Let G=(G j ) j≥0 be a strictly increasing linear recurrent sequence of integers with G 0 =1 having characteristic polynomial X d -a 1 d-1 -⋯-a X-a . It is well known that each positive integer ν can uniquely represented by the so-called greedy expansion ν=ε (ν)G +⋯+ε ℓ for ℓ∈ℕ satisfying ≤ν<G ℓ+1 Here digits are defined recursively in way 0≤ν-ε -⋯-ε <G holds 0≤j≤ℓ. In present paper we study sum...

This paper presents the investigation of convolutional neural network (CNN) prediction successfully recognizing temperature nonequilibrium phase transitions in two-dimensional (2D) Ising spins on a square lattice. The model uses image snapshots ferromagnetic 2D spin configurations as an input shape to provide average output predictions. By considering supervised machine learning techniques, we ...

Peripheral nerve regeneration can be enhanced by chemical and mechanical cues for neurite growth. Aligned and randomly oriented electrospun nanofibers of poly(ε-caprolactone) (PCL) or a blend of PCL and elastin were fabricated to test their potential to provide contact guidance to embryonic chick dorsal root ganglia for peripheral nerve regeneration. Scanning electron microscopy was used to ana...

A pruned variant of polar coding is proposed for binary erasure channel (BEC). Fix any BEC. For sufficiently small ε > 0, we construct a series capacity achieving codes with block length N = ε-4.9, code rate R Capacity - O(ε), error probability P ε, and encoding decoding time complexity bC O(log|log ε|) per information bit. The given per-bit log-logarithmic in N, R, P. Beyond BEC, there general...

After updating the determination of the combination of Kobayashi-Maskawa elements Im V ∗ tsVtd according to a new estimate of the parameter B̂K , we study the CP -violating ratio ε/ε by means of hadronic matrix elements computed to O(p4) in the chiral expansion and NLO Wilson coefficients. It is the first time that this order in chiral perturbation theory is included in the analysis. The most im...

Using data collected in 1998 by the NA48 experiment, a preliminary measurement of the direct CP violation parameter Re (ε/ε) is here presented, together with a discussion of the experimental method, data analysis and systematic studies. The result is Re (ε/ε) = (12.2± 4.9) × 10, and combined with the previously published NA48 result (based from data collected in 1997) gives Re (ε/ε) = (14.0± 4....

Recently, we pointed out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. As a consequence, new operators appear in (partially) quenched QCD penguins, introducing ambiguities which should be considered a quenching artifact. Here we discuss more specifically the effects of this phenomenon on the quenched ∆I = 1/2 K →...