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Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
The monic irreducible polynomial x 8 + x 4 + x 3 + x 2 + 1 over GF(2) is primitive, and all 8 roots are generators of GF(2 8). All GF(2 8 ) have a total of 128 generators (see Number of primitive elements ), and for a primitive polynomial, 8 of them are roots of the reducing polynomial.
The Athlon 64 X2 is the first native dual-core desktop central processing unit (CPU) designed by Advanced Micro Devices (AMD). It was designed from scratch as native dual-core by using an already multi-CPU enabled Athlon 64, joining it with another functional core on one die, and connecting both via a shared dual-channel memory controller/north bridge and additional control logic.
The Tianhe-2 supercomputer uses 4096 Galaxy FT-1500 processors with 16 cores, OpenSPARC architecture based and 65 W TDP. They are made with 40 nm technology, processor cores work at 1.8 GHz. [ 10 ] Peak performance of FT-1500 is 115–144 GFLOPS; every core may execute up to 8 interleaving threads and supports 256-bit wide SIMD vector ...
OC-48 is a network line with transmission speeds of up to 2488.32 Mbit/s (payload: 2405.376 Mbit/s (2.405376 Gbit/s); overhead: 82.944 Mbit/s). With relatively low interface prices, with being faster than OC-3 and OC-12 connections, and even surpassing gigabit Ethernet , OC-48 connections are used [ when? ] as the backbones of many regional ISPs.
For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x.
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
In particular, x 2 ≡ a (mod p) has at most 2 solutions for each a. This immediately implies that besides 0 there are at least p − 1 / 2 distinct quadratic residues modulo p : each of the p − 1 possible values of x can only be accompanied by one other to give the same residue.