The relation between algebraic properties of a monoid and its test complexity (with respect to these problems) is studied. In both cases it can be shown that the set of all finite monoids partitions into exactly
The error is measured for the Nth root computation with N=5. Table 11 compares the RMSE and max(AE) for the proposed method and approaches presented in25 and 26. The number of stages used to measure the error is also mentioned in Table 11. Hyperbolic and binary logarithmic CORDIC repeats...
The result of quadruple-precision computation of (1) using the MPFR library is\(y=1.172603940053179\), and the result with higher precision computation with 122 bits for the mantissa of each number is\(y=-0.8273960599468214\), which is sufficiently accurate. However, a closer look at the compu...
In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝ 1 c log z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as...
In addition, we shall use a logarithmic-linear grid, as appropriate for electron-emission processes as well as a (default) Fermi model with nuclear charge 𝑍=12Z=12 for the nucleus. An average single-configuration (cascade) approach [cf. Section 3.3] is utilized for the representation of ...
In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The main novelty is the singularity of the Gibbs measure with respect to the Gaussian free field. The singularity has several consequences in both measure-the...