Related papers: An Accessible Formulation for Defining the SI Seco…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
A frequency stabilized laser referenced to an unperturbed atomic two level system acts as the most accurate clock with femtosecond clock ticks. For any meaningful use, a Femtosecond Laser Frequency Comb (FLFC) is used to transfer the atomic…
We consider a recent proposal [1] to redefine the kilogram in terms of natural constants. In our opinion, the main objective of the redefinition should be to build such a version of the SI system in which the electric measurements are…
An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the $5s^2 {}^1S_0 \to 5s5p {}^3P_0$ transition of ${}^{87}{\rm Sr}$ atoms as a…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
We experimentally investigate an optical clock based on $^{171}$Yb ($I=1/2$) atoms confined in an optical lattice. We have evaluated all known frequency shifts to the clock transition, including a density-dependent collision shift, with a…
We introduce a new tool for predicting the evolution of an option for the cases where at some specific time, there is a high-degree of uncertainty for identifying its price. We work over the special case where we can predict the evolution…
The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. The research focus has mostly been on improving the accuracy and efficiency of classifiers,…
A new method for examining the possible space-time variation of the fine structure constant ($\alpha$) is proposed. The technique uses a relatively simple measurement with an optical resonator to compare atom-stabilized optical frequency…
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…
Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point…
Optical clocks with unprecedented accuracy of 10^(-18) will lead to innovations in many research areas. All the applications of optical clocks rely on the ability of precisely converting the frequency from one optical clock to another, or…
We report new measurements of branching fractions for 20 UV and blue lines in the spectrum of neutral silicon (Si I) originating in the 3$s^{2}$3$p$4$s$ $^{3}$P$^{\rm o}_{1,2}$, $^{1}$P$^{\rm o}_{1}$ and 3$s$3$p^{3}$ $^{1}$D$^{\rm o}_{1,2}$…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
Results from higher order mean field calculations of light interacting with atom arrays are presented for calculations of one- and two-time expectation values. The atoms are approximated as two-levels and are fixed in space. Calculations…
We demonstrate a means of detecting weak optical transitions in cold atoms that undergo cyclic routines with high sensitivity. The gain in sensitivity is made by probing atoms on alternate cycles leading to a regular modulation of the…
A symmetry-guided definition of time may enhance and simplify the analysis of historical series with recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a…
The choice of vibrational coordinates is crucial for the accuracy, efficiency, and interpretability of molecular vibrational dynamics and spectra calculations. We explore the recently proposed normalizing-flow vibrational coordinates, which…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
We describe an optical atomic clock based on quantum-logic spectroscopy of the $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ transition in $^{27}$Al$^{+}$ with a systematic uncertainty of ${9.4 \times 10^{-19}}$ and a frequency stability of…