Quaternionic Mass Matrices and CP Symmetry

A viable formulation of gauge theory with extra generations in terms of quaternionic fields is presented. For the theory to be acceptable, the number of generations should be equal to or greater than 4. The quark-lepton mass matrices are generalized into quaternionic matrices.It is concluded that explicit CP violation automatically disappears in both strong- and weak-interaction sectors.Comment: 10 pages, LaTe

Rapid method for interconversion of binary and decimal numbers

Decoding tree consisting of 40-bit semiconductor read-only memories interconverts binary and decimal numbers 50 to 100 times faster than current methods. Decimal-to-binary conversion algorithm is based on a divided-by-2 iterative equation, binary-to-decimal conversion algorithm utilizes multiplied-by-2 iterative equation

Functionals in stochastic thermodynamics: how to interpret stochastic integrals

In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the 'interpretation' of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat-and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients

A decoding procedure for the Reed-Solomon codes

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method

Augmented burst-error correction for UNICON laser memory

A single-burst-error correction system is described for data stored in the UNICON laser memory. In the proposed system, a long fire code with code length n greater than 16,768 bits was used as an outer code to augment an existing inner shorter fire code for burst error corrections. The inner fire code is a (80,64) code shortened from the (630,614) code, and it is used to correct a single-burst-error on a per-word basis with burst length b less than or equal to 6. The outer code, with b less than or equal to 12, would be used to correct a single-burst-error on a per-page basis, where a page consists of 512 32-bit words. In the proposed system, the encoding and error detection processes are implemented by hardware. A minicomputer, currently used as a UNICON memory management processor, is used on a time-demanding basis for error correction. Based upon existing error statistics, this combination of an inner code and an outer code would enable the UNICON system to obtain a very low error rate in spite of flaws affecting the recorded data

Concurrent error detecting codes for arithmetic processors

A method of concurrent error detection for arithmetic processors is described. Low-cost residue codes with check-length l and checkbase m = 2 to the l power - 1 are described for checking arithmetic operations of addition, subtraction, multiplication, division complement, shift, and rotate. Of the three number representations, the signed-magnitude representation is preferred for residue checking. Two methods of residue generation are described: the standard method of using modulo m adders and the method of using a self-testing residue tree. A simple single-bit parity-check code is described for checking the logical operations of XOR, OR, and AND, and also the arithmetic operations of complement, shift, and rotate. For checking complement, shift, and rotate, the single-bit parity-check code is simpler to implement than the residue codes