In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H_2(G, \Z) of a group G. It was introduced by in his work on projective representations.
|
|
The deficiency of a finite presentation is just and the deficiency of a finitely presented group G, denoted def(G), is the maximum of the deficiency over all presentations of G. The deficiency of a finite group is non-positive. The Schur multiplicator of a finite group G can be generated by −def(G) generators, and G is efficient if this number is required.
|
|
She also exhibited her work in Copenhagen, often participating in person as she did in 1888. In 1899, she started to produce enamel jewelry and cufflinks embedded with photographs using direct positives produced with a four-lensed multiplicator camera. She had made special arrangements for the equipment to be imported from the United States to facilitate the work. The jewelry was shown at a Christmas exhibition at Copenhagen's Industry Association, attracting the attention of the royal family.
|
|
The Portable 386 got its name due to the socketed Intel 386DX CPU with 20MHz. There is also an additional socket for a 20MHz 387 FPU option, which was not included in the basic configuration of the Portable. Since the whole system bus runs with CPU frequency, there is no way to improve the CPU performance by installing a 386DX CPU with more than 20MHz other than the rare Cyrix 486DRx2 20/40 which has a multiplicator of 2 for the frequency while being still pinout compatible with the 386 socket.
|
|
He said that the apparatus by which it was generated was called a "generator" or "multiplicator", from where it was then passed into a "receiver" and from there to the cylinders of a steam engine. The "generator" was reported as being about , made of Austrian gunmetal in one piece, and holding about 10 or 12 gallons of water. Its inside was made up of cylindrical chambers connected by pipes and fitted with stopcocks and valves. The "receiver" or "reservoir" was about long by in diameter and connected to the "generator" by a diameter pipe.
|
|
In papyrus texts from the Ptolemaic period onwards, numeric sampi occurs with some regularity. At an early stage in the papyri, the numeral sampi was used not only for 900, but, somewhat confusingly, also as a multiplicator for 1000, since a way of marking thousands and their multiples was not yet otherwise provided by the alphabetic system. Writing an alpha over sampi (x16px or, in a ligature, x16px) meant "1×1000", a theta over sampi (x16px) meant "9×1000", and so on. In the examples cited by Gardthausen, a slightly modified shape of sampi, with a shorter right stem (Ͳ), is used.
|
|
Several approaches have been taken to simplify the drawing linkages that result from Kempe's universality theorem. Some of the complexity arises from the linkages Kempe used to perform addition and subtraction of two angles, the multiplication of an angle by a constant, and translation of the rotation of a link in one location to a rotation of a second link at another location. Kempe called these linkages additor, reversor, multiplicator and translator linkages, respectively. The drawing linkage can be simplified by using bevel gear differentials to add and subtract angles, gear trains to multiply angles and belt or cable drives to translate rotation angles.
|
|
In 1833, Carl Friedrich Gauss, together with the physics professor Wilhelm Weber in Göttingen installed a wire above the town's roofs. Gauss combined the Poggendorff-Schweigger multiplicator with his magnetometer to build a more sensitive device, the galvanometer. To change the direction of the electric current, he constructed a commutator of his own. As a result, he was able to make the distant needle move in the direction set by the commutator on the other end of the line. Diagram of alphabet used in a 5 needle Cooke and Wheatstone Telegraph, indicating the letter GAt first, Gauss and Weber used the telegraph to coordinate time, but soon they developed other signals and finally, their own alphabet.
|
|
By 1844 he is referred to as a "university mechanic".Verhandlungen der k.k. Gesellschaft der Ärzte zu Wien, Vienna 1844, p. 25 An announcement in a paper describes his range of products as follows: "[Ekling] makes all sorts mathematical and physical instruments and apparatuses, air pumps with glass barrel chambers, travel barometers, goniometers,Ekling built this instrument according to instructions received from Friedrich Mohs (1773-1839) chemical and mineralogical apparatuses".Notizen über Produktion, Kunst, Fabriken und Gewerbe, Wien 1833, p. 48 His multiplicator was used for the analysis of mineral waters among other things and praised for its sensitivity.Adolph Pleischl, Ueber die Thermalwasser zu Gastein und Carlsbad in chemisch-physicalischer Hinsicht, 1846, p. 6 Ekling was granted patents for induction machines, cameras and improvements to the Bain telegraph, which were taken over by the Austrian railway. Ekling’s last invention was a "Galvanic Induction Machine for Medical Purposes".
|
|
The antiparallelogram is an important feature in the design of Hart's inversor, a linkage that (like the Peaucellier–Lipkin linkage) can convert rotary motion to straight-line motion.. An antiparallelogram-shaped linkage can also be used to connect the two axles of a four-wheeled vehicle, decreasing the turning radius of the vehicle relative to a suspension that only allows one axle to turn.. A pair of nested antiparallelograms was used in a linkage defined by Alfred Kempe as part of his universality theorem stating that any algebraic curve may be traced out by the joints of a suitably defined linkage. Kempe called the nested-antiparallelogram linkage a "multiplicator", as it could be used to multiply an angle by an integer. Antiparallelogram braced to stop it turning into a normal parallelogram. The points PQRS are the midpoints of the sides and are collinear, and X can be any distance away on the perpendicular bisector of SQ. With this linkage .
|
|
An associative algebra over K is given by a K-vector space A endowed with a bilinear map A × A → A having two inputs (multiplicator and multiplicand) and one output (product), as well as a morphism K → A identifying the scalar multiples of the multiplicative identity. If the bilinear map A × A → A is reinterpreted as a linear map (i. e., morphism in the category of K-vector spaces) A ⊗ A → A (by the universal property of the tensor product), then we can view an associative algebra over K as a K-vector space A endowed with two morphisms (one of the form A ⊗ A → A and one of the form K → A) satisfying certain conditions that boil down to the algebra axioms. These two morphisms can be dualized using categorial duality by reversing all arrows in the commutative diagrams that describe the algebra axioms; this defines the structure of a coalgebra.
|
|
On December 14, 1881 the stockholders of the Keely Motor Company held a meeting at which a report was read that complained that while they had faith in the merits of Keely's invention, the inventor was unreasonably secretive of the principles and operating methods of his apparatus. He had assured them that the "generator" had been perfected a year before, and that the "multiplicator" was also now perfected, and they considered it only fair and reasonable that the secrets of the machinery be revealed to them. They recommended that some intelligent and trustworthy person be taken into Keely's confidence "so that in the case of accident they would not be totally without a clue to the invention". The report complained at some length about Keely's uncommunicativeness and said that it was the experience of everyone who had come into contact with him over the previous ten years that "any attempt at a serious investigation of his operations has been met on his part with deception and misrepresentation". Keely was reluctant to reveal his secrets, and filed a demurrer on January 20, 1882 to the bill in equity presented against him by the Keely Motor Company's stockholders.
|
|