A non-empty word $w$ is a border of the word $u$ if $\vert w\vert<\vert u\vert$ and $w$ is both a prefix and a suffix of $u$. A word $u$ with the border $w$ is closed if $u$ has exactly two occurrences of $w$. A word $u$ is privileged if $\vert u\vert\leq 1$ or if $u$…
Let $d$ be an odd square-free integer, $m\geq 3$, $k$:$=\mathbb{Q}(\sqrt{d}, \sqrt{-1})$, $\mathbb{Q}(\sqrt{-2}, \sqrt{d})$ or $\mathbb{Q}(\sqrt{-2}, \sqrt{-d})$, and $L_{m,d}:=\mathbb{Q}(\zeta_{2^m},\sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}:=\mathbb{Q}(\zeta_{2^m},\sqrt{d})$, with $m\geq 3$ is an integer, such that the class number of $L_{m, d}$ is odd. Furthermore, using the cyclotomic $\mathbb{Z}_2$-extensions of $k$, we compute the…
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of non-Gaussian processes obtained by regular non-linear transformations of Gaussian processes. We provide the increasing-domain asymptotic properties of the (Gaussian) maximum likelihood…
The 1965 Penrose singularity theorem demonstrates the utterly inevitable and unavoidable formation of spacetime singularities under physically reasonable assumptions, and it remains one of the main results in our understanding of black holes. It is standard lore that quantum gravitational effects will always tame these singularities in black hole interiors. However, the Penrose’s theorem provides…
We consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a L\’evy process with heavy tails. The process is observed continuously on a long time interval $[0,T]$, $T\to\infty$. We prove that the statistical model is locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically efficient.
A mathematical model of measurement of the perception of well-being for groups with increasing incomes, but proportionally unequal is proposed. Assuming that welfare grows with own income and decreases with relative inequality (income of the other concerning one’s own), possible scenarios for long-term behavior in welfare functions are concluded. Also, it is proved that a…
Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work (Sanaei & Cummings…
In this work we present an efficient numerical algorithm for the solution of interfacial statistical associating fluid theory (iSAFT) in cylindrical geometry to facilitate the study of inhomogeneous fluids having curvatures. The new solution algorithm is shown to have a better time scaling than the elliptic function method by Malijevsky, and the transform method by…
We propose a model for synaptic plasticity based on a calcium signaling cascade. The model simplifies the full signaling pathways from a calcium influx to the phosphorylation (potentiation) and dephosphorylation (depression) of glutamate receptors that are gated by fictive C1 and C2 catalysts, respectively. This model is based on tangible chemical reactions, including fictive catalysts,…
One of the physically least understood characteristics of continuous nonsuspended sediment transport is the dependency of the transport rate $Q$ on the properties of the driving Newtonian fluid (e.g., the shear stress $\tau$ applied onto the sediment bed), especially the physical reason for the observed difference between air-driven (linear scaling $Q(\tau)$) and liquid-driven transport (nonlinear…