Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-$N_c$ limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.Comment: 6 pages, PDFLatex uses elsarticle class. Invited talk at the Conference Light Cone: Relativistic Hadronic and Particle Physics, 10-15 December 2012, Delhi, Indi

Simple and Efficient Bilayer Cross Counting

We consider the problem of counting the interior edge crossings when a bipartite graph G=(V,E) with node set V and edge set E is drawn such that the nodes of the two shores of the bipartition are on two parallel lines and the edges are straight lines. The efficient solution of this problem is important in layered graph drawing.Our main observation is that it can be reduced to counting the inversions of a certain sequence. This leads to an O(|E|+|C|) algorithm, where C denotes the set of pairwise interior edge crossings, as well as to a simple O(|E|log|V_{m small}|) algorithm, where V_{m small} is the smaller cardinality node set in the bipartition of the node set |V| of the graph. We present the algorithms and the results of computational experiments with these and other algorithms on a large collection of instances

Automatic infrasound signal detection using the Hough transform

The Hough transform is a mathematical device that allows the retrieval of parametric curve information from binary-pixelated data in the presence of noise. This slope-intercept transform maps each point in the image space S into a straight line in parameter space P and has the very useful property that all points in S that lie along the same straight-line map to the same number of straight lines in P with a common intersection point. Thus with a suitable counting procedure, the problem of extended straight-line detection in noisy pixelated data becomes one of local peak finding, a problem that may be substantially more tractable. In this study, an algorithm that utilizes the Hough transform for the detection of signals in International Monitoring System style infrasonic array data by seeking periods of constant backazimuth that are associated with coherent acoustic signals is described. A system of synthetic signal implants is used to assess the performance of the detection algorithm by generating a set of pseudo Receiver Operator Characteristic curves. A feature of the detection algorithm is the ability to accommodate full three-dimensional array geometry

The Detection and Quantification of Straight-Lined Irregularities on Surfaces

Under the microscope, scratches or abrasions on hard otherwise flat surfaces are usually revealed as straight-lined irregularities. At a more macroscopic level creases in thin sheets such as of paper and textile fabrics are also observed to be straight-lined. A computer-aided image analytical method is described here not only for identifying such features but also for counting them, measuring their lengths and evaluating their contrast. Further measures are derived that are in accord with the qualitative visual impact of each line within the milleau of lines in the original image. The method makes use of a parametric transformation from two orthogonally-illuminated images of the surface using the equation p=x∙cos(θ) + y∙sin(θ) where x,y are image coordinates, θ is the angle that a straight line makes with the x-axis and p is the perpendicular distance of that line from the coordinate origin. As distinct from the well-known Hough transform, estimates are made for θ at all points in the initial images that are illuminated at a low angle from two orthogonal directions

Analisis Kesalahan Menyelesaikan Soal Persamaan Garis Lurus pada Siswa Kelas VIII SMP Negeri 2 Wonogiri

This study aims to find out the mistakes made by students in solving equations straight line. This research is a qualitative research. Data collection techniques used were interviews, observation, and documentation. The results of the analysis indicate the type of errors students, among others: (a) errors language with highest percentage in the problem section gradient is 13.125% (classified as very low), language mistakes are often made students an understanding of mathematical symbols and sentence comprehension questions that granted (b) the misconceptions with highest percentage in the problem section gradient of 15% (classified as very low), the misconceptions that often do students a requirement of two lines perpendicular to each other, arithmetic operations between the numbers of positive and negative, and describes the line equation straight or coordinate point in a graph (c) the error count with the highest percentage in the problem section gradient is 12.5% (classified as very low), counting errors are often made of students is surgery plus, minus, times, and for the numbers positive and negative; and move the segment, so it can be said to be an error in solving equations straight line contained in section gradient and relatively very low

Hamiltonian Cycles on Random Eulerian Triangulations

A random Eulerian triangulation is a random triangulation where an even number of triangles meet at any given vertex. We argue that the central charge increases by one if the fully packed O(n) model is defined on a random Eulerian triangulation instead of an ordinary random triangulation. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case one should see a change in the entropy exponent from the value gamma=-1 to the irrational value gamma=(-1-\sqrt{13})/6=-0.76759... when going from a usual random triangulation to an Eulerian one. A direct enumeration of configurations confirms this change in gamma.Comment: 22 pages, 9 figures, references and a comment adde