Byte padding can be applied to messages that can be encoded as an integral number of bytes.
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There are over 400 classes in the U.S. Patent Classification System, each having a title descriptive of its subject matter and each being identified by a class number. Each class is subdivided into a number of subclasses. Each subclass bears a descriptive title and is identified by a subclass number. The subclass number may be an integral number or may contain a decimal portion and/or alpha characters.
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UTC differs from TAI by an integral number of seconds. UTC is kept within 0.9 second of UT1 by the introduction of one-second steps to UTC, the "leap second". To date these steps (and difference "TAI-UTC") have always been positive. Standard time or civil time in a region deviates a fixed, round amount, usually a whole number of hours, from some form of Universal Time, now usually UTC.
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Standard cells have a fixed height equal to a row's height, but have variable widths. The width of a cell is an integral number of sites. On the other hand, blocks are typically larger than cells and have variable heights that can stretch a multiple number of rows. Some blocks can have preassigned locations — say from a previous floorplanning process — which limit the placer's task to assigning locations for just the cells.
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If the path lengths of the beams differ by a half-integral number of wavelengths (e.g., 0.5, 1.5, 2.5 ...), constructive interference will yield a strong signal. The results are opposite if a cube beam-splitter is used, because a cube beam-splitter makes no distinction between a front- and rear-surface reflection. Use of partially monochromatic light (yellow sodium light) during initial alignment enabled the researchers to locate the position of equal path length, more or less easily, before switching to white light.
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Miniature synchronous motor used in analog clocks. The rotor is made of permanent magnet. Small synchronous motor with integral stepdown gear from a microwave oven A synchronous electric motor is an AC motor in which, at steady state, the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of AC cycles. Synchronous motors contain multiphase AC electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line current.
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Most disk partitioning schemes are designed to have files occupy an integral number of sectors regardless of the file's actual size. Files that do not fill a whole sector will have the remainder of their last sector filled with zeroes. In practice, operating systems typically operate on blocks of data, which may span multiple sectors. Geometrically, the word sector means a portion of a disk between a center, two radii and a corresponding arc (see Figure 1, item B), which is shaped like a slice of a pie.
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Euclid does not define the term "measure" as used here, However, one may infer that if a quantity is taken as a unit of measurement, and a second quantity is given as an integral number of these units, then the first quantity measures the second. These definitions are repeated, nearly word for word, as definitions 3 and 5 in book VII. Definition 3 describes what a ratio is in a general way. It is not rigorous in a mathematical sense and some have ascribed it to Euclid's editors rather than Euclid himself.
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Primarily for mathematics, the Invisible Separator (U+2063) provides a separator between characters where punctuation or space may be omitted such as in a two-dimensional index like ij. Invisible Times (U+2062) and Function Application (U+2061) are useful in mathematics text where the multiplication of terms or the application of a function is implied without any glyph indicating the operation. Unicode 5.1 introduces the Mathematical Invisible Plus character as well (U+2064) which may indicate that an integral number followed by a fraction should denote their sum, but not their product.
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Since the carrier frequency received can vary due to Doppler shift, the points where received PRN sequences begin may not differ from O by an exact integral number of milliseconds. Because of this, carrier frequency tracking along with PRN code tracking are used to determine when the received satellite's PRN code begins. Unlike the earlier computation of offset in which trials of all 1,023 offsets could potentially be required, the tracking to maintain lock usually requires shifting of half a pulse width or less. To perform this tracking, the receiver observes two quantities, phase error and received frequency offset.
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Each satellite repeatedly transmits its assigned segment of the master code, restarting every Sunday at 00:00:00 GPS time. (The GPS epoch was Sunday January 6, 1980 at 00:00:00 UTC, but GPS does not follow UTC leap seconds. So GPS time is ahead of UTC by an integral number of seconds.) The P code is public, so to prevent unauthorized users from using or potentially interfering with it through spoofing, the P-code is XORed with W-code, a cryptographically generated sequence, to produce the Y-code. The Y-code is what the satellites have been transmitting since the anti-spoofing module was set to the "on" state.
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An electromagnetic (EM) wave directed vertically onto a graphene surface excites the graphene into oscillations that interact with those in the dielectric on which the graphene is mounted, thereby forming surface plasmon polaritons (SPP). When the antenna becomes resonant (an integral number of SPP wavelengths fit into the physical dimensions of the graphene), the SPP/EM coupling increases greatly, efficiently transferring energy between the two. A phased array antenna 100 µm in diameter could produce 300 GHz beams only a few degrees in diameter, instead of the 180 degree radiation from tsa conventional metal antenna of that size. Potential uses include smart dust, low-power terabit wireless networks and photonics.
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Systematics came in part out of the Pythagorean historical tradition but was influenced by twentieth century movements such as A. N. Whitehead's philosophy of organism, C. S. Peirce's pragmatism, and Bertrand Russell's logical atomism, theory of types, and logic of relations. However, it was independent of Bertalanffy's general systems theory and other systems thinking work. The strongest personal influence was from Gurdjieff and his writings. Gurdjieff had taught the significance of the 'law of three' and the 'law of seven' in a meta-scientific context, but Bennett proposed that there was a 'law' for every integral number, and that this could help people understand practical things such as management and education.
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ATM Adaptation Layer 5 (AAL5) is an ATM adaptation layer used to send variable-length packets up to 65,535 octets in size across an Asynchronous Transfer Mode (ATM) network. Unlike most network frames, which place control information in the header, AAL5 places control information in an 8-octet trailer at the end of the packet. The AAL5 trailer contains a 16-bit length field, a 32-bit cyclic redundancy check (CRC) and two 8-bit fields labeled UU and CPI that are currently unused. Each AAL5 packet is divided into an integral number of ATM cells and reassembled into a packet before delivery to the receiving host.
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Neither Shannon–Fano algorithm is guaranteed to generate an optimal code. For this reason, Shannon–Fano codes are almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest possible expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits. This is a constraint that is often unneeded, since the codes will be packed end-to-end in long sequences. If we consider groups of codes at a time, symbol-by-symbol Huffman coding is only optimal if the probabilities of the symbols are independent and are some power of a half, i.e.
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The surface advances by the lateral motion of steps which are one interplanar spacing in height (or some integral multiple thereof). An element of surface undergoes no change and does not advance normal to itself except during the passage of a step, and then it advances by the step height. It is useful to consider the step as the transition between two adjacent regions of a surface which are parallel to each other and thus identical in configuration — displaced from each other by an integral number of lattice planes. Note here the distinct possibility of a step in a diffuse surface, even though the step height would be much smaller than the thickness of the diffuse surface.
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A simple succinct solution can be obtained by directly utilizing the recursive structure of the problem: There were five divisions of the coconuts into fifths, each time with one left over (putting aside the final division in the morning). The pile remaining after each division must contain an integral number of coconuts. If there were only one such division, then it is readily apparent that 51+1=6 is a solution. In fact any multiple of five plus one is a solution, so a possible general formula is 5k - 4, since a multiple of 5 plus 1 is also a multiple of 5 minus 4. So 11, 16, etc also work for one division.
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His research uncovered fundamental properties of synapses, the junctions across which nerve cells signal to each other and to other types of cells. By the 1950s, he was studying the biochemistry and action of acetylcholine, a signalling molecule found in synapses linking motor neurons to muscles,The Release of Neural Transmitter Substances (The Sherrington Lectures X), Charles C Thomas Publisher, Springfield (Illinois) 1969, pp. 60 used to stimulate contraction. Katz won the Nobel for his discovery with Paul Fatt that neurotransmitter release at synapses is "quantal", meaning that at any particular synapse, the amount of neurotransmitter released is never less than a certain amount, and if more is always an integral number times this amount.
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Hypocoristics with modified stems are derived by adding -chan to a stem consisting of an integral number, usually one but occasionally two, of feet, where a foot consists of two moras. A mora is the unit of which a light syllable contains one and a heavy syllable two. For example, the stems that may be derived from Tarō are /taro/, consisting of two light syllables, and /taa/, consisting of a single syllable with a long vowel, resulting in Taro-chan and Tā-chan. The stems that may be derived from Hanako are /hana/, with two light syllables, /han/, with one syllable closed by a consonant, and /haa/, with one syllable with a long vowel, resulting in Hanachan, Hanchan, and Hāchan.
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In general this is not an integral number. Since each of the terminal atoms contributes equal numbers of electrons to the bond, the bond valence is also equal to the number of valence electrons that each atom contributes. Further, since within each atom, the negatively charged valence shell is linked to the positively charged core by an electrostatic flux that is equal to the charge on the valence shell, it follows that the bond valence is also equal to the electrostatic flux that links the core to the electrons forming the bond. The bond valence is thus equal to three different quantities: the number of electrons each atom contributes to the bond, the number of electron pairs that form the bond, and the electrostatic flux linking each core to the bonding electron pair.
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Larger Lie groups, as higher-dimensional manifolds, may be imagined as smooth surfaces composed of many circles (and hyperbolas) twisting around one another. At each point in a N-dimensional Lie group there can be N different orthogonal circles, tangent to N different orthogonal directions in the Lie group, spanning the N-dimensional Lie algebra of the Lie group. For a Lie group of rank R, one can choose at most R orthogonal circles that do not twist around each other, and so form a maximal torus within the Lie group, corresponding to a collection of R mutually-commuting Lie algebra generators, spanning a Cartan subalgebra. Each elementary particle state can be thought of as a different orthogonal direction, having an integral number of twists around each of the R directions of a chosen maximal torus.
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These perturbations are important, as they are responsible for the subtle physics that result in the cosmic microwave background anisotropy. In this epoch, the amplitude of perturbations that enter the horizon oscillate sinusoidally, with dense regions becoming more rarefied and then becoming dense again, with a frequency which is related to the size of the perturbation. If the perturbation oscillates an integral or half-integral number of times between coming into the horizon and recombination, it appears as an acoustic peak of the cosmic microwave background anisotropy. (A half-oscillation, in which a dense region becomes a rarefied region or vice versa, appears as a peak because the anisotropy is displayed as a power spectrum, so underdensities contribute to the power just as much as overdensities.) The physics that determines the detailed peak structure of the microwave background is complicated, but these oscillations provide the essence.
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1926 Gilbert N. Lewis letter which brought the word "photon" into common usage The word quanta (singular quantum, Latin for how much) was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1900, the German physicist Max Planck was studying black-body radiation, and he suggested that the experimental observations, specifically at shorter wavelengths, would be explained if the energy stored within a molecule was a "discrete quantity composed of an integral number of finite equal parts", which he called "energy elements". In 1905, Albert Einstein published a paper in which he proposed that many light- related phenomena—including black-body radiation and the photoelectric effect—would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete wave-packets.. An English translation is available from Wikisource. He called such a wave-packet the light quantum (German: das Lichtquant).
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The chromatic circle, the outer level of Lerdahl's model of pitch-class space In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones that are separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space. Since pitch-class space is a circle, we return to our starting point by taking a series of steps in the same direction: beginning with C, we can move "upward" in pitch-class space, through the pitch classes C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, and B, returning finally to C. By contrast, pitch space is a linear space: the more steps we take in a single direction, the further we get from our starting point.
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