We study the asymptotic expansion of transmission eigenvalues for anisotropic thin layers. establish a rigorous second-order simple with respect to thickness layer. The convergence analysis is based on generalization Osborn's Theorem non-linear eigenvalue problems by Moskow [Nonlinear approximation compact operators. J Math Phys. 2015;56(11):113512]. also provide formal derivation in more gener...

In this paper, exact formulæ of the input-output weight distribution function and its exponential growth rate are derived for truncated convolutional encoders. In particular, these weight distribution functions are expressed in terms of generating functions of error events associated with a minimal realization of the encoder. Although explicit analytic expressions can be computed for relatively...

In this paper, exact formulæ of the input-output weight distribution function and its exponential growth rate are derived for truncated convolutional encoders. In particular, they are expressed in terms of generating functions of error events associated with a minimal realization of the encoder. Although explicit analytic expressions can be computed for relatively small truncation lengths, the ...

In order to obtain the full asymptotic expansion for Pólya trees, i.e. rooted unlabelled and non-plane trees, Flajolet and Sedgewick observed that their specification could be seen as a slight disturbance of the functional equation satisfied by the Cayley tree function. Such an approach highlights the complicated formal expressions with some combinatorial explanation. They initiated this proces...

A conversion of standard ordinary least-squares results into inference which is robust under endogeneity of some regressors has been put forward in Ashley and Parmeter, Economics Letters, 137 (2015) 70-74. However, their conversion is based on an incorrect (though by accident conservative) asymptotic approximation and entails a neglected but avoidable randomness. By a very basic example it is i...

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...

Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/1 queue, the complementary busy-period cdf is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as ρ → 1), where the scaling parameters are based on the asymptotics as t → ∞. We c...

Experimental studies have shown that the protein abundance in living cells varies from few tens to several thousands molecules per species. Molecular fluctuations roughly scale as the inverse square root of the number of molecules due to the random timing of reactions. It is hence expected that intrinsic noise plays an important role in the dynamics of biochemical networks. The Chemical Master ...

This paper establishes error orders for integral limit approximations to traces of powers (to the p’th order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices are Fourier transforms of functions which we allow to be bounded, unbounded, or even to vanish on [−π,...

We propose a technique to compute the effect of a dielectric multilayer radome. This technique uses a gaussian beam expansion associated with an evaluation of the physical optics spectral integrals using the asymptotic steepest descent path method. Then, we compare an iterative and a global process to take into account the multiple reflections inside the radome. Finally, a numeric validation is...