Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of Dynamic Mode Decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" [1]. Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data, and two that show potential applications of the Koopman eigenfunctions

HAL/SM system software requirements specification

For abstract, see N76-14843

HAL/SM system functional design specification

The functional design of a preprocessor, and subsystems is described. A structure chart and a data flow diagram are included for each subsystem. Also a group of intermodule interface definitions (one definition per module) is included immediately following the structure chart and data flow for a particular subsystem. Each of these intermodule interface definitions consists of the identification of the module, the function the module is to perform, the identification and definition of parameter interfaces to the module, and any design notes associated with the module. Also described are compilers and computer libraries

Phase transition from hadronic matter to quark matter

We study the phase transition from nuclear matter to quark matter within the SU(3) quark mean field model and NJL model. The SU(3) quark mean field model is used to give the equation of state for nuclear matter, while the equation of state for color superconducting quark matter is calculated within the NJL model. It is found that at low temperature, the phase transition from nuclear to color superconducting quark matter will take place when the density is of order 2.5$\rho_0$ - 5$\rho_0$. At zero density, the quark phase will appear when the temperature is larger than about 148 MeV. The phase transition from nuclear matter to quark matter is always first order, whereas the transition between color superconducting quark matter and normal quark matter is second order.Comment: 18 pages, 11 figure