Number Of Straight Lines Research Articles

On Triple Lines and Cubic Curves: The Orchard Problem Revisited

Planar point sets with many triple lines (which contain at least three distinct points of the set) have been studied for 180 years, started with Jackson and followed by Sylvester. Green and Tao (Discret Comput Geom 50(2):409–468, 2013) have shown that the maximum possible number of triple lines for an n-element set is ⌊n(n-3)/6⌋+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lfloor n\\hspace{0.33325pt}(n - 3)/6\\rfloor + 1$$\\end{document}. Here we address the related problem of describing the structure of the asymptotically near-optimal configurations, i.e., of those for which the number of straight lines which go through three or more points has a quadratic (i.e., best possible) order of magnitude. We pose the problem whether such point sets must always be related to cubic curves. To support this conjecture we settle various special cases; some of them are also related to the four-in-a-line problem of Erdős.

Lines on K3 quartic surfaces in characteristic 3

We investigate the number of straight lines contained in a K3 quartic surface X defined over an algebraically closed field of characteristic 3. We prove that if X contains 112 lines, then X is projectively equivalent to the Fermat quartic surface; otherwise, X contains at most 67 lines. We improve this bound to 58 if X contains a star (ie four distinct lines intersecting at a smooth point of X). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided.

Indoor and outdoor image classification

PurposeThe purpose of this paper is to classify the given image as indoor or outdoor with higher success rate by mixing various features like brightness, number of straight lines, number of Euclidean shapes and recursive shapes.Design/methodology/approachFor annotating an image, it is very easy, if the image is categorized as indoor or outdoor. Many methods are proposed to classify the given image in these criteria but still the rate of uncategorized images occupies considerable area. This proposed work is the extension of the existing works already proposed by experts in this field. Some of the parameters mainly focused to classify are color histogram, orientation of edges, straightness of edges, discrete cosine transform coefficients, etc. In addition to that, this work includes finding of Euclidean shapes i.e. closed contours and recursive shapes in the given image. When the Euclidean shaped object dominates the recursive shapes then it is classified as indoor object and if the recursive shapes dominates, it is categorized as outdoor object.FindingsThis work is carried out on the standard image data sets. The data sets are Microsoft Research Cambridge (MRC) object recognition image database 1.0. and Kodak and Coral image data set. Totally 540 images are taken into account and the images are classified 95.4 percent correctly.Originality/valueMany methods are proposed to classify the given image in these criteria but still the rate of uncategorized images occupies considerable area. This proposed work is the extension of the existing works already proposed by experts in this field. Some of the parameters mainly focused to classify are color histogram, orientation of edges, straightness of edges, discrete cosine transform coefficients, etc. In addition to that, this work includes finding of Euclidean shapes i.e. closed contours and recursive shapes in the given image. When the Euclidean shaped object dominates the recursive shapes then it is classified as indoor object and if the recursive shapes dominates, it is categorized as outdoor object. This work is carried out on the standard image data sets. The data sets are MRC object recognition image database 1.0. and Kodak and Coral image data set. Totally 540 images are taken into account and the images are classified 95.4 percent correctly.

An image overall complexity evaluation method based on LSD line detection

In the artificial world, whether it is the city's traffic roads or engineering buildings contain a lot of linear features. Therefore, the research on the image complexity of linear information has become an important research direction in digital image processing field. This paper, by detecting the straight line information in the image and using the straight line as the parameter index, establishing the quantitative and accurate mathematics relationship. In this paper, we use LSD line detection algorithm which has good straight-line detection effect to detect the straight line, and divide the detected line by the expert consultation strategy. Then we use the neural network to carry on the weight training and get the weight coefficient of the index. The image complexity is calculated by the complexity calculation model. The experimental results show that the proposed method is effective. The number of straight lines in the image, the degree of dispersion, uniformity and so on will affect the complexity of the image.

Multiphase Oscillator Using Traveling Pulses Developed in a System of Transmission Lines with Regularly Spaced Resonant-tunneling Diodes

A scheme is proposed for generating multiphase oscillatory signals in millimeter-wave frequencies based on the dynamics of a traveling pulse developed in a closed transmission line periodically loaded with resonant-tunneling diodes (RTDs) that is coupled with several straight RTD lines. When supplied with an appropriate voltage at the end of an RTD line, a pulse edge is shown to exhibit a spatially extended limit-cycle oscillation on the line. We consider the case where several RTD lines are connected halfway to a closed one at even intervals. In this case, the oscillatory edge developed in each straight RTD line is mutually synchronized such that a pulse-shaped rotary traveling wave develops on the closed RTD line. The oscillating edge on each straight line is also synchronized with the traveling pulse on the closed line, such that the leading edge of the traveling pulse on the closed line and the forward edge on the straight line pass the cross point simultaneously. As a result, when N L straight lines are connected to the closed line, the phase difference between two adjacent oscillatory edges becomes 2π/N L . On the other hand, the trailing edge of the traveling pulse at the cross point breaks the voltage wave on the straight line into two pieces, one of which travels forward to form a solitary wave and the other of which travels backward to reach the input end, where it is reflected and starts to travel forward and this forward moving edge is supposed to be synchronized with the leading edge of the traveling pulse. It means that a back-and-forth edge and a forward-moving solitary wave develop periodically on each straight line. Because the time required for the traveling pulse to go around the closed line must be coincident with the period of the edge oscillation on each straight line, a unique traveling pulse cannot synchronize with each oscillating edge when the cell size of the closed line becomes large, resulting in the development of multiple traveling pulses on the closed line. In this paper, the design criteria are discussed concerning the connecting point between the straight and closed lines, the number of straight lines, and the size of the closed line. In addition, we describe several measurement results that validate the essential properties of the traveling pulse and then show several results of full-wave analysis of a monolithically integrated RTD line.

Формальное представление условий инцидентности в многомерных проективных пространствах

Synthetic and analytical methods are usually used to investigate multidimensional spaces and sets of subspaces. Shortcomings of a synthetic method — the appeal to spatial imagination and the researcher´s intuition, impossibility of formalization, need of creation of big and complex logical constructions don´t allow to go beyond four-dimensional space, with rare exceptions. The theory of enumerative geometry submitted as geometry of conditions with a basic element – a multidimensional flags incidence condition allows solve many problems which up to now were considered as insoluble ones. The simplest of such problems is a classical problem for calculation of final number of given space’s subspaces meeting the set of given conditions (the normal problem of algebraic geometry). A more serious problem – calculation a number and values of algebraic characteristics for given variety in given space. For this problem solution it was necessary to develop a formalized method, as well as technique algorithmization. This problem has been solved by professor. V.Ya. Volkov in his doctoral dissertation by means of developed by him so-called e-calculations. For an understanding of e-calculation fundamentals or calculation of Schubert conditions a rather good mathematical background and method promotion are necessary. The last demands consideration of various approaches to conditions calculation problem. In the present paper are considered the simplest cases of a tabular method for conditions calculation, in relation to conditions of incidence which is understood in a general sense. Calculation of one-, two- and ((k + 1) (n – k) – 1)-dimensional conditions are considered. Conditions calculation formalization and incidence conditions reduction are explained. The problem about a final number of straight lines crossing the set number of k-planes in n-dimensional space is considered as an example. In particular, the problem about a number of straight lines crossing some number of the set straight lines can be correct only in three- and four-dimensional spaces. Conditions of the minimum multiplicity equal to three exist only in (3k + 1)-dimensional spaces. Conditions of the multiplicity equal to four exist only in odd dimensionality spaces. And so on. The concrete number of straight lines in all cases can be counted by reduction of the corresponding conditions.

First Integrals and Phase Portraits of Planar Polynomial Differential Cubic Systems with the Maximum Number of Invariant Straight Lines

In the article Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite.

Determination of the Indirect Orientation of Orbital PUSHBROOM Images Using Control Straight Lines

Abstract The aim of this paper is to present an experimental assessment of two models that use “control lines” for the indirect orientation of pushbroom imagery. Since pushbroom image acquisition is not instantaneous, six exterior orientation parameters (EOPs) must be estimated for each scanned line. The sensor position and attitude parameters are modelled with a time‐dependent polynomial. The relationship between a straight line in the image space and its homologous form in the object space is established in the first model, based on the principle that the position vector containing an image point (projection ray) and the vector normal to the projection plane in the object space are orthogonal. The second model is based on the equivalence between the vector normal to the projection plane in the image space and the vector normal to the rotated projection plane in the object space. The equivalence property between planes was adapted to consider the pushbroom geometry. A model based on collinearity equations using points adapted to the pushbroom geometry was also implemented, aiming at a comparison of the methodologies. Six experiments using different sets of observations for indirect estimation of EOPs of images from the China–Brazil Earth Resources Satellite (CBERS) were carried out, by varying the geometric distribution and the number of straight lines. Also, experiments combining points and straight lines were accomplished. The results showed that an accuracy of around twice the ground sample distance (GSD) in the check points can be achieved with the models studied, which can then be used to estimate the EOPs of pushbroom images. Several other factors affecting the accuracy, such as the distribution and number of control features, were also assessed.

Automatic infrasonic 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.

A review and analyses of plumb‐line calibration

Abstract Radial and decentring distortion parameters have long been reported as fundamental elements in camera calibration, especially in digital close range photogrammetry. This paper reports on an investigation for the determination of both radial and decentring distortion parameters using analytical plumb‐line calibration. Straight line patterns, ranging from 1, 2, 4, 10 and up to 20 lines, not strictly plumb, are examined on a set of distorted imagery. Additionally, not only the number of straight lines but also the linear image distribution is analysed. For that purpose, linear features have been distributed in different positions and orientations over the whole of the imagery. Furthermore, the relationship between the parameters mentioned and the location of the principal point is also analysed, and shows how sensitive they are to deviations from the centre of the sensor. The motivation for this paper is the measurement of the minimum number of linear features for proper calibration of non‐metric digital cameras. Both radial and decentring distortion parameters are examined. Finally, some line patterns are recommended for making the plumb‐line calibration technique a reliable, easy and fast procedure. Photogrammetrists could use it as a first step in the procedure of camera calibration; users who are not experts in photogrammetry could employ it as a final step.

Histomorphometric assessment of spiral ganglion neurite outgrowth in vitro

During the last years, various groups of growth factors have been identified to influence spiral ganglion cell survival and neurite extension in the mammalian cochlea. To evaluate and compare the effects of different growth factors, a precise histomorphometrical analysis of neurite outgrowth patterns has to be applied. The here presented technique is compared to already published methods, that only approximately estimate the neurite length. A software has been developed to analyse digitalised scans of spiral ganglion cells and to measure the length of the neurites. Therefore, the neurites are being separated in any given number of straight lines. The totals of these lines can then be added like a polygon. This polygon method was compared to a semi-quantitative procedure in which the neurite length was determined by concentric circles that were crossed by the neurites in a certain distance. The accuracy of both methods was analysed. Both methods were performed in 20 specimen of neonatal rat spiral ganglion cells after in vitro stimulation with neurotrophic factors. The semi-quantitative method has shown to involve a systematic error between +/- 10 to 15 %. The polygon method, on the contrary, has a systematic error of around +/- 1 %, which admits much more accurate measurement of spiral ganglion neurite outgrowth. With the described polygon method, spiral ganglion neurite growth patterns in cell culture studies can be characterised more precisely and, thus, helps to better differentiate the action domain of neurotrophic factors.

Line spectral analysis for harmonizable processes.

Harmonizable processes with spectral mass concentrated on a number of straight lines are considered. The asymptotic behavior of the bias and covariance of a number of spectral estimates is described. The results generalize those obtained for periodic and almost periodic processes.

Numerically efficient angle, width, offset, and discontinuity determination of straight lines by the discrete Fourier-bilinear transformation algorithm

We introduce a new method for determining the number of straight lines, line angles, offsets, widths, and discontinuities in complicated images. In this method, line angles are obtained by searching the peaks of a hybrid discrete Fourier and bilinear transformed line angle spectrum. Numerical advantages and performance are demonstrated.

Electromagnetic transmission through a small radome of arbitrary shape

A simple moment solution is presented for the problem of electromagnetic transmission through a small radome of arbitrary shape. The radome is excited by either a plane wave (receive mode) or an elementary dipole inside the radome (transmit mode). The equivalence principle is used to replace the radome by a set of equivalent electric and magnetic surface currents radiating into an unbounded medium. A set of coupled integral equations involving the surface currents is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the radome are approximated by planar triangular patches and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. In the receive mode, the total field inside the radome is computed along a number of straight lines and in the transmit mode the far transmitted field is computed. A spherical and a Von Karman radome are studied. The computed results are in excellent agreement with the exact or other available published data.

Kinetics of ATP hydrolysis by F1-ATPase and the effects of anion activation, removal of tightly bound nucleotides, and partial inhibition of the ATPase by covalent modification.

Eadie-Hofstee plots (v/[S] vs. v) of the kinetics of ATP hydrolysis by purified bovine heart mitochondrial F1-ATPase (MF1) over a substrate (MgATP) concentration range of 1-5000 microM were curvilinear, indicating negative cooperativity with respect to [MgATP] as originally shown by Ebel & Lardy (1975) [Ebel, R. E., & Lardy, H. A. (1975) J. Biol. Chem. 250, 191-196]. The data were computer analyzed for the best fit of the least number of straight lines, each representing a different apparent Km and Vmax. The best fits for MF1 and TF1 from the thermophilic bacterium PS3 were three lines in each case. The upper limits of the apparent Km values for MF1 were of the order of 10(-6), 10(-4), and 10(-3) M, and the corresponding apparent Vmax values (per minute per milligram of protein) were in the range of micromoles or less for the lowest Km line and decamicromoles for the other two. The results for TF1 were very similar. The presence of an activating anion (10 mM KHCO3) in the MF1 assay medium increased the overall Vmax by about 50% and eliminated the high Km but had essentially no effect on the intermediate and low Km's, indicating retention of negative cooperativity in the corresponding substrate concentration range. Kinetic data for MgITP as substrate also yielded two Km values (in the absence of KHCO3) differing by about 10(4)-fold. The relationship between [14C]dicyclohexylcarbodiimide [( 14C]-DCCD) binding to MF1 and activity inhibition was linear up to approximately 1 mol of DCCD bound/mol of MF1. At this point, the degree of inhibition was about 95%.(ABSTRACT TRUNCATED AT 250 WORDS)

Grain‐size distribution of suspended load in relation to bed materials and flow velocity

ABSTRACTGrain‐size frequency distributions of suspended loads at different flow velocities and over sand beds of four different grain‐size patterns were studied in a laboratory flume. The proportion of bed material which went into suspension increased with decrease of grain‐size in each case, but the modes of the suspended loads occurred in the size classes intermediate between the coarsest and the finest. With increase of flow velocity, as also with decrease of the bed's mean grain‐size, the total amount of material in suspension markedly increased, mainly due to addition of particles to the medium size classes.The coarsest grains in the bed resisted erosion due to their weight, whereas the finest ones were either not available in sufficient quantities or resisted erosion due to their homogeneity. The finest of the erodible grains which were abundantly available in bed were therefore, lifted up in large quantities. This size sorting took place at or near the bed surface and was closely related to the process of bed form migration.Large accumulation of medium sized particles in suspension at high velocities led to lognormal grain‐size distributions when the nature of the bed (source) material was suitable. At lower velocities, or over other types of bed materials, the phi (log)‐probability plots of cumulative grain‐size distributions of the suspended loads resolved into a number of straight lines. Mixtures of linear segments on phi‐probability graphs therefore, need not necessarily indicate different modes of sediment transportation, as is commonly believed, but might reflect the conditions of flow and the nature of the source material.

Numerical characteristics of systems of straight lines on complete intersections

We obtain an equation for the number of straight lines on the complete intersection of hypersurfaces and find Hilbert's polynomial for the variety of straight lines of a cubic three-dimensional hypersurface.

Schwartz's integral for a class of functions which are regular in a denumerable-connected circular ?-region

We construct an expression which generalizes the familiar Schwartz expression to the case of a denumerable-connected circularδ-region for which the centers of the boundary circles lie on a finite number of straight lines of the same bundle. Using this expression we can construct a regular and single-valued function of a sufficiently general form inside the region under consideration, from the values of its real part on the boundary of the region.

図形の相関関数の測定とその応用

Discussed in this paper is a two-dimensional autocorrelation function as a means of treating tow-dimensional signals. Autocorrelation functions of various patterns are measured and their interesting properties are pointed out. One of them is the following: when a pattern has straight lines in it and none of them are parallel with each other, the same number of straight lines as the original ones appear in the correlation plane parallel to the original straight lines and passing through the origin of the plane. By using this property, it is possible to detect the presence of straight lines and their relative orientation in the pattern by means of a photoelectric device. An analogue correlation method is also proposed to classify these detected signals.

A Method of Calculating the Characteristic Impedance of a Strip Transmission Line to a Given Degree of Accuracy

The calculation of the characteristic impedance of the strip transmission line TEM-mode can be reduced to the solution of a two-dimensional potential equation with the strip cross section determining the boundary conditions. Usually this potential equation is solved by conformal mapping, but only the most simple shapes permit exact mapping. Approximations may require considerable work and their accuracy is uncertain. This paper describes an alternative numerical method which is particularly suitable for boundaries consisting of any number of straight lines and right angles. It is based on relaxation methods, but by using also variational principles it derives an approximate value for the impedance, and an upper and lower bound with a difference as small as desirable.