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

Structure of S and T Parameters in Gauge-Higgs Unification

We investigate the divergence structure of one-loop corrections to S and T parameteres in gauge-Higgs unification. We show that these parameters are finite in five dimensions, but divergent in more than five dimensions. Remarkably, a particular linear combination of S and T parameters becomes finite in six dimension case, which is indicated from the operator analysis in a model independent way.Comment: 7 pages, Talk given at 2006 International Workshop SCGT 06 "Origin of Mass and Strong Coupling Gauge Theories" 21-24 November 2006, Nagoya, Japa

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

Quasi-perfect FIFO: Synchronous or asynchronous with application in controller design for the UNICON laser memory

The first-in-first-out memory buffer (FIFO), is an elastic digital memory whose main application is in data buffering between devices operating at different rates. Data written into the top is moved autonomously down toward the bottom of the FIFO to the lowest unoccupied location, and data read from the bottom of the FIFO will cause data from the top to move autonomously down toward the bottom. The FIFO is available in MOS LSI asynchronous form with data rate in the 1 MHz region. The FIFO described yields a simple high-speed iterative implementation, either synchronous of asynchronous. Because of this simple iterative structure, the FIFO is expandable in both number of words and bits per word, and it is attractive from the viewpoint of integrated-circuit production. For the synchronous FIFO, a model was built and successfully used in the controller for the UNICON laser memory. For the asynchronous FIFO, a model was built and also successfully used in a high-performance magnetic tape controller

NASF transposition network: A computing network for unscrambling p-ordered vectors

The viewpoints of design, programming, and application of the transportation network (TN) is presented. The TN is a programmable combinational logic network that connects 521 memory modules to 512 processors. The unscrambling of p-ordered vectors to 1-ordered vectors in one cycle is described. The TN design is based upon the concept of cyclic groups from abstract algebra and primitive roots and indices from number theory. The programming of the TN is very simple, requiring only 20 bits: 10 bits for offset control and 10 bits for barrel switch shift control. This simple control is executed by the control unit (CU), not the processors. Any memory access by a processor must be coordinated with the CU and wait for all other processors to come to a synchronization point. These wait and synchronization events can be a degradation in performance to a computation. The TN application is for multidimensional data manipulation, matrix processing, and data sorting, and can also perform a perfect shuffle. Unlike other more complicated and powerful permutation networks, the TN cannot, if possible at all, unscramble non-p-ordered vectors in one cycle