in $\mathbb{C} \setminus \lbrace 0, 1\rbrace$. (iv) For each $N \geq 5$ and $N \neq 6$, we calculate the number of the real $j$-values of zeros of the Eisenstein series $\mathfrak{E}^N_1 (\tau ; k_1, k_2)$ of weight one, where $(k_1, k_2)$ runs over ${[0, N-1]}^2$ with $\mathrm{gcd}(k_1, k_2, N) = 1$. The geometry of the critical points of the Green function on a flat torus $E_{\tau}$, as $\tau$ varies in the moduli $\mathcal{M}_1$, plays a fundamental role in our analysis of the Painlevé VI equation. In particular, the conjectures raised in “Elliptic functions, Green functions and the mean field equations on tori” [C.-S. Lin and C.-L. Wang, Annals of Math. 172 (2010), no. 2, 911–954] on the shape of the domain $\Omega_5 \subset \mathcal{M}_1$, which consists of tori whose Green function has extra pair of critical points, are completely solved here.

Control of the Singular Points Location for Miniature Switches with Magnetically Driven Contacts.

This paper presents and discusses usefulness and possibility of control of the singular points location of a driving magnetic field under as structure considerations as well as selection of energizing magnet systems for miniature electromagnetic switches. The sample results of theoretical analysis and experimental testing concern selected reed switches with normally open contacts as well as a developed miniature switch with a metallic ball contact. It must be noted that the switch with the contact performed by means of the metallic tiny ball can be effectively used both as a change-over switch as well as a detector of the energizing magnetic field distribution under designing and assembling of any electromagnetic contact device preferably with an increased degree of integration and miniaturization.

CONCEPTUAL DESIGN OF NON-IDEAL MIXTURE SEPARATION WITH LIGHT ENTRAINERS

A method is proposed to study the separation of minimum-, maximum-boiling azeotropic, and low volatility mixtures with a light entrainer, to investigate feasible regions of the key operating parameters reboil ratio (S) and entrainer - feed flowrate ratio (FE/F) for continuous processes. The thermodynamic topological predictions are carried out for 1.0–2, 1.0–1a, and 0.0–1 Serafimov’s class diagrams. It relies upon the knowledge of residue curve maps, along with the univolatility line, and it enables the prediction of possible products at the bottom of the column and limiting values of FE/F. The profiles of the stripping, extractive, and rectifying sections are calculated by equations considering S and FE/F, and they bring information about the location of singular points and possible composition profile separatrices that could impair process feasibility. Providing specified product composition and recovery, the approximate calculations are compared with rigorous simulations of extractive distillation processes. Separating non-ideal mixtures using a light entrainer provides more opportunities for the case when it is not easy to find an appropriate heavy or intermediate entrainer

The Use of Spherical Statistics to Analyze Digital Elevation Models: An Example From LIDAR and ASTER GDEM

The use of spherical statistics for comparing and analyzing different digital elevation models (DEMs) is proposed in this letter by the new software package VecStatGraphs3D. Spherical data deal with angular data such as unit vector in 3-D space and are used in disciplines such as meteorology, geomatics, biology, and geology. Usually, the most common descriptor to analyze DEMs is the root-mean-square error (linear statistic), but this statistic itself cannot describe the error positional distributions. Comparing homologous points in two different DEMs generates 3-D vectors, which can be analyzed by means of spherical statistics. A 3-D vector is defined by its module (linear statistics) and colatitude and longitude (spherical statistics). While several graphical and statistical tools are available for the analysis of directional data in 3-D, these tools consider only the angular magnitude and work with unit vectors. In this letter, the open-source software package VecStatGraphs3D is described. It works in the R environment and provides statistics for modules (linear), colatitude and longitude (spherical), and graphics for the joint analysis of 3-D vectors. The spatial locations of singular points between two DEMs of different spatial resolution: LIDAR (5 m) and ASTER Global Digital Elevation Map (30 m) are compared as examples using VecStatGraphs3D. The interactive 3-D graphics reveal spatial patterns and assist in understanding the effect of the DEM resolution on the uncertainty of the spatial locations of relief.

Circuit Design and System Error Analysis Based on MR / GPS Combination Measuring Projectile Roll Angle

In the control process of trajectory correction projectile, a real-time accurate measurement of projectile roll angle information is required. Geomagnetic and GPS measurement principle is applied for the establishment of the projectile measured roll angle combinations mathematical calculation model, the designing of MR and GPS measuring circuits, and derivation of the singular points of the system and error resolution type. Numerical simulation methods are applied to verify the location of singular points of the combination of measurements and the linear spline combination of interpolation method of compensation the position of the magnetic vector error and the ellipsoid fitting calibration algorithm compensate for magnetic measurement error. The geomagnetic error has less effects on the combination of measured roll angle error, while the pitch angle and yaw angle error has greater impact on the roll angle error. Remove the singular point area, projectile roll angle error is less than 2°when measured by the combination of MR / GPS .

Systems of elliptic equations involving multiple inverse-square potentials and critical exponents

In this paper, a system of elliptic equations is investigated, which involves multiple critical Sobolev exponents and singular points. The best Sobelev constant related to the system is studied, which is verified to be independent of the location of singular points. By a variant of the concentration compactness principle and the mountain-pass argument, the existence of positive solutions to the system is proved. At last, the existence of sign-changing solutions to the system is also established on the basis of the mountain-pass-type positive solutions.

Tropical Surface Singularities

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.

A variational formulation for fingerprint orientation modeling

Orientation pattern is an important feature for characterizing fingerprint and plays critical roles in fingerprint recognition and fingerprint classification. This paper proposes a framework for modeling the fingerprint orientation field based on the variational principle, where the orientation pattern can be estimated through solving the associated Euler-Lagrange equation. Compared with existing methods, our proposed method has the following features. Firstly, it does not require any prior information about the structure of the acquired fingerprint, such as location of singular point(s). Secondly, it explicitly provides freedom for modeling the singularity in the orientation field. Thirdly, it has less number of parameters. Comparison has been made with respect to state-of-the-arts in fingerprint orientation modeling in terms of modeling accuracy, fingerprint enhancement and singular point detection. Advantages of the proposed method are demonstrated.

Fingerprint Singular Point Detection Using Orientation Field Reliability

Singular point detection is the most important step in Automatic Fingerprint Identification System (AFIS) and is used in fingerprint alignment, fingerprint matching, and particularly in classification. The computation of orientation field of a fingerprint can be verified by computing orientation field reliability. The most unreliable portion in orientation field can be the possible location of singular points. In this paper we have proposed a novel algorithm for detecting singular points using reliability of the fingerprint orientation field. Experimental results show that the proposed algorithm accurately detects singular points (core and delta) with the detection rate of 92.6 %.

Single-Phase-to-Earth Fault Detection for High Voltage Transmission Line Based on Wavelet Analysis

The voltage and current signals are transient signals with singularity and mutability when single-phase-to-earth fault occurs in high-voltage transmission line, of which the singular point and mutations parts contain rich fault information. However, wavelet analysis just has the nature of singularity detection and zoom properties, which is very effective in singularity analysis and singular points location. Based on the basic principle of wavelet analysis and signal singularity detection, simulation and detection of singularity of fault voltage and current signals in high voltage transmission line are made by db5 wavelet multi-scale comprehensive analysis method. The singularity detection and calculation program are accomplished in M-file form by programming in MATLAB, the simulation results show that db5 wavelet can detect the singularity of fault signal and determine the fault occurrence and end time fast and accurately. This method enhanced accuracy and reliability of single-phase-to-earth fault detection.

Finding limiting flows of batch extractive distillation with interval arithmetic

AbstractA feasibility study on batch extractive distillation is based on analyzing profile maps. The existence and location of singular points and separatrices in these maps depend on process parameters. The limiting flows of the process are related to those parameter values where the map changes shape. Graphical tools can be used to roughly estimate these values. If a singularity is not found using graphical methods, one cannot guarantee that a singularity does not exist. Reliable computation of all zeroes of a nonlinear multidimensional function can be used to determine these points. This can be accomplished using interval arithmetic. An interval arithmetic–based branch‐and‐bound optimizer is applied to find the singular points and bifurcations. All the singular points of the maps at specified process parameters are found in this way. Limiting flows are determined with the same methodology by finding the bifurcation points and the corresponding parameter values. © 2006 American Institute of Chemical Engineers AIChE J, 2006

An effective method for extracting singular points in fingerprint images

In most algorithms of fingerprint identification and fingerprint classification, extracting the number and the precise location of singular points (SPs) is of great importance. In this paper, a new algorithm based on the distribution of Gaussian–Hermite moments is presented for detection of SPs. All other SPs extraction methods can only extract two types of SPs (core and delta). They often ignore a true pair of core–delta that are close to each other. Our algorithm can detect not only the core and the delta, but also a pair of core–delta. It is shown how very accurate detection of the SPs. These estimates can for instance be used for fingerprint classification and accurate registration of two fingerprints in a fingerprint verification system.

Localization of Singular Points in Fingerprint Images Based on the Gaussian-Hermite Moments

In most fingerprint classification and identification algorithms, extracting the number and precise location of singular points (core and delta) is of great importance. In this paper, an adaptive algorithm for singular points detection is proposed, which is based on the behavior of Gaussian-Hermite moments. In order to detect singular point accurately, the distribution of Gaussian-Hermite moments of different orders of the fingerprint image in multiple scales is used. A PCA-based (principal component analysis) method is used to analyze the distribution of Gaussian-Hermite of fingerprint image. Experimental results show that the proposed algorithm is able to locate singular points in fingerprint with high accuracy.

Study on structure of singular points 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.

An Adaptive Approach to Singular Point Detection in Fingerprint Images

This paper presents a novel algorithm for detection of singular points, the core and delta points, in fingerprint images. The number and location of singular points, are used to classify fingerprint images into five general groups; and therefore to narrow down the search space in large fingerprint databases. Using the proposed directional masks in the first step, we detect the neighborhood of the singular points. In the second stage by implementing the proposed algorithm, an adaptive singular point detection method, is designed to extract the exact location of core and delta points. Usage of the proposed directional masks speeds up the process and the proposed adaptive singular point detection method increases the accuracy of the algorithm.

Evaluations of certain hypersingular integrals on interval

AbstractIn this paper, we investigate a hypersingular integral on an interval. The definition of Hadamard's finite‐part integrals and some of its properties are given. Some numerical methods on approximate computation of the finite‐part integrals are constructed. The new method is very simple, easy to implement, reliable, and above all, not affected by the location of singular point. Some numerical experiments are carried out using the current formulae, and numerical results show that the current methods are feasible and effective. Copyright © 2001 John Wiley & Sons, Ltd.

Hadamard regularization

Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g., 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they admit a power-like singular expansion. We review the concepts of (i) Hadamard “partie finie” of such functions at the location of singular points, (ii) the partie finie of their divergent integral. We present and investigate different expressions, useful in applications, for the latter partie finie. To each singular function, we associate a partie-finie (Pf) pseudo-function. The multiplication of pseudo-functions is defined by the ordinary (pointwise) product. We construct a delta-pseudo-function on the class of singular functions, which reduces to the usual notion of Dirac distribution when applied on smooth functions with compact support. We introduce and analyze a new derivative operator acting on pseudo-functions, and generalizing, in this context, the Schwartz distributional derivative. This operator is uniquely defined up to an arbitrary numerical constant. Time derivatives and partial derivatives with respect to the singular points are also investigated. In the course of the paper, all the formulas needed in the application to the physical problem are derived.