Aided by ultrahigh resolution spectroscopy, the overall systematic uncertainty of the 1S0-3P0 clock resonance for lattice-confined 87Sr has been characterized to 9 x 10(-16). This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 42...

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A Wieferich prime is a prime p such that 2p−1 ≡ 1 (mod p2). Despite several intensive searches, only two Wieferich primes are known: p = 1093 and p = 3511. This paper describes a new search algorithm for Wieferich primes using double-precision Montgomery arithmetic and a memoryless sieve, which runs significantly faster than previously published algorithms, allowing us to report that there are ...

Let’s consider several Gaussian Bayes classification Models for the classification problem P (Y |X). All models here assume there are two classes (Y ∈ {0, 1}), that X is a vector of real-valued features, and P (X|Y = 1) and P (X|Y = 0) are modeled by two different Gaussian distributions. Please complete the following table by filling in the number of parameters and VC dimension of different Gau...

We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by...

Parahydrogen is demonstrated to efficiently transfer its nuclear spin hyperpolarization to nitrogen-15 in pyridine and nicotinamide (vitamin B(3) amide) by conducting "signal amplification by reversible exchange" (SABRE) at microtesla fields within a magnetic shield. Following transfer of the sample from the magnetic shield chamber to a conventional NMR spectrometer, the (15)N NMR signals for t...