Related papers: New separation between $s(f)$ and $bs(f)$
In this short note we prove the logarithmic Sobolev inequality with derivatives of fractional order on $\mathbb{R}^n$ with an explicit expression for the constant. Namely, we show that for all $0<s<\frac{n}{2}$ and $a>0$ we have the…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
Motivated by the possibility that it may be misleading to assume SU(3) symmetry in the analysis of hyperon \beta-decays, we study the sensitivity of the polarized parton densities, derived from the world data on inclusive polarized deep…
Given a Boolean function f, the quantity ess(f) denotes the largest set of assignments that falsify f, no two of which falsify a common implicate of f. Although ess(f)$ is clearly a lower bound on cnf_size(f) (the minimum number of clauses…
The "spectral correlation function" analysis we introduce in this paper is a new tool for analyzing spectral-line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the spectral…
We have carried out concurrent optical frequency measurements of the $(6s^{2})\,^{1}S_{0} -(6s6p)\,^{3}P_{1}$ ($F=\frac{3}{2}$) and $(6s^{2})\,^{1}S_{0} -(6s6p)\,^{3}P_{0}$ transitions in $^{171}$Yb, and in so doing have determined the…
We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely…
In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance.
In this paper, we prove some inequalities for the differences and ratios of the beta function.
First observations of the $B^0_s \rightarrow \psi(2S) \eta$, $B^0 \rightarrow \psi(2S) \pi^+ \pi^-$ and $B^0_s \rightarrow \psi(2S) \pi^+ \pi^-$ decays are made using a dataset corresponding to an integrated luminosity of 1.0~$fb^{-1}$…
Aims. The purpose of this work is to investigate a new frequency separation of stellar p-modes and its characteristics. Methods. Frequency separations are deduced from the asymptotic formula of stellar p-modes. Then, using the theoretical…
We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species,…
The B_s to mu+ mu- decay plays an outstanding role in tests of the Standard Model and physics beyond it. The LHCb collaboration has recently reported the first evidence for this decay at the 3.5 sigma level, with a branching ratio in the…
We report an observation of the decay Bs -> Ds- pi+ in p pbar collisions at sqrt(s) = 1.96 TeV using 115 pb^(-1) of data collected by the CDF II detector at the Fermilab Tevatron. We observe 83 +/- 11 Bs -> Ds- pi+ candidates, representing…
In this paper, we study the Hamming distance between vectorial Boolean functions and affine functions. This parameter is known to be related to the non-linearity and differential uniformity of vectorial functions, while the calculation of…
The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…
Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher-order…
We report measurements of the branching fractions for $B^0\to\pi^+\pi^-$, $K^+\pi^-$, $K^+K^-$ and $K^0\pi^0$, and $B^+\to\pi^+\pi^0$, $K^+\pi^0$, $K^0\pi^+$ and $K^+\bar{K}{}^0$. The results are based on 10.4 fb$^{-1}$ of data collected on…