"was a passenger derivative of the Class FD 1’E1’-h2 (2-10-2) freight locomotive and had many parts in common with the Class FD. The Soviet 2-8-4 was the most numerous single Berkshire class built in the world. Kolomna Locomotive Works built the first four locomotives. In 1935, production was transferred to the enlarged and modernised former which was renamed Voroshilovgrad Locomotive Works. A lotal of 649 locomotives of the two variants, Class IS20 and Class IS21 (later Class FDp), were built between 1932 and 1942. After Germany attacked the Soviet Union on 22 June 1941, the Russians evacuated all semi-completed class"
"which are graphical dingbats). Eighth notes in , , , and are beamed three eighth notes at a time. A single eighth note is always stemmed with a flag, while two or more are usually beamed in groups . Eighth note An eighth note (American) or a quaver (British) is a musical note played for half the value of a quarter note (crotchet) and twice that of the sixteenth note (semiquaver), which amounts to one quarter the duration of a half note (minim), one eighth the duration of whole note (semibreve), one sixteenth the duration of a double whole note"
"Eighth note An eighth note (American) or a quaver (British) is a musical note played for half the value of a quarter note (crotchet) and twice that of the sixteenth note (semiquaver), which amounts to one quarter the duration of a half note (minim), one eighth the duration of whole note (semibreve), one sixteenth the duration of a double whole note (breve), and one thirty-second the duration of a longa, hence the name. It is the equivalent of the ""fusa"" in mensural notation Eighth notes are notated with an oval, filled-in note head and a straight note stem with one"
"maximal number of nodes on a quartic is 16, and in this case they are all simple nodes (to show that formula_8 is simple project from another node). A quartic which obtains these 16 nodes is called a Kummer Quartic, and we will concentrate on them below. Since formula_8 is a simple node, the tangent cone to this point is mapped to a conic under the double cover. This conic is in fact tangent to the six lines (w.o proof). Conversely, given a configuration of a conic and six lines which tangent to it in the plane, we may define"
"The meter is a simple time signature that represents three quarter notes (crotchets). It is felt as ""Compound"": In principle, comprises not three groups of two eighth notes (quavers) but two groups of three eighth-note (quaver) subdivisions. It is felt as These examples assume, for simplicity, that continuous eighth notes are the prevailing note values. The rhythm of actual music is typically not as regular. Time signatures indicating ""two"" beats per bar (whether in simple or compound meter) are called ""duple meter"", while those with ""three"" beats to the bar are ""triple meter"". Terms such as ""quadruple"" (4), ""quintuple"" (5),"
"sheets of vellum or parchment, i.e. 8 leaves, 16 sides. The term ""quaternion"" (or sometimes ""quaternum"") designates such a quire. A quire made of a single folded sheet (i.e. 2 leaves, 4 sides) is a ""bifolium"" (plural ""bifolia""); a ""binion"" is a quire of two sheets (i.e. 4 leaves, 8 sides); and a ""quinion"" is five sheets (10 leaves, 20 sides). This last meaning is preserved in the modern Italian term for quire, ""quinterno di carta"". Formerly, when paper was packed at the paper mill, the top and bottom quires were made up of slightly damaged sheets (""outsides"") to protect"
"each gathering will have two or more short stretches of thread visible at the central fold. In medieval manuscripts a gathering, or quire, was most often formed of 4 folded sheets of vellum or parchment, i.e. 8 leaves, 16 sides. The term ""quaternion"" (or sometimes ""quaternum"") designates such a unit. A gathering made of a single folded sheet (i.e. 2 leaves, 4 sides) is a ""bifolium"" (plural ""bifolia""); a ""binion"" is a quire of two sheets (i.e. 4 leaves, 8 sides); and a ""quinion"" is five sheets (10 leaves, 20 sides). This last meaning is preserved in the modern Italian"
"Quaternary cubic In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables. The zeros form a cubic surface in 3-dimensional projective space. and studied the ring of invariants of a quaternary cubic, which is a ring generated by invariants of degrees 8, 16, 24, 32, 40, 100. The generators of degrees 8, 16, 24, 32, 40 generate a polynomial ring. The generator of degree 100 is a skew invariant, whose square is a polynomial in the other generators given explicitly by Salmon. Salmon also gave an explicit formula for the discriminant as a polynomial in"
"Prime quadruplet A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {""p"", ""p""+2, ""p""+6, ""p""+8}. This represents the closest possible grouping of four primes larger than 3, and is the only prime constellation of length 4. The first eight prime quadruplets are: All prime quadruplets except {5, 7, 11, 13} are of the form {30""n"" + 11, 30""n"" + 13, 30""n"" + 17, 30""n"" + 19} for some integer ""n"". (This structure is necessary to ensure that none of the four primes is divisible by 2, 3 or 5). A prime quadruplet of"
"and spin. They are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as ""fundamental forces"" (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge. There are six types, known as ""flavors"", of quarks: up, down, strange, charm, bottom, and top. Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay: the transformation from a higher mass"
"Down quark The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up quarks, one down quark) of atomic nuclei. It is part of the first generation of matter, has an electric charge of − ""e"" and a bare mass of . Like all quarks, the down quark is an elementary fermion with spin , and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong"
"18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, ... (The quotient can be any natural number, and the quotient = 1 if and only if ""n"" is a prime or a Carmichael number (561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, ... ), the quotient = 2 if and only if ""n"" is in the sequence: 4, 6, 15, 91, 703, 1891, 2701, 11305, 12403, 13981, 18721, ... ) The least number with ""n"" values of ""b"" are (or 0 if no such"
"are also serially arranged, 3+5+1+4+2 quavers. Added to the durations of the preceding sounding notes, the five segments come to 4 + 8 + 16 + 10 + 12 quavers. In the clarinet-viola duet, this formula is first presented in its plainest form, and then is subjected to a succession of elaborations resembling the method followed in ""Mantra"", only in this case the duet texture permits the formula to be presented simply in one instrument, while the other embellishes it. Despite the elaborate serial system used to produce it, the result recalls Béla Bartók's ""Contrasts"" . The overall form of"
"Up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quarks, one down quark) of atomic nuclei. It is part of the first generation of matter, has an electric charge of + ""e"" and a bare mass of .. Like all quarks, the up quark is an elementary fermion with spin , and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong"
"Half note In music, a half note (American) or minim (British) is a note played for half the duration of a whole note (or semibreve) and twice the duration of a quarter note (or crotchet). It was given its Latin name (""minima"", meaning ""least or smallest"") because it was the shortest of the five note values used in early medieval music notation . In time signatures with 4 as the bottom number, such as or , the half note is two beats long. However, when 2 is the bottom number (including ""alla breve"", ), the half note is one beat"
"1 basic invariant and 3 basic covariants. There are 2 basic invariants and 5 basic covariants. There are 4 basic invariants (essentially the covariants of a cubic) and 13 basic covariants. There are 5 basic invariants (essentially the basic covariants of a quartic) and 20 basic covariants. There are 23 basic invariants (essentially the basic covariants of a quintic) and 94 basic covariants. The ring of invariants of ""n"" linear forms is generated by ""n""(""n""–1)/2 invariants of degree 2. The ring of covariants of ""n"" linear forms is essentially the same as the ring of invariants of ""n""+1 linear forms."
"the generators, though pointed out that the formula has a widely copied misprint in it. A generic quaternary cubic can be written as a sum of 5 cubes of linear forms, unique up to multiplication by cube roots of unity. This was conjectured by Sylvester in 1851, and proven 10 years later by Clebsch. The union of the 5 planes where these 5 linear forms vanish is called the Sylvester pentahedron. Quaternary cubic In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables. The zeros form a cubic surface in 3-dimensional projective space. and studied"
"41 + 43 + 47), Motzkin number, self number. A Lucas and Fibonacci pseudoprime. ""See 323 (disambiguation)"" 324 = 2 × 3 = 18. 324 is the sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, untouchable number, and a Harshad number. 325 = 5 × 13. 325 is a triangular number, hexagonal number, nonagonal number, centered nonagonal number. 325 is the smallest number to be the sum of two squares in 3 different ways: 1 + 18, 6 + 17 and 10 + 15. 325 is also the smallest"
"is based on quavers. It then goes into triplets, or three notes per beat, and then semiquavers, or four notes per beat, and then five, and then six, and then seven, and then finally eight where the movement climaxes emotionally (and academically, because there is no more increase in the subdivisions of the beat after this moment). After this climax, the main theme recapitulates, but is soon succeeded by a more intense melody in octaves along with triplet semiquavers in the left hand (this shows how Alkan kept the amount of intensity/anxiety in the music directly proportionate with the amount"
"the order of the smallest non-trivial groups that are not simple. Four is the only integer ""n"" for which the (non trivial) alternating group ""A"" is not simple. Four is the maximum number of dimensions of a real associative division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius. The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this. The largest planar complete graph"
"are integers slightly over 1024. 1024×768 pixels and 1280×1024 pixels are common standards of display resolution. 1024 (number) 1024 is the natural number following 1023 and preceding 1025. 1024 is a power of two: formula_1 (2 to the 10th power). It is the lowest power of two requiring four decimal digits, and the lowest power of two containing the digit 0 in its decimal representation (excluding any leading zeroes). It is also the square of 32: formula_2. 1024 is the smallest number with ""exactly"" 11 divisors (but note that there are smaller numbers with more than 11 divisors; e.g., 60"
"There are 3 basic invariants and 6 basic covariants. The ring of invariants of a sum of ""m"" linear forms and ""n"" quadratic forms is generated by ""m""(""m""–1)/2 + ""n""(""n""+1)/2 generators in degree 2, ""nm ""(""m""+1)/2 + ""n""(""n""–1)(""n""–2)/6 in degree 3, and m""(""m""+1)""n""(""n ""–1)/4 in degree 4. For the number of generators of the ring of covariants, change ""m"" to ""m""+1. There are 5 basic invariants and 15 basic covariants There are 6 basic invariants and 18 basic covariants There are 29 basic invariants and 92 basic covariants There are 20 basic invariants and 63 basic covariants There are 8"
"mechanism, which is associated to the Higgs boson. It is hoped that further research into the reasons for the top quark's large mass of ~173 GeV/c, almost the mass of a gold atom, might reveal more about the origin of the mass of quarks and other elementary particles. Quarks are treated as zero-dimensional point-like entities of zero size in QCD; the lack of any detectable size in experiments puts an upper bound on their size of 10^-4 the size of a proton, i.e. less than 10^-19 metres The following table summarizes the key properties of the six quarks. Flavor quantum"
"8 8 (eight) is the natural number following 7 and preceding 9. 8 is: A number is divisible by 8 if its last three digits, when written in decimal, are also divisible by 8, or its last three digits are 0 when written in binary. There are a total of eight convex deltahedra. A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers. A polyhedron with eight faces is an octahedron. A cuboctahedron has as faces six equal squares and eight equal regular triangles. A cube has eight vertices. Sphenic numbers always"
"the light quark flavour symmetry dubbed the Eightfold Way (physics). The quarks possess colour quantum numbers and form the fundamental (triplet) representation of an group. The group is a subgroup of group , the group of all 3×3 unitary matrices. The unitarity condition imposes nine constraint relations on the total 18 degrees of freedom of a 3×3 complex matrix. Thus, the dimension of the group is 9. Furthermore, multiplying a ""U"" by a phase, leaves the norm invariant. Thus can be decomposed into a direct product of . Because of this additional constraint, has dimension 8. Every unitary matrix can"
"with the D or [3] symmetry group.A lowest symmetry construction is based on a dual of an 8-orthotope, called an 8-fusil. Cartesian coordinates for the vertices of an 8-cube, centered at the origin are Every vertex pair is connected by an edge, except opposites. It is used in its alternated form 5 with the 8-simplex to form the 5 honeycomb. 8-orthoplex In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells ""4-faces"", 1792 ""5-faces"", 1024 ""6-faces"", and 256 ""7-faces"". It has two constructive forms, the first"
"8-8 duoprism In geometry of 4 dimensions, a 8-8 duoprism or octagonal duoprism is a polygonal duoprism, a 4-polytope resulting from the Cartesian product of two octagons. It has 64 vertices, 128 edges, 80 faces (64 squares, and 16 octagons), in 16 octagonal prism cells. It has Coxeter diagram , and symmetry , order 512. The uniform ""8-8 duoprism"" can be constructed from [8]×[8] or [4]×[4] symmetry, order 256 or 64, with extended symmetry doubling these with a 2-fold rotation that maps the two orientations of prisms together. These can be expressed by 4 permutations of uniform coloring of the"
"crossing number 4, and is the smallest cubic graph with that crossing number . Additionally, it provides an example of a graph all of whose subgraphs' crossing numbers differ from it by two or more. However, it is a toroidal graph: it has an embedding in the torus in which all faces are hexagons . The dual graph of this embedding is the hyperoctahedral graph ""K"". There is an even more symmetric embedding of Möbius–Kantor graph in the double torus which is a regular map, with six octagonal faces, in which all 96 symmetries of the graph can be realized"
"necessarily 8, hence the distinction of ""bytes"" and ""octets"" or of ""nibbles"" and ""quartets"" (or ""quadbits""). Today, the terms 'byte' and 'nibble' almost always refer to 8-bit and 4-bit collections respectively and are very rarely used to express any other sizes. The sixteen nibbles and their equivalents in other numeral systems: The terms ""low nibble"" and ""high nibble"" are used to denote the nibbles containing, respectively, the less significant bits and the more significant bits within a byte. In graphical representations of bits within a byte, the leftmost bit could represent the most significant bit (MSB), corresponding to ordinary decimal"
"and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron. The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices. It is the only self-dual regular polyhedron. Four-dimensional space is the highest-dimensional space featuring more than three convex regular figures: Four-dimensional differential manifolds have some unique properties. There is only one differential structure on ℝ except when , in which case there are uncountably many. The smallest non-cyclic group has four elements; it is the Klein four-group. Four is also"
"this rule as outdated. Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being twenty-four. Twelve is the smallest abundant number, since it is the smallest integer for which the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) is greater than itself. Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there"
"""p""+2, ""p""+6, ""p""+8} and {""q"", ""q""+2, ""q""+6, ""q""+8} is ""q"" - ""p"" = 30. The first occurrences of this are for ""p"" = 1006301, 2594951, 3919211, 9600551, 10531061, ... (). If {""p"", ""p""+2, ""p""+6, ""p""+8} is a prime quadruplet and ""p""−4 or ""p""+12 is also prime, then the five primes form a prime quintuplet which is the closest admissible constellation of five primes. The first few prime quintuplets with ""p""+12 are: The first prime quintuplets with ""p""−4 are: A prime quintuplet contains two close pairs of twin primes, a prime quadruplet, and three overlapping prime triplets. It is not known"
"Quaternion In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Quaternions are generally represented in the form: where ""a"", ""b"", ""c"", and ""d"" are real numbers, and i, j, and k are the fundamental ""quaternion units"". Quaternions find uses in both pure"