Regular crystal structures are periodically arranged in neatly fitted shapes like cubes (four-fold symmetry) or triangles (three-fold symmetry), but quasicrystals are arranged in non-periodic patterns such as pentagonal, five-fold symmetries.
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When combined with the lightcurve of the orbit of a planet, this could produce non-periodic and very noisy lightcurves, like those observed around KIC 8462852, which you may know asTabby's Star or Boyajian's Star.
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In this way, setisets can produce non-periodic tilings. However, none of the non-periodic tilings thus far discovered qualify as aperiodic, because the prototiles can always be rearranged so as to yield a periodic tiling. Figure 5 shows the first two stages of inflation of an order 4 set leading to a non-periodic tiling.
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The comets are in a highly eccentric orbit and are non-periodic.
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In geometry, pinwheel tilings are non-periodic tilings defined by Charles Radin and based on a construction due to John Conway. They are the first known non-periodic tilings to each have the property that their tiles appear in infinitely many orientations.
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The asteroid 112328 Klinkerfues is named in his honour, as were 6 non-periodic comets.
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Printed publications: "Vpered" (magazine of the left wing of the party), "Ukrainian News", "Ukrainian Prometheus", non-periodic magazine "Our Positions" (since 1948).
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That is, each tile in the tiling must be congruent to one of these prototiles. A tiling that has no periods is non-periodic. A set of prototiles is said to be aperiodic if all of its tilings are non-periodic, and in this case its tilings are also called aperiodic tilings. Penrose tilings are among the simplest known examples of aperiodic tilings of the plane by finite sets of prototiles.
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The Penrose tiling is an example of an aperiodic tiling; every tiling it can produce lacks translational symmetry. An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are the best-known examples of aperiodic tilings.
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A given set of tiles, in the Euclidean plane or some other geometric setting, admits a tiling if non- overlapping copies of the tiles in the set can be fitted together to cover the entire space. A given set of tiles might admit periodic tilings — that is, tilings which remain invariant after being shifted by a translation (for example, a lattice of square tiles is periodic). It is not difficult to design a set of tiles that admits non-periodic tilings as well as periodic tilings (for example, randomly arranged tilings using a 2×2 square and 2×1 rectangle will typically be non-periodic). However, an aperiodic set of tiles can only produce non-periodic tilings.
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This is a list of comets (bodies that travel in elliptical, parabolic, and sometimes hyperbolic orbits and display a tail behind them) listed by type. Comets are sorted into four categories: periodic comets (e.g. Halley's Comet), non-periodic comets (e.g. Comet Hale–Bopp), comets with no meaningful orbit (the Great Comet of 1106), and lost comets (5D/Brorsen), displayed as either P (periodic), C (non-periodic), X (no orbit), and D (lost).
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Non-periodic tilings can also be obtained by projection of higher-dimensional structures into spaces with lower dimensionality and under some circumstances there can be tiles that enforce this non-periodic structure and so are aperiodic. The Penrose tiles are the first and most famous example of this, as first noted in the pioneering work of de Bruijn.N. G. de Bruijn, Nederl. Akad. Wetensch. Indag. Math. 43, 39–52, 53–66 (1981).
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However, the non-periodic comet C/1925 F1 (Shajn-Comas Solá; also known as Comet 1925 VI or Comet 1925a) was co-discovered by her husband rather than by her.
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Amman's A and B pair of A5 tiles, decorated with matching rules; any tiling by these tilings is necessarily non- periodic, and the tiles are therefore aperiodic. Ammann A5 substitution rules, used to prove that the A5 tiles can only form non-periodic hierarchical tilings and thus are aperiodic tiles. This tiling exists in a 2D orthogonal projection of a 4D 8-8 duoprism constructed from 16 octahedral prisms. Amman's A and B tiles in his pair A5 a 45-135-degree rhombus and a 45-45-90 degree triangle, decorated with matching rules that allowed only certain arrangements in each region, forcing the non-periodic, hierarchical, and quasiperiodic structures of each of the infinite number of individual Ammann–Beenker tilings.
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Astronomers believed that planets captured non-periodic comets into elliptical orbits; each planet had a "family" of comets that it captured, with Jupiter's the largest. In 1907 A. O. Leuschner proposed that many non-periodic comets would have elliptical orbits if studied longer, making most comets permanent parts of the solar system, even those with orbital periods of thousands of years. This implied a large group of comets outside the orbit of Neptune, the Oort cloud.
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The term aperiodic has been used in a wide variety of ways in the mathematical literature on tilings (and in other mathematical fields as well, such as dynamical systems or graph theory, with altogether different meanings). With respect to tilings the term aperiodic was sometimes used synonymously with the term non-periodic. A non-periodic tiling is simply one that is not fixed by any non-trivial translation. Sometimes the term described – implicitly or explicitly – a tiling generated by an aperiodic set of prototiles.
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The Great Comet of 1577, seen over Prague on November 12. Engraving made by Jiri Daschitzky. The Great Comet of 1577 (official designation: C/1577 V1) is a non-periodic comet that passed close to Earth during the year 1577 AD. Having an official designation beginning with "C" classes it as a non-periodic comet, and so it is not expected to return. In 1577, the comet was visible to all of Europe, and was recorded by many contemporaries of the time, including the famous Danish astronomer Tycho Brahe and Turkish astronomer Taqi ad-Din.
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Coin showing Caesar's Comet as a star with eight rays, tail upward Non- periodic comets are seen only once. They are usually on near-parabolic orbits that will not return to the vicinity of the Sun for thousands of years, if ever. Periodic comets usually have elongated elliptical orbits, and usually return to the vicinity of the Sun after a number of decades. The official names of non-periodic comets begin with a "C"; the names of periodic comets begin with "P" or a number followed by "P".
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Hafner, I. and Zitko, T. Introduction to golden rhombic polyhedra. Faculty of Electrical Engineering, University of Ljubljana, Slovenia. This figure is another spacefiller, and can also occur in non-periodic spacefillings along with the rhombic triacontahedron, the rhombic icosahedron and rhombic hexahedra.
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Fourier discovered that every continuous, periodic function could be described as an infinite sum of trigonometric functions. Even non-periodic functions can be represented as an integral of sines and cosines through the Fourier transform. This has applications to quantum mechanics and communications, among other fields.
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The observatory discovered the periodic comets 60P/Tsuchinshan and 62P/Tsuchinshan, as well as the non-periodic (Tsuchinshan), also known as Comet 1977 X, and . Many asteroids were also discovered, including the Trojan asteroids 2223 Sarpedon, 2260 Neoptolemus, 2363 Cebriones, 2456 Palamedes, and the eponymous 3494 Purple Mountain.
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Thus, the anti-de Sitter space contains a conformal Minkowski space at infinity ("infinity" having y-coordinate zero in this patch). In AdS space time is periodic, and the universal cover has non- periodic time. The coordinate patch above covers half of a single period of the spacetime.
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Periodic comets sometimes bear the same name repeatedly (e.g. the nine Shoemaker–Levy comets or the twenty-four NEAT comets); the IAU system distinguishes between them either through the number prefix or by the full designation (e. g. 181P and 192P/Shoemaker–Levy are both "Comet Shoemaker–Levy"). In the literature, an informal numbering system is applied to periodic comets (skipping the non-periodic ones), thus 181P and 192P are known as Comet Shoemaker–Levy 6 and Comet Shoemaker–Levy 1, respectively. Non- periodic Shoemaker–Levy comets are interleaved in this sequence: C/1991 B1 between 2 and 3, C/1991 T2 between 5 and 6, C/1993 K1 and C/1994 E2 after Shoemaker–Levy 9.
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Comets which do not fulfill the "periodic" requirements receive the "C" prefix (e.g. C/2006 P1, the Great Comet of 2007). Comets initially labeled as "non- periodic" may, however, switch to "P" if they later fulfill the requirements. Comets which have been lost or have disintegrated are prefixed "D" (e.g.
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160 mm in diameter (females). Adults produce unsheathed and non-periodic (sub-periodic in M. perstans) microfilariae that reach the blood stream. A midge or black fly ingests microfilariae during a blood meal. After ingestion, the microfilariae migrate from the midgut through the hemocoel to the thoracic muscles of the arthropod.
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C/2008 T2 (Cardinal), is a non-periodic comet. It was discovered by Rob. D. Cardinal from the University of Calgary. It was visible as a telescopic and binocular object during 2009. It passed near the Perseus star clusters NGC 1528 on March 15 and NGC 1545 on March 17, 2009.
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Consider a periodic tiling by unit squares (it looks like infinite graph paper). Now cut one square into two rectangles. The tiling obtained in this way is non-periodic: there is no non-zero shift that leaves this tiling fixed. But clearly this example is much less interesting than the Penrose tiling.
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C/1874 H1 (Coggia) is a famous non-periodic comet, which in the summer of 1874 could be seen by naked eye observation. On the basis of its brightness, the comet has been called the Great Comet of 1874; on July 13 the magnitude of the brightness was between 0 and 1.
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C/1890 V1 (Zona) is a non-periodic comet discovered on 15 November 1890 by the Italian astronomer Temistocle Zona with an equatorially mounted Merz telescope at the Osservatorio Astronomico di Palermo.Osservazioni della Cometa 1890 IV (Zona Nov. 15) Whilst attempting to observe this comet, Spitaler discovered the eponymous 113P/Spitaler in 1890.
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They also showed that illusory motion reversal occurs with non-uniform and non-periodic stimuli (for example, a spinning belt of sandpaper), which also cannot be compatible with discrete sampling. Kline and Eagleman proposed instead that the effect results from a "motion during-effect", meaning that a motion after- effect becomes superimposed on the real motion.
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More complex coordinate-dependent proportions can lead to nonlinear material gradients as well as periodic and non-periodic substructure. The proportion formula can also refer to a texture map using the function. Reference to material-id "0" (void) is reserved and may be used to specify porous structures. Reference to the function can be used to specify pseudo-random materials.
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In Russia, advertising alcohol products is banned from almost all media (including television and billboards) since January 2013. Before that, alcohol advertising was restricted from using images of people drinking since mid-2000s. In Sweden, since 2010 advertisements are legal for wine and beer, but not on television and radio. Non-periodic magazines are allowed to advertise alcoholic beverages above 15%.
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Taylor and Socolar remark that the 3D monotile aperiodically tiles three-dimensional space. However the tile does allow tilings with a period, shifting one (non-periodic) two dimensional layer to the next, and so the tile is only "weakly aperiodic". Physical copies of the three-dimensional tile could not be fitted together without allowing reflections, which would require access to four-dimensional space.
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C/1980 E1 is a non-periodic comet discovered by Edward L. G. Bowell on 11 February 1980 and which came closest to the Sun (perihelion) in March 1982. It is leaving the Solar System on a hyperbolic trajectory due to a close approach to Jupiter. Since its discovery only 1I/ʻOumuamua and 2I/Borisov have been identified with a faster such trajectory.
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A similar effect is available for peak functions. For non- periodic functions, however, methods with unequally spaced points such as Gaussian quadrature and Clenshaw–Curtis quadrature are generally far more accurate; Clenshaw–Curtis quadrature can be viewed as a change of variables to express arbitrary integrals in terms of periodic integrals, at which point the trapezoidal rule can be applied accurately.
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Non-commutative spaces arise naturally, even inevitably, from some constructions. For example, consider the non-periodic Penrose tilings of the plane by kites and darts. It is a theorem that, in such a tiling, every finite patch of kites and darts appears infinitely often. As a consequence, there is no way to distinguish two Penrose tilings by looking at a finite portion.
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C/2007 E2 (Lovejoy) is a non-periodic comet discovered by Terry Lovejoy on 15 March 2007. Its perihelion was 27 March 2007, while its closest approach to Earth was 25 April 2007 in Hercules at a distance of 0.44 AU. Maximum apparent magnitude was approximately +8. The discovery was made using a Canon EOS 350D consumer grade digital camera, and not a CCD survey camera.
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He discovered or co-discovered thirteen comets. Among these were the periodic comets 18D/Perrine–Mrkos, 45P/Honda–Mrkos–Pajdušáková, 124P/Mrkos and 143P/Kowal–Mrkos. He also discovered the bright non-periodic comet C/1957 P1 (or, in the nomenclature of the time, comet 1957d). He discovered a number of asteroids (273 in total), including the Amor asteroid 5797 Bivoj and Trojan asteroid 3451 Mentor.
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A radial hyperbolic trajectory is a non-periodic trajectory on a straight line where the relative speed of the two objects always exceeds the escape velocity. There are two cases: the bodies move away from each other or towards each other. This is a hyperbolic orbit with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1 this is not a parabolic orbit.
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The Skolem problem is the problem of determining whether a given recurrence sequence has a zero. There exist an algorithm to test whether there are infinitely many zeros, and if so to find the decomposition of these zeros into periodic sets guaranteed to exist by the Skolem–Mahler–Lech theorem. However, it is unknown whether there exists an algorithm to determine whether a recurrence sequence has any non-periodic zeros .
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In a subsequent work, the method was extended further—PSGAN can learn both periodic and non-periodic images in an unsupervised way from single images or large datasets of images. In addition, flexible sampling in the noise space allows to create novel textures of potentially infinite output size, and smoothly transition between them. This makes PSGAN unique with respect to the types of images a texture synthesis method can create.
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The condition that the dynamical system be on the plane is necessary to the theorem. On a torus, for example, it is possible to have a recurrent non-periodic orbit. In particular, chaotic behaviour can only arise in continuous dynamical systems whose phase space has three or more dimensions. However the theorem does not apply to discrete dynamical systems, where chaotic behaviour can arise in two- or even one- dimensional systems.
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62 In electronics, the term is usually applied to periodically varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds—variations of pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal. The term can also be used for non-periodic signals, like chirps and pulses.
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Comet C/ (LINEAR) (also written C/2006 VZ13), is a non-periodic comet discovered November 13, 2006 by the LINEAR. The object was initially believed to be a minor planet due to its stellar appearance in the early images. However, observers soon detected a small coma and the telltale green cometary cast. The comet peaked at approximately magnitude +7.5,Comet C/ at Seiichi Yoshida home page much brighter than predicted.
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The taste of the day not yet emancipated from the influence of the Sicilian rhetoric probably demanded a large use of antithesis. Lysias excels in vivid description; he has also the knack of marking the speaker's character by light touches. The structure of his sentences varies a good deal according to the dignity of the subject. He has equal command over the periodic style (κατεστραμμένη λέξις) and the non-periodic or continuous (εἰρομένη, διαλελυμένη).
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Many of the earlier comets to be observed in history are designated with an X or D due to not having the tools to measure a comet's orbit accurately and eventually losing it. X/1106 C1 (the Great Comet of 1106) is a good example. The orbital elements for the older non-periodic comets in the list assume that the comet has an eccentricity of roughly 1, and therefore the calculations are only approximate.
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A chaotic system may have sequences of values for the evolving variable that exactly repeat themselves, giving periodic behavior starting from any point in that sequence. However, such periodic sequences are repelling rather than attracting, meaning that if the evolving variable is outside the sequence, however close, it will not enter the sequence and in fact, will diverge from it. Thus for almost all initial conditions, the variable evolves chaotically with non-periodic behavior.
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Comet West, which appeared three years later, had much lower expectations but became an extremely impressive comet. The Great Comet of 1577 is a well known example of a great comet. The Great Comet of 1577 passed near Earth as a non-periodic comet and was seen by many, including well-known astronomers Tycho Brahe and Taqi ad-Din. Observations of this comet led to several significant findings regarding cometary science, especially for Brahe.
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The comet passed about from the Earth on 1861-May-05 and last came to perihelion (closest approach to the Sun) on 1861-Jun-03. C/1861 G1 is listed as a long-period "non-periodic comet" because it has not yet been observed at two perihelion passages. When it is seen to come back around 2283, it should receive the P/ designation. The comet is the parent body of the April Lyrids meteor shower.
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General mathematical techniques for analyzing non- periodic functions fall into the category of Fourier analysis. The Fourier transform of a function produces a frequency spectrum which contains all of the information about the original signal, but in a different form. This means that the original function can be completely reconstructed (synthesized) by an inverse Fourier transform. For perfect reconstruction, the spectrum analyzer must preserve both the amplitude and phase of each frequency component.
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In this case, the prototile is an elongated irregular nonagon, or nine-sided figure. Because it has no translational symmetries, the Voderberg tiling is technically non-periodic, even though it exhibits an obvious repeating pattern. This tiling was the first spiral tiling to be devised, preceding later work by Branko Grünbaum and Geoffrey C. Shephard in the 1970s. A Voderberg tiling is depicted on the cover of Grünbaum and Shephard's 1987 book Tilings and Patterns..
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Other comets that bore the possessive include "Biela's Comet" (3D/Biela) and "Miss Herschel's Comet" (35P/Herschel–Rigollet, or Comet Herschel–Rigollet). Most bright (non-periodic) comets were referred to as 'The Great Comet Of...' the year in which they appeared. In the early 20th century, the convention of naming comets after their discoverers became common, and this remains today. A comet is named after its first independent discoverers, up to a maximum of three names, separated by hyphens.
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The sequence of tilings where b is centred at 1,2,4, \ldots,2^n,\ldots converges – in the local topology – to the periodic tiling consisting of as only. Thus T is not an aperiodic tiling, since its hull contains the periodic tiling For well-behaved tilings (e.g. substitution tilings with finitely many local patterns) holds: if a tiling is non-periodic and repetitive (i.e. each patch occurs in a uniformly dense way throughout the tiling), then it is aperiodic.
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He has also discovered non-periodic comets C/2010 E5 (Scotti) and C/2010 F3 (Scotti). Scotti's research interests include the origin of comets, the dynamical evolution of comets and asteroids, the near-Earth asteroids, and the outer Solar System. Scotti is also an avid space enthusiast and is interested in the history of space exploration and particularly of the Apollo Program. He has contributed to the Apollo Lunar Surface Journal, which details the Apollo lunar explorations.
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There are a few constructions of aperiodic tilings known. Some constructions are based on infinite families of aperiodic sets of tiles. Those constructions which have been found are mostly constructed in a few ways, primarily by forcing some sort of non-periodic hierarchical structure. Despite this, the undecidability of the Domino Problem ensures that there must be infinitely many distinct principles of construction, and that in fact, there exist aperiodic sets of tiles for which there can be no proof of their aperiodicity.
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The first weather forecasts derived this way used barotropic (single-vertical-level) models, and could successfully predict the large-scale movement of midlatitude Rossby waves, that is, the pattern of atmospheric lows and highs. In 1959, the UK Meteorological Office received its first computer, a Ferranti Mercury. In the 1960s, the chaotic nature of the atmosphere was first observed and mathematically described by Edward Lorenz, founding the field of chaos theory.Edward N. Lorenz, "Deterministic non-periodic flow", Journal of the Atmospheric Sciences, vol.
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PARSEC is a package designed to perform electronic structure calculations of solids and molecules using density functional theory (DFT). The acronym stands for Pseudopotential Algorithm for Real-Space Electronic Calculations. It solves the Kohn–Sham equations in real space, without the use of explicit basis sets. One of the strengths of this code is that it handles non-periodic boundary conditions in a natural way, without the use of super-cells, but can equally well handle periodic and partially periodic boundary conditions.
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Inflation and deflation yield a method for constructing kite and dart (P2) tilings, or rhombus (P3) tilings, known as up-down generation. The Penrose tilings, being non-periodic, have no translational symmetry - the pattern cannot be shifted to match itself over the entire plane. However, any bounded region, no matter how large, will be repeated an infinite number of times within the tiling. Therefore, no finite patch can uniquely determine a full Penrose tiling, nor even determine which position within the tiling is being shown.
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In 1955 he was elected a founding academician of the Chinese Academy of Sciences. Zhang devoted himself to observing and calculating the orbits of minor planets and comets. Many asteroids were discovered at Purple Mountain Observatory, as well as three new comets: two periodic, 60P/Tsuchinshan (Tsuchinshan 2) and 62P/Tsuchinshan (Tsuchinshan 1), and one non-periodic, C/1977 V1. Tsuchinshan is the Wade-Giles transliteration corresponding to the pinyin Zĭjīn Shān, which is Mandarin Chinese for "Purple Mountain", named after the observatory he oversaw.
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Substitution tiling systems provide a rich source of aperiodic tilings. A set of tiles that forces a substitution structure to emerge is said to enforce the substitution structure. For example, the chair tiles shown below admit a substitution, and a portion of a substitution tiling is shown at right below. These substitution tilings are necessarily non- periodic, in precisely the same manner as described above, but the chair tile itself is not aperiodic—it is easy to find periodic tilings by unmarked chair tiles.
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It faded rapidly, becoming visible only in telescopes and was last seen on February 17, 1912. The comet sported a tail 8 to 10 degrees in length. In mid-October, the comet was visible in the evening sky together with another bright comet, C/1911 O1 Brooks.Bortle, J The Bright Comet Chronicles, International Comet Quarterly, 1998 Comet Beljawsky is a long-period (non-periodic) comet noteworthy for having a hyperbolic orbit and so it is not expected to return to the inner Solar System again.
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It has the systematic designation C/2020 F3, indicating a non-periodic comet which was the third discovered in the second half of March 2020. Comet NEOWISE made its closest approach to the Sun (perihelion) on July 3, 2020, at a distance of . This passage through the planetary region increases the comet's orbital period from about 4400 years to about 6700 years. Its closest approach to Earth occurred on July 23, 2020, 01:09 UT, at a distance of while located in the constellation of Ursa Major.
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The secular variation of a time series is its long-term non-periodic variation (see Decomposition of time series). Whether something is perceived as a secular variation or not depends on the available timescale: a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend.
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In microstructured fibers, a completely different approach is applied. Fiber is built of one material (usually silica) and light guiding is obtained through the presence of air holes in the area surrounding the solid core. The holes are often arranged in the regular pattern in two dimensional arrays, however other patterns of holes exist, including non-periodic ones. While periodic arrangement of the holes would justify the use of term "photonic crystal fiber", the term is reserved for those fibers where propagation occurs within a photonic defect or due to photonic bandgap effect.
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Chowning is known for having discovered the FM synthesis algorithm in 1967 (; ; ). In FM (frequency modulation) synthesis, both the carrier frequency and the modulation frequency are within the audio band. In essence, the amplitude and frequency of one waveform modulates the frequency of another waveform producing a resultant waveform that can be periodic or non-periodic depending upon the ratio of the two frequencies. Chowning's breakthrough allowed for simple—in terms of process—yet rich sounding timbres, which synthesized 'metal striking' or 'bell like' sounds, and which seemed incredibly similar to real percussion.
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Its rotation combines two separate periodic motions into a non-periodic result; to someone on the surface of Toutatis, the Sun would seem to rise and set in apparently random locations and at random times at the asteroid's horizon. It has a rotation period around its long axis (Pψ) of 5.38 days. This long axis is precessing with a period (Pφ) of 7.38 days. The asteroid may have lost most of its original angular momentum and entered into this tumbling motion as a result of the YORP effect.
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How a 1 Hz square wave can be represented as a summation of sine waves (harmonics) and the corresponding frequency spectrum. Click and go to full resolution for an animation The Fourier transform of the square wave generates a frequency spectrum that presents the magnitude of the harmonics that make up the square wave (the phase is also generated, but is typically of less concern and therefore is often not plotted). The Fourier transform can also be used to analyze non-periodic functions such as transients (e.g. impulses) and random functions.
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Comet C/2009 F6 (Yi–SWAN) is a non-periodic comet which appeared in March 2009. March 26, 2009 -- it was discovered by Korean Dae-am Yi using a simple hand-held Canon 5D camera and 90-mm lens valued at US$249. According to legend, it is the first comet discovered by a Korean in the modern age. April 4th, 2009 -- Rob Matson reported he discovered it in the SWAN instrument photographs on the SOHO (Solar and Heliospheric Observatory) spacecraft website; the estimated cost is believed to exceed US$160,000,000,000.
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A lattice arrangement (commonly called a regular arrangement) is one in which the centers of the spheres form a very symmetric pattern which needs only n vectors to be uniquely defined (in n-dimensional Euclidean space). Lattice arrangements are periodic. Arrangements in which the spheres do not form a lattice (often referred to as irregular) can still be periodic, but also aperiodic (properly speaking non-periodic) or random. Lattice arrangements are easier to handle than irregular ones—their high degree of symmetry makes it easier to classify them and to measure their densities.
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Frequently the term aperiodic was just used vaguely to describe the structures under consideration, referring to physical aperiodic solids, namely quasicrystals, or to something non-periodic with some kind of global order. The use of the word "tiling" is problematic as well, despite its straightforward definition. There is no single Penrose tiling, for example: the Penrose rhombs admit infinitely many tilings (which cannot be distinguished locally). A common solution is to try to use the terms carefully in technical writing, but recognize the widespread use of the informal terms.
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The following is a list of comets discovered, co-discovered and re-discovered by the Lincoln Laboratory Near-Earth Asteroid Research project (LINEAR), an Earth-based automated sky survey. In comet nomenclature, the letter before the "/" is either "C" (a non-periodic comet), "P" (a periodic comet), "D" (a comet which has been lost or has disintegrated), "X" (a comet for which no reliable orbit could be calculated — usually historical comets), or "A" for an object that was mistakenly identified as a comet, but is a minor planet.
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Comet McNaught, also known as the Great Comet of 2007 and given the designation C/2006 P1, is a non-periodic comet discovered on 7 August 2006 by British-Australian astronomer Robert H. McNaught using the Uppsala Southern Schmidt Telescope. It was the brightest comet in over 40 years, and was easily visible to the naked eye for observers in the Southern Hemisphere in January and February 2007. With an estimated peak magnitude of −5.5, the comet was the second-brightest since 1935. Around perihelion on 12 January, it was visible worldwide in broad daylight.
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There are few constructions of aperiodic tilings known, even forty years after Berger's groundbreaking construction. Some constructions are of infinite families of aperiodic sets of tiles. Those constructions which have been found are mostly constructed in a few ways, primarily by forcing some sort of non-periodic hierarchical structure. Despite this, the undecidability of the Domino Problem ensures that there must be infinitely many distinct principles of construction, and that in fact, there exist aperiodic sets of tiles for which there can be no proof of their aperiodicity.
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In applied mathematics, stretching fields provide the local deformation of an infinitesimal circular fluid element over a finite time interval ∆t. The logarithm of the stretching (after first dividing by ∆t) gives the finite-time Lyapunov exponent λ for separation of nearby fluid elements at each point in a flow. For periodic two-dimensional flows, stretching fields have been shown to be closely related to the mixing of a passive scalar concentration field. Until recently, however, the extension of these ideas to systems that are non- periodic or weakly turbulent has been possible only in numerical simulations.
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Penrose's first tiling uses pentagons and three other shapes: a five- pointed "star" (a pentagram), a "boat" (roughly 3/5 of a star) and a "diamond" (a thin rhombus). To ensure that all tilings are non-periodic, there are matching rules that specify how tiles may meet each other, and there are three different types of matching rule for the pentagonal tiles. Treating these three types as different prototiles gives a set of six prototiles overall. It is common to indicate the three different types of pentagonal tiles using three different colors, as in the figure above right.
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Tie and Navette tiling (in red on a Penrose background) The three variants of the Penrose tiling are mutually locally derivable. Selecting some subsets from the vertices of a P1 tiling allows to produce other non-periodic tilings. If the corners of one pentagon in P1 are labeled in succession by 1,3,5,2,4 an unambiguous tagging in all the pentagons is established, the order being either clockwise or counterclockwise. Points with the same label define a tiling by Robinson triangles while points with the numbers 3 and 4 on them define the vertices of a Tie-and-Navette tiling.
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Comet Pojmański is a non-periodic comet discovered by Grzegorz Pojmański on January 2, 2006 and formally designated C/2006 A1. Pojmański discovered the comet at Warsaw University Astronomic Observatory using the Las Campanas Observatory in Chile as part of the All Sky Automated Survey (ASAS). Kazimieras Cernis at the Institute of Theoretical Physics and Astronomy at Vilnius, Lithuania, located it the same night and before the announcement of Pojmański's discovery, in ultraviolet images taken a few days earlier by the SWAN instrument aboard the SOHO satellite. A pre-discovery picture was later found from December 29, 2005.
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In computer science, a grid file or bucket grid is a point access method which splits a space into a non-periodic grid where one or more cells of the grid refer to a small set of points. Grid files (a symmetric data structure) provide an efficient method of storing these indexes on disk to perform complex data lookups. It provides a grid of n-dimensions where n represents how many keys can be used to reference a single point. Grid files do not contain any data themselves but instead contain references to the correct bucket.
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Comet ISON seen from the Mount Lemmon SkyCenter on 8 October 2013, as it passes through the constellation of Leo Comet ISON's formal designation was C/2012 S1.The "C" indicates that it was non-periodic, followed by the year of discovery. The "S" represents the half-month of discovery – in the case of C/2012 S1, the second half of September – and the number "1" shows that this was the first comet found in that half-month. It was named "ISON" after the organization where its discovery was made, the Russia-based International Scientific Optical Network.
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The FHI-aims software package is an all-electron, full-potential electronic structure code utilizing numeric atom-centered basis functions for its electronic structure calculations. The localized basis set enables the accurate treatment of all electrons on the same footing in periodic and non-periodic systems without relying on approximation for the core states, such as pseudopotentials. Importantly, the basis sets enable high numerical accuracy on par with the best available all-electron reference methods while remaining scalable to system sizes up to several thousands of atoms. The workload of the simulations is efficiently distributable for parallel computing using the MPI communication protocol.
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Edward L. G. "Ted" Bowell (born 1943 in London), is an American astronomer. Bowell was educated at Emanuel School London, University College, London, and the University of Paris. He was principal investigator of the Lowell Observatory Near-Earth-Object Search (LONEOS). He has discovered a large number of asteroids, both as part of LONEOS and in his own right before LONEOS began. Among the latter are the Jovian asteroids 2357 Phereclos, 2759 Idomeneus, 2797 Teucer, 2920 Automedon, 3564 Talthybius, 4057 Demophon, and (4489) 1988 AK. He also co-discovered the periodic comet 140P/Bowell-Skiff and the non-periodic comet C/1980 E1.
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Comet Arend–Roland was discovered on November 8, 1956, by Belgian astronomers Sylvain Arend and Georges Roland on photographic plates. As the eighth comet found in 1956, it was named Arend–Roland 1956h after its discoverers. Because it was the third comet to pass through perihelion during 1957, it was then renamed 1957 III. Finally, it received the standard IAU designation C/1956 R1 (Arend–Roland), with the "C/" indicating that it was a non-periodic comet and the "R1" showing that it was the first comet reported as discovered in the half-month designated by "R".
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Although commonly attributed to the paper in which Kondo model was obtained from the Anderson impurity model by J.R. Schrieffer and P.A. Wolff., Joaquin Mazdak Luttinger and Walter Kohn used this method in an earlier work about non-periodic k·p perturbation theory . Using the Schrieffer–Wolff transformation, the high energy charge excitations present in Anderson impurity model are projected out and a low energy effective Hamiltonian is obtained which has only virtual charge fluctuations. For the Anderson impurity model case, the Schrieffer–Wolff transformation showed that Kondo model lies in the strong coupling regime of the Anderson impurity model.
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Quasicrystals had been investigated and observed earlier, but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter. In 2009, after a dedicated search, a mineralogical finding, icosahedrite, offered evidence for the existence of natural quasicrystals. Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g.
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But in 1982 Beenker published a similar mathematical explanation for the octagonal case which became known as the Ammann–Beenker tiling.Beenker FPM, "Algebraic theory of non periodic tilings of the plane by two simple building blocks: a square and a rhombus", TH Report 82-WSK-04 (1982), Technische Hogeschool, Eindhoven In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry. The decagonal covering of the Penrose tiling was proposed in 1996 and two years later F. Gahler proposed an octagonal variant for the Ammann–Beenker tilingS. Ben Abraham and F. Gahler, Phys. Rev.
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Comet Lulin (official designation C/2007 N3 (Lulin), Traditional Chinese:鹿林彗星) is a non-periodic comet. It was discovered by Ye Quanzhi and Lin Chi-Sheng from Lulin Observatory. It peaked in brightness and arrived at perigee for observers on Earth on February 24, 2009, at magnitude +5, and at from Earth. The comet was near conjunction with Saturn on February 23, and outward first headed towards its aphelion, against the present position of background stars, in the direction of Regulus in the constellation of Leo, as noted on February 26 and 27, 2009. It was expected to pass near Comet Cardinal on May 12, 2009.
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While conducting a program of observations designed to uncover near-Earth objects, the Shoemakers and Levy discovered Comet Shoemaker–Levy 9 on the night of March 24, 1993, in a photograph taken with the Schmidt telescope at the Palomar Observatory in California. The comet was thus a serendipitous discovery, but one that quickly overshadowed the results from their main observing program. Comet Shoemaker–Levy 9 was the ninth periodic comet (a comet whose orbital period is 200 years or less) discovered by the Shoemakers and Levy, hence its name. It was their eleventh comet discovery overall including their discovery of two non-periodic comets, which use a different nomenclature.
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Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called sound. Most sound that people recognize as musical is dominated by periodic or regular vibrations rather than non-periodic ones; that is, musical sounds typically have a definite pitch. The transmission of these variations through air is via a sound wave. In a very simple case, the sound of a sine wave, which is considered the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very pure tone.
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During the period 1819–21 the German mathematician and physicist Johann Franz Encke computed the orbits for a series of comets that had been observed in 1786, 1795, 1805, and 1818, and he concluded that they were same comet, and successfully predicted its return in 1822. By 1900, seventeen comets had been observed through more than one passage through their perihelions, and then recognized as being periodic comets. , 305 cometsPeriodic Comet Numbers, Periodic Comet Numbers have achieved this distinction, although several of these have disintegrated or been lost. By 1900 comets were categorized as "periodic", with elliptical orbits, or "non- periodic", one-time with parabolic or hyperbolic orbits.
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Instead, two-photon absorption is utilized to induce a dramatic change in the solubility of the resist for appropriate developers. Hence, multiphoton lithography is a technique for creating small features in a photosensitive material, without the use of complex optical systems or photomasks. This method relies on a multi-photon absorption process in a material that is transparent at the wavelength of the laser used for creating the pattern. By scanning and properly modulating the laser, a chemical change (usually polymerization) occurs at the focal spot of the laser and can be controlled to create an arbitrary three-dimensional periodic or non-periodic pattern.
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Comet Hale–Bopp's systematic name is C/1995 O1. The famous Comet Shoemaker–Levy 9 was the ninth periodic comet jointly discovered by Carolyn Shoemaker, Eugene Shoemaker, and David Levy (the Shoemaker–Levy team has also discovered four non-periodic comets interspersed with the periodic ones), but its systematic name is D/1993 F2 (it was discovered in 1993 and the prefix "D/" is applied, because it was observed to crash into Jupiter). Some comets were first spotted as minor planets, and received a temporary designation accordingly before cometary activity was later discovered. This is the reason for such comets as (Catalina 2) or (Spacewatch–LINEAR).
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To date, there is not a formal definition describing when a tiling has a hierarchical structure; nonetheless, it is clear that substitution tilings have them, as do the tilings of Berger, Knuth, Läuchli and Robinson. As with the term "aperiodic tiling" itself, the term "aperiodic hierarchical tiling" is a convenient shorthand, meaning something along the lines of "a set of tiles admitting only non-periodic tilings with a hierarchical structure". Each of these sets of tiles, in any tiling they admit, forces a particular hierarchical structure. (In many later examples, this structure can be described as a substitution tiling system; this is described below).
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M.F. Howland, J. Bossuyt, L.A. Martínez-Tossas,J. Meyers & C. Meneveau: “Wake Structure of Wind Turbines in Yaw under Uniform Inflow Conditions” (2016), J. Sust. Renew. Energy 8, 043301. B. Chen, D. Yang, C. Meneveau & M. Chamecki: “ENDLESS: An Extended Non-periodic Domain Large-Eddy Simulation Approach for Scalar Plumes” (2015), Ocean Modeling 101, 121-132. R.J.A.M. Stevens, D. Gayme & C. Meneveau, “Generalized coupled wake boundary layer model: applications and comparisons with field and LES data for two real wind-farm” (2016), Wind Energy 19, 2023-2040. X.I.A. Yang, I. Marusic & C. Meneveau: “Moment generating functions and scaling laws in the inertial layer of turbulent wall bounded flows” (2016), J. Fluid Mech.
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Hecataeus of Miletus (6th-5th century BC), in his Genealogiai, was the first of them to attempt (not entirely successfully) to separate the mythic past from the true historic past, which marked a crucial step in the development of genuine historiography. He is the only source that Herodotus cites by name. After Herodotus, the genre declined but regained some popularity in the Hellenistic era. The logographers, though they worked within the same mythic tradition, were distinct from the epic poets of the Trojan War cycle because they wrote in prose, in a non-periodic style which Aristotle (Rhetoric, 1409a 29) calls λέξις εἰρομένη (lexis eiromenê, from εἴρω, eiro, "attach, join up"), that is, a "continuous" or "running" style.
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This philosophy taught that man is mortal, that the cosmos is the result of accident, that there is no providential god, and that the criteria of a good life are pleasure and temperance. Philodemus' connections with Piso brought him an opportunity to influence the young students of Greek literature and philosophy who gathered around him at Herculaneum and Naples. Much of his work was discovered in about a thousand papyrus rolls in the philosophical library recovered at Herculaneum. Although his prose work is detailed in the strung-out, non-periodic style typical of Hellenistic Greek prose before the revival of the Attic style after Cicero, Philodemus surpassed the average literary standard to which most epicureans aspired.
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In addition, if the planet is massive enough, it can cause slight variations of the host stars' orbital periods. Despite being harder to find circumbinary planets due to their non-periodic transits, it is much easier to confirm them, as timing patterns of transits cannot be mimicked by an eclipsing binary or a background star system. In addition to transits, planets orbiting around their stars undergo reflected-light variations—like the Moon, they go through phases from full to new and back again. Because Kepler cannot resolve the planet from the star, it sees only the combined light, and the brightness of the host star seems to change over each orbit in a periodic manner.
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One such generalization is to allow an infinitely repeated word on one or both sides of the Turing machine input, thus extending the definition of universality and known as "semi-weak" or "weak" universality, respectively. Small weakly universal Turing machines that simulate the Rule 110 cellular automaton have been given for the (6, 2), (3, 3), and (2, 4) state-symbol pairs.Neary and Woods, 2009b The proof of universality for Wolfram's 2-state 3-symbol Turing machine further extends the notion of weak universality by allowing certain non-periodic initial configurations. Other variants on the standard Turing machine model that yield small UTMs include machines with multiple tapes or tapes of multiple dimension, and machines coupled with a finite automaton.
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The Strejc system identification method allows the estimate of the transfer function of a non-periodic, black box-type system based on its step response and is widely used in all branches of industrial and mechanical engineering. It allows specifically to estimate the order n of the studied system, its time constant and its delay. To use the Strejc method, it is necessary to apply a step signal to the system and record its tu and tg parameters by observing the inflection point of the response curve. These parameters are then compared with the ones in the numeric table to estimate what order approximates better the system's behaviour and then find the time constant t with the second column (using the appropriate order).
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To understand this aspect of lightning detection one needs to know that a lightning 'flash' generally consists of several strokes, a typical number of strokes from a CG flash is in the range 3 to 6 but some flashes can have more than 10 strokes. The initial stroke leaves an ionized path from the cloud to ground and subsequent 'return strokes', separated by an interval of about 50 milliseconds, go up that channel. The complete discharge sequence is typically about ½ second in duration while the duration of the individual strokes varies greatly between 100 nanoseconds and a few tens of microseconds. The strokes in a CG flash can be seen at night as a non-periodic sequence of illuminations of the lightning channel.
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Light curves of four Mira variables in the galaxy Centaurus A Long period variables are pulsating cool giant, or supergiant, variable stars with periods from around a hundred days, or just a few days for OSARGs, to more than a thousand days. In some cases, the variations are too poorly defined to identify a period, although it is an open question whether they are truly non-periodic. LPVs have spectral class F and redwards, but most are spectral class M, S or C. Many of the reddest stars in the sky, such as Y CVn, V Aql, and VX Sgr are LPVs. Most LPVs, including all Mira variables, are thermally-pulsing asymptotic giant branch stars with luminosities several thousand times the sun.
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Tidal currents are in phase with the tide, hence are quasiperiodic; they may form various knots in certain places, most notably around headlands. Non-periodic currents have for origin the waves, wind and different densities. The wind and waves create surface currents (designated as “drift currents”). These currents can decompose in one quasi-permanent current (which varies within the hourly scale) and one movement of Stokes drift under the effect of rapid waves movement (at the echelon of a couple of seconds).).Étude de la dérive à la surface sous l’effet du vent, Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface, F. Ardhuin, L. Marié, N. Rascle, P. Forget, and A. Roland, 2009: J. Phys. Oceanogr.
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"I" and "Z" are not used when describing the half of a particular month the comet was discovered. Prefixes are also added to indicate the nature of the comet, with P/ indicating a periodic comet, C/ indicating a non-periodic comet, X/ indicating a comet for which no reliable orbit could be calculated (typically comets described in historical chronicles), D/ indicating a comet that has broken up or been lost, and A/ indicating an object at first thought to be a comet but later reclassified as an asteroid (C/2017 U1 became A/2017 U1, then finally 1I/ʻOumuamua). Objects on hyperbolic orbits that do not show cometary activity also receive an A/ designation (example: A/2018 C2, which became C/2018 C2 (Lemmon) when cometary activity was detected).
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C/2012 S4 (PANSTARRS) is a non-periodic comet with the largest listed aphelion of any object on the JPL Small-Body Database. But the listed aphelion distance of from the Sun is a generic near-perihelion unperturbed two-body solution that assumes the Sun and comet are the only two objects in the Universe. Other comets, such as C/ and C/2017 A3 (Elenin) have had epoch-dependent solutions with aphelia of more than .Archive of C/2015 TQ209 (LINEAR) JPL 4 (epoch 2015-Oct-23) observation arc of 24 daysArchive of C/2017 A3 (Elenin) JPL 3 (epoch 2017-Jan-08) observation arc of 12 days As a comparison, the closest star, Proxima Centauri, is about 4.24 light years from the Sun, and Wolf 359 is 7.78 light years away.
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A patch of 25 monotiles, showing the triangular hierarchical structure The Socolar–Taylor tile is a single non-connected tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the plane (due to the Sierpinski's triangle-like tiling that occurs), with rotations and reflections of the tile allowed.. It is the first known example of a single aperiodic tile, or "einstein". The basic version of the tile is a simple hexagon, with printed designs to enforce a local matching rule, regarding how the tiles may be placed. It is currently unknown whether this rule may be geometrically implemented in two dimensions while keeping the tile a connected set. This is, however, confirmed to be possible in three dimensions, and, in their original paper, Socolar and Taylor suggest a three-dimensional analogue to the monotile.
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A Penrose tiling In 1961, Hao Wang asked whether determining if a set of tiles admits a tiling of the plane is an algorithmically unsolvable problem or not. He conjectured that it is solvable, relying on the hypothesis that every set of tiles that can tile the plane can do it periodically (hence, it would suffice to try to tile bigger and bigger patterns until obtaining one that tiles periodically). Nevertheless, two years later, his student Robert Berger constructed a set of some 20,000 square tiles (now called "Wang tiles") that can tile the plane but not in a periodic fashion.A New Kind of Science As further aperiodic sets of tiles were discovered, sets with fewer and fewer shapes were found. In 1976 Roger Penrose discovered a set of just two tiles, now referred to as Penrose tiles, that produced only non-periodic tilings of the plane.
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Donald Machholz Donald Machholz Donald Edward Machholz, born October 7, 1952 in Portsmouth, Virginia, is an American amateur astronomer and science writer who is the most successful living visual comet discoverer. Credited with the discovery of 12 comets, that include the periodic comets 96P/Machholz, 141P/Machholz, the non-periodic C/2004 Q2 (Machholz) that were visible with binoculars in the northern sky in 2004 and 2005, C/2010 F4 (Machholz), and most recently C/2018 V1 (Machholz-Fujikawa-Iwamoto) In 1985, comet Machholz 1985-e, was discovered using a homemade cardboard telescope with a wide aperture, 10 inches across, that gave it a broader field of view than most commercial telescopes. Amateur astronomer Machholz utilizes a variety of methods in his comet discoveries, in 1986 using 29×130 binoculars he discovered 96P/Machholz. Machholz is one of the inventors of the Messier Marathon, which is a race to observe all the Messier objects in a single night.
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Observations of the luminosity of the star by the Kepler space telescope show small, frequent, non-periodic dips in brightness, along with two large recorded dips in brightness two years apart. The amplitude of the changes in the star's brightness, and the aperiodicity of the changes, mean that this star is of particular interest for astronomers. The star's changes in brightness are consistent with many small masses orbiting the star in "tight formation". The first major dip, on 5 March 2011, reduced the star's brightness by up to 15%, and the next 726 days later (on 28 February 2013) by up to 22%. (A third dimming, around 8%, occurred 48 days later.) In comparison, a planet the size of Jupiter would only obscure a star of this size by 1%, indicating that whatever is blocking light during the star's major dips is not a planet, but rather something covering up to half the width of the star.
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Because of the simple nature of the dynamics when the iterates are viewed in binary notation, it is easy to categorize the dynamics based on the initial condition: If the initial condition is irrational (as almost all points in the unit interval are), then the dynamics are non-periodic—this follows directly from the definition of an irrational number as one with a non-repeating binary expansion. This is the chaotic case. If x0 is rational the image of x0 contains a finite number of distinct values within [0, 1) and the forward orbit of x0 is eventually periodic, with period equal to the period of the binary expansion of x0. Specifically, if the initial condition is a rational number with a finite binary expansion of k bits, then after k iterations the iterates reach the fixed point 0; if the initial condition is a rational number with a k-bit transient (k ≥ 0) followed by a q-bit sequence (q > 1) that repeats itself infinitely, then after k iterations the iterates reach a cycle of length q.
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One of the first tasks of the Committee for a Free Lithuania was to supply data, documents, and witnesses to the Kersten Committee, a select committee of the United States House of Representatives that investigated the occupation of the Baltic states. It also provided information on forced labor in the Soviet Union to the United Nations Economic and Social Council, published non-periodic Lithuanian-language political magazine Lietuva (Lithuania) in 1952–1956, joined Latvian and Estonian committees to establish the Baltic Freedom House and publish Baltic Review in English, French, and Spanish, organized events to mark the Captive Nations Week, monitored the Soviet press, and collected and analyzed information from behind the Iron Curtain. In November 1952, Radio Free Europe cancelled planned broadcasts in Lithuanian, Latvian, and Estonian (they were finally established in 1975) – one of the initial stated goals of the Committee for a Free Lithuania was to provide information and other support to the planned radio program. The cancellation was mandated by the United States Department of State which officially stated that such radio programs would duplicate the programs on the Voice of America.
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