Intersection Of Circles Research Articles

Method of designing astigmatic compensation cavity for mode-locked laser based on propagation circle

The cavities of ultrashort pulsed lasers are mostly based on folded resonators with multi-mirrors. Astigmatism is an important issue to affect the performance of the mode-locked laser. An effective method of astigmatic ally compensating a continuous-wave passively mode-locked laser is presented in this paper. This method, in which the resonator propagation circle graphic theory is used, is easy and intuitive to seek the optimal location of the semiconductor saturable absorber mirror (SESAM), where the astigmatism can be compensated. Theoretical results show that the tangential and the sagittal spot size at the SESAM are equal and that the astigmatism can be compensated, when an SESAM is located at the tangential and the sagittal propagation circle intersection. The mode-locked resonator is insensitive to external perturbation including the vibration and the change of the thermal lens focal length, which leads to the instability of the mode locking operation. The antijamming ability of the resonator is outstanding. The experimental results indicate that the mode-locked laser works in a stabilized continuous-wave mode locking state and operates extremely steadily, when the SESAM is located at the tangential and the sagittal propagation circle intersection. The experimental results of the mode locking lasers show good agreement with the theoretical studies.

Research on the Underwater Acoustic Image Measurement based on Line Array Sound Source Depth with Circle Intersection

Research on the Underwater Acoustic Image Measurement based on Line Array Sound Source Depth with Circle Intersection

An algorithmic solution for computing circle intersection areas and its applications to wireless communications

ABSTRACTA novel iterative algorithm for the efficient computation of the intersection areas of an arbitrary number of circles is presented. The algorithm, on the basis of a trellis structure, hinges on two geometric results, which allow the existence check and the computation of the area of the intersection regions generated by more than three circles by simple algebraic manipulations of the intersection areas of a smaller number of circles. The presented algorithm is a powerful tool for the performance analysis of wireless networks and finds many applications, ranging from sensor to cellular networks. As an example of practical application, an insightful study of the uplink outage probability in a wireless network with cooperative access points as a function of the transmission power and access point density is presented. Copyright © 2012 John Wiley & Sons, Ltd.

E–W extension and block rotation of the southeastern Tibet: Unravelling late deformation stages in the eastern Himalayas (NW Bhutan) by means of pyrrhotite remanences

In the Himalayan chain the collision of India into Eurasia has produced some of the most complex crustal interactions along the Himalayan–Alpine Orogen. In NW Bhutan, middle to late Miocene deformation has been partitioned between conjugate strike-slip faulting, E–W extension along the Yadong-Gulu graben and kilometre-scale folding. To better understand the late deformation stages and their implications for the evolution of the eastern Himalayas, the palaeomagnetism in the erosional remnant of the Tethyan Himalayan rocks outcropping in NW Bhutan has been studied. Their position to the south of the trace of the inner South Tibetan Detachment, to the south of the Tibetan Plateau offers a unique possibility to study the Tertiary rotation of the Himalayas. Pyrrhotite is the carrier of the characteristic magnetisation based on 270–325 °C unblocking temperatures. The age of the remanence is ca. 13 Ma indicated by illite 40K/40Ar cooling ages and a negative fold test. Small circle intersection method applied to the pyrrhotite components shows a ca. 32° clockwise rotation with respect to stable India since 13 Ma. We suggest that this clockwise rotation is related to strain partitioning between NE-directed shortening, sinistral-slip along the Lingshi fault, and east–west extension. This represents a field-based explanation and a minimum onset age for present-day eastward motion of the upper-crust of SE-Tibet and NE-Himalayas.

On the Constructibility of Real 5th Roots of Rational Numbers with Marked Ruler and Compass

We demonstrate that there are infinitely many real numbers constructible by marked ruler and compass which are unique real roots of irreducible quintic polynomials over the field of rational numbers. This result can be viewed as a generalization of the historical open question of the constructibility by marked ruler and compass of real 5th roots of rational numbers. We obtain our results through marked ruler and compass constructions involving the intersection of conchoids and circles, and the application of number theoretic divisibility criteria.

Research on connectivity to Localized Area Coverage algorithm In wireless Sensor Networks

In wireless sensor networks, the area coverage sensing technology is the one of the key foundation technologies. IT is concerned about how to prolong the network lifetime based on meeting user sensing demands. Among the study of area coverage sensing technology, localized area coverage algorithm is gradually attracting wide attention for its less traffic and lower single-node computation. At present, the existing localized area coverage algorithms mainly depends on connectivity critical condition proposed by Xing. This condition is concerned about how to improve the perceived quality to coverage full area, ignores further studying for the network node connectivity. So, this connectivity condition is from the perspective of single node connectivity, resulting in limited conditions for algorithm application. For above issues, firstly, the coverage node set connectivity is introduced for localized area coverage algorithm in this paper. Secondly, the loose connectivity critical condition to ensure coverage and connectivity is re-analyzed from the perspective of network connectivity. Finally, a circle intersection localized coverage algorithm under different conditions to maintain connectivity is designed, to extend the application scene. Simulation results show that the algorithm, under different conditions, can maintain network node connectivity on the basis of ensuring full area coverage.

Mathematical model for designing the traffic circle control

This article sets up mathematic model for the traffic circle intersection to determine how best to control traffic flow. The model figures out the largest traffic capacity through Wardrop's formula. When there is no signal control, we use the service priority algorithm of queuing theory which regulates the running mode of inside circle and setting up avoidance signs at traffic intersections to keep passing vehicles in order. When the signal control is needed, a linkage time solving model is setup, which proves the number of seconds of every green light and work out the delay time. At last, the simulation software VISSIM is used for an example to work out the average delay time under the signal control. The result matches with this model.

Compact distributed target-tracking algorithm with binary sensors

A popular family of sensing systems work using binary sensors. In this study, the behaviour of binary sensing methods is investigated where the individual sensors only return information regarding the target's presence or absence within their own sensing range. In order to enhance their performance the authors propose a new compact distributed algorithm based on a triplet circle intersection principle where they take the central point of their common intersection arc among the sensor detection circles is considered as the target's position. It was shown that the new model can reduce the cost of resourcing as well as decreasing overhead communication traffics; it therefore fits very well with low-power sensor network applications. The experimental test-bench results verify the superior performance of our algorithm. Moreover, the results reveal improved performance criteria for conventional tracking evaluation of the average error and the root-mean-square error because of inherent measurement effectiveness of the target-tracking problem.

A Smooth Flow of Traffic Circle Model

This article sets up mathematic model for the traffic circle to determine how best to control traffic flow. In order to make the traffic at the circle intersection smooth in maximum, this model figures out the largest traffic capacity through Wardrop’s formula. When the signal control is needed, a linkage time solving model is set up, which proves the number of seconds of every green light and work out the delay time. At last, the simulation software VISSIM is used for an example to work out the average delay time under the signal control. The result matches with this model.

William Blake and the Hunt Circle

THE TENSIONS WITHIN ROMANTICISM ARE FULLY MANIFESTED IN THE ANIMOSITIES that existed between William Blake and the Hunt circle. The once marginal Leigh Hunt (and to a lesser degree his brothers John and Robert) has received due scholarly attention in recent years, (1) and we can now appreciate him for his own works, his commitment to reform, and his ability to cultivate connections among writers. Jon Mee has reminded us, however, that a significant part of Leigh Hunt's project was a fierce campaign again Methodism and religious enthusiasm. (2) Hunt's campaign was embodied in a series of essays for The Examiner, entitled An Attempt to Shew the Folly and Danger of Methodism, which appeared as a slightly revised pamphlet in 1809. The original publication of these essays overlapped with Robert Hunt's critical reviews of Blake's edition of The Grave on August 7, 1808, and of his exhibition of paintings on September 17, 1809. Blake, accordingly, became the most significant casualty of the Hunts' campaign against enthusiasm, and the campaign undoubtedly contributed to Blake's retreat into obscurity and poverty. But the clash also had an immensely fruitful influence on Blake's later works. Not only did it give birth to the villainous Hand, a major character of Blake's later mythology whose name plays on the indicator symbol used by the Hunts as a signature, it also shaped, as Mee notes, Blake's defense of Methodists and his conception of literary and religious enthusiasm in Milton and Jerusalem. (3) Since Mee focuses chiefly on what the conflict between Blake and the Hunts says about enthusiasm, I want to revisit this contentious relationship in light of an unrecorded reference to Blake by Leigh Hunt in the short lived quarterly The Reflector (1810/11--12), which is not found in Bentley's Blake Records. Dating from late 1810 or early 1811, this reference comes more than a year after the review of Blake's exhibition, and it shows that the Hunts maintained their interest in Blake for a sustained period. For Blake, the new attack would have come as he was working on several important projects, most of which were already in dialogue with the Hunts. These projects included the engraving of his Chaucer painting, his Public Address to the Chalcographic Society (a group formed for the encouragement of engraving and which was promoted by the Hunts and Robert Cromek, the publisher of The Grave), several notebook poems on the Hunts and his other enemies, Milton, and Jerusalem. (4) The Reflector influenced many of these works, and in light of the new reference to Blake, I also want to underscore Blake's awareness of the topics discussed in The Examiner and the degree to which Blake's circle of friends and acquaintances overlapped with that of the Hunts. While the Hunts were not Blake's only enemies, by figuring Hand as the eldest son of Albion, Blake signaled his recognition of the leadership of the Hunt circle in a new generation of writers. Blake clearly had an enduring interest in the activities and controversies of the Hunt circle, and his concern with Lord Byron, to whom he dedicated The Ghost of Abel (1822), may be an extension of this attention. Ultimately, the intersection of Blake's and Hunt's circles will help us better understand the personal and professional context of Blake's public engagement and the intended audience of his later works. I Blake and the Hunts had many avenues for information about each other. The Hunts were the nephews of Benjamin West, who, as President of the Royal Academy, subscribed to The Grave along with several other members of the Academy. The Hunts knew Cromek and worked with him on promoting several projects. The Hunts' friend, Henry Crabb Robinson, wrote an article on Blake in 1808 and attended his exhibition in 1810. Robinson's diary shows that Blake was a frequent subject of conversation; between 1811 and 1813, Robinson discussed him with William Rough, William Hazlitt, Robert Southey, Charles Lamb, William Wordsworth, Thomas Barnes, and Barron Field, all of whom knew Hunt. …

Position Identification by Actively Localizing Spacial Sound Beacons

In this paper, we propose a method for robot self-position identification by active sound localization. This method can be used for autonomous security robots working in room environments. A system using an AIBO robot equipped with two microphones and a wireless network is constructed and used for position identification experiments. Differences in arrival time to the robot's microphones are used as localization cues. To overcome the ambiguity of front-back confusion, a three-head-position measurement method is proposed. The position of robot can be identified by the intersection of circles restricted using the azimuth differences among different sound beacon pairs. By localizing three or four loudspeakers as sound beacons positioned at known locations, the robot can identify its position with an average error of 7cm in a 2.5×3.0m2 working space in the horizontal plane. We propose adjusting the arrival time differences (ATDs) to reduce the errors caused when the sound beacons are high mounted. A robot navigation experiment was conducted to demonstrate the effectiveness of the proposed position-identification system.

Analytical methods for error propagation in planar space–time prisms

The space–time prism demarcates all locations in space–time that a mobile object or person can occupy during an episode of potential or unobserved movement. The prism is central to time geography as a measure of potential mobility and to mobile object databases as a measure of location possibilities given sampling error. This paper develops an analytical approach to assessing error propagation in space–time prisms and prism–prism intersections. We analyze the geometry of the prisms to derive a core set of geometric problems involving the intersection of circles and ellipses. Analytical error propagation techniques such as the Taylor linearization method based on the first-order partial derivatives are not available since explicit functions describing the intersections and their derivatives are unwieldy. However, since we have implicit functions describing prism geometry, we modify this approach using an implicit function theorem that provides the required first-order partials without the explicit expressions. We describe the general method as well as details for the two spatial dimensions case and provide example calculations.

Paleomagnetic, petromagnetic, and terrigenous—Mineralogical studies of Upper Bathonian—Lower Callovian sediments in the Prosek section, Nizhni Novgorod region

The Bathonian—Callovian boundary section located near the Prosek Settlement (Nizhni Novgorod region) is described with the characteristic of its grain-size composition and terrigenous—mineralogical, petromagnetic, and paleomagnetic properties. Based on lithological—mineralogical and petromagnetic data, the section is subdivided into four members corresponding to the most significant sedimentation rhythms. No sharp changes in the composition of sediments are noted through the section, which indicates its relative continuity. Despite the significant re magnetization of these sediments during the Quaternary, the characteristic component (ChRM) is definable by the method of the intersection of large circles. The similarity between coordinates of the calculated virtual geomagnetic pole (VGMP) and the positions of standard virtual geomagnetic poles in the stable European continent during corresponding periods serves as an important argument in favor of the primary nature of the ChRM. The compiled magnetostratigraphic section is well consistent with the paleomagnetic zonation, established in the coeval sediments of “West Europe. As compared with the Bathonian—Callovian boundary section in the Albstadt—Pfeffingen of Germany, which claims to the GSSP role, the Prosek section represents a more favorable object for paleomagnetic studies. Combined with the lack of large-scale gaps in the sedimentary record and, with other conditions being equal, this makes this section a more preferable candidate for the Callovian GSSP standard.

Diachronous pervasive remagnetization in northern Iberian basins during Cretaceous rotation and extension

Northern Iberia exposes a series of Mesozoic sedimentary basins, whose final formation history is tied to a rotation episode of Iberia during the Aptian, related to the opening of the Bay of Biscay. Many of these basins experienced widespread remagnetization, previously loosely tied to a ‘Mid-Cretaceous thermal event’. Here we make use of the improved apparent polar wander path (APWP) of Iberia to narrowly constrain the age of their remagnetization to show that several basins experienced a regional diachronous remagnetization. We apply the small circle intersection (SCI) method to reconstruct the paleomagnetic field direction during remagnetization in the Organyà Basin in the Southern Pyrenees, Spain, where the age of remagnetization is stratigraphically well-dated to around the Barremian–Aptian boundary, and where the paleomagnetic direction during remagnetization has been well-established. The resulting direction of D/ I = 316.8 ± 5.7°/54.8° ± 3.3° (where the uncertainty in declination is approximated by α 95 / cos I and the error in inclination by α 95) corresponds closely to a recently improved APWP of Iberia, providing support for the applicability of this method. Application of the SCI method allows us to show that the older portion of the remagnetized beds was already tilted by ~ 15–20° to the South during the remagnetization as a result of half-graben formation in the Organyà Basin. Moreover, the positive outcome of the SCI technique enables us to argue that previously published results from three other basins—the Cabuérniga and Cameros Basins and the Iberian Range—can be straightforwardly compared to the APWP. Hence, we show that the four pervasively remagnetized basins under consideration all acquired their remagnetization at different times. The remagnetization events were thus confined to these sedimentary basins on an individual ‘per basin’ scale—albeit occurring on a regional scale over a period of at least ~ 10–15 Myr. Therefore, we propose that the Cretaceous remagnetization events in northern Iberia are related to the extensional tectonic rifting. The pervasive remagnetization is most likely basin confined because there is no apparent overall regional or temporal trend among the basins. Reasonable explanations for remagnetization are those that can occur on the scale and within the context of individual sedimentary basins. These include the interplay of burial depth and an elevated geothermal gradient to reach the diagenetic temperatures required for magnetite-producing reactions. In the Iberian situation, there is no need to invoke more speculative regional Iberia-wide mechanisms.

The Localized Area Coverage Algorithm Based on Delayed Start Scheme For WSN

The Coverage Control Technology is the one of the basic technologies of wireless sensor network, and is mainly concerned about how to prolong the network lifetime on the basis of meeting user’s perception demand. Among this technology, localized area coverage algorithm in the study of area coverage technology is gradually attracting wide attention, for its less traffic and lower single-node computation. However, the existing localized area coverage algorithm has either phenomenon of coverage holes and can’t meet user’s perception demand or phenomenon of Nibble and leads to too much active nodes and shortens network lifetime. Therefore, localized area coverage algorithm based on delayed start scheme is proposed. It applies time round mechanism without knowing the network topology in advance and uses circle intersection coverage evaluation algorithm to ensure fully covered area and avoid the phenomenon of coverage loopholes. What is more, the application of delayed start scheme reduces the phenomenon of Nibble. According to the experimental results, compared with the existing localized area coverage algorithms, this algorithm can prolong the network lifetime on the basis of meeting user’s perception demand.

Early Paleocene Paleomagnetic Results from Southern Tibet, and Tectonic Implications

Paleomagnetic studies were carried out on the Paleocene sedimentary rocks at Dingri, Tibet (28°42'N, 86°50'E) along the northern margin of the Indian plate. Thirteen sites (about 120 cores) were sampled from limestone of the Zongpu Formation. Three magnetic components were identified after stepwise thermal demagnetization. The middle-temperature component records a remagnetization event, which is inferred to be a consequence of thermal remagnetization during the collision between India and Eurasia. The age of remagnetization, ~54.0 Ma, was estimated by comparing the measured paleolatitude and the expected paleolatitude from the apparent polar wander path (APWP) of the Indian plate, which corresponds to the time of final suturing between India and Eurasia. The preliminary result for the high-temperature component was determined by the intersection of great circles, which passed a regional fold test. The magnetic remanence reflects the primary origin, and probably was acquired at ~65.5-61.7 Ma. By comparing our Paleocene results with those from the stable Indian plate, we infer that the Dingri area was a stable part of the Indian block, and crustal shortening across the Main Central thrust (MCT) and the Main Boundary fault (MBF) in the southern Himalayas was paleomagnetically insignificant. The extension of greater India is estimated as ~1000 km.

General approach to simple algorithms for 2-D positioning techniques in cellular networks

Finding the location of an object is one of the important features of autonomous and the 3G/4G wireless communication systems. Many valuable location based services can be enabled by this feature. Position estimation from Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Angle of Arrival (AOA) measurements are the commonly used techniques. These approaches use the location parameters received from different sources, and they are based on intersections of circles, hyperbolas, and lines, respectively. The location is determined using standard complex computation methods that are usually implemented in software. In this paper, we propose a general approach to design new hardware-oriented algorithms that use only simple add and shift operations in the computation and therefore can be easily implemented in hardware or firmware. In addition to their implementation simplicity, the proposed algorithms outperform the conventional ones in terms of the required number of operations for a specific accuracy level.

A variational principle for weighted Delaunay triangulations and hyperideal polyhedra

We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hyperbolic space. Thus, the main theorem states necessary and sufficient conditions for the existence and uniqueness of such polyhedra with prescribed combinatorial type and dihedral angles. More generally, we consider weighted Delaunay triangulations in piecewise flat surfaces, allowing cone singularities with prescribed cone angles in the vertices. The material presented here extends work by Rivin on Delaunay triangulations and ideal polyhedra.

FLUXO GÊNICO ENTRE ARROZ VERMELHO E ARROZ CULTIVADO ESTIMADO POR MEIO DE MARCADORES MICROSSATÉLITES

The study aimed to evaluate the capacity of SSR markers to detect the gene flow between the red rice (RR) and the cultivated rice (CR). SSR is currently used in plant genomic analysis due to the high information content, to be co-dominant, and based on the PCR reaction. The field experiment was organized in ten concentric circles, 5 m to 50 m apart from a central red rice plant, assumed as the pollen donor. One hundred twenty rice CR plants, cv. BR-Irga 409, were planted in the intersections of the concentric circles and the twelve radii. From 51 SSR markers, four were selected due to their capacity to detect the polymorphism between RR and CR, aiming to identify RR alleles in seeds produced by BR-Irga 409 plants. The maximum distance found for gene flow between RR and CR plants was 10 m from the RR plant. In theory, at 0.1% cross pollination rate, this distance can generate 4,710 hybrids between RR and CR. In the next generation, about 3,532 plants would produce exclusively rice grains with red color. The SSR markers were able to identify the gene flow between RR and CR; therefore, they can be useful to increase the precision of cross pollination rate estimates in rice, mainly if used with other methodologies (e.g., herbicide tolerant plants). KEY WORDS: Cross pollination; microsatellite markers; Oryza sativa.

Intersections of Lines and Circles

A method is presented for determining barycentric coordinates of points of intersection of a line and a circle. The method is applied specifically to the Euler line, the line of the circumcenter and incenter, the Brocard axis, and several circles, including the circumcircle, incircle, nine-point circle, and Brocard circle. The method also applies to intersections of certain pairs of lines, harmonic conjugate pairs, and to centers of similitude of pairs of circles.