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In algebra, the length of a module over a ring is a generalization of the dimension of a vector space which measures its size. [ 1 ] page 153 It is defined to be the length of the longest chain of submodules .
A cable in this usage cable is a thick rope or by transference a chain cable. [1] The OED gives quotations from c. 1400 onwards. A cable's length (often "cable length" or just "cable") is simply the standard length in which cables came, which by 1555 had settled to around 100 fathoms (600 ft; 180 m) or 1 ⁄ 10 nautical mile (0.19 km; 0.12 mi). [1]
The β service level is a quantity-oriented performance measure describing the proportion of total demand within a reference period which is delivered without delay from stock on hand: β = 1 − E x p e c t e d b a c k o r d e r s p e r t i m e p e r i o d E x p e c t e d p e r i o d d e m a n d {\displaystyle \beta =1-{\frac {Expected ...
As the length of an antenna is made shorter than its fundamental resonant length (a half-wavelength for a dipole antenna and a quarter-wavelength for a monopole), the radiation resistance the antenna presents to the feedline decreases with the square of the electrical length, that is the ratio of physical length to wavelength, (/). As a result ...
Figure A.1 shows a maximum length of 1,200 meters (3,900 ft), but this is with a termination, and the annex discusses the fact that many applications can tolerate greater timing and amplitude distortion, and that experience has shown that the cable length may be extended to several kilometers.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series , algebraic numbers, and transcendental functions . [ 3 ]