Related papers: A composition theorem for the Fourier Entropy-Infl…

We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen-Cooper-Schrieffer superfluids to Bose-Einstein condensates, by developing an improved random phase approximation…

As the two basic fuzzy inference models, fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) have the important application in artificial intelligence. In order to solve FMP and FMT problems, Zadeh proposed a compositional rule of…

Assuming the Riemann hypothesis, we improve the current upper and lower bounds for the average value of Montgomery's function $F(\alpha, T)$ over long intervals by means of a Fourier optimization framework. The function $F(\alpha, T)$ is…

The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$.…

The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…

We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions in the family of all characters modulo $q$, with $Q/2 < q\leq Q$. For test functions whose Fourier transform is supported in $(-3/2, 3/2)$, we calculate this…

Let $\G\subset \mathrm{SL}_{2}(\R)$ be a cofinite Fuchsian subgroup, and let $i\infty$ be a cusp of $\G$. For $k\in\Z_{\geq 0}$, let $\Sk$ denote the complex vector space of cusp forms of weight-$k$, with respect to the Fuchsian subgroup…

We present a purely numerical approach in Cartesian grid, for efficient computation of Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm [Liu…

In 1974, M. Shub stated Topological Entropy Conjecture, that is, the inequality $\log\rho\leq ent(f)$ is valid or not, where $f$ is a continuous self-map on a compact manifold $M$, $ent(f)$ is the topological entropy of $f$ and $\rho$ is…

Let $\Phi$ be a $C^\omega (\mathbb{C})$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the transfer operator corresponding to the derivative…

We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…

Let $Y=(y_1,y_2,...)$, $y_1\ge y_2\ge...$, be the list of sizes of the cycles in the composition of $c n$ transpositions on the set $\{1,2,...,n\}$. We prove that if $c>1/2$ is constant and $n\to\infty$, the distribution of $f(c)Y/n$…

We consider a previously proposed non-extensive statistical mechanics in which the entropy depends only on the probability, this was obtained from a f(\beta) distribution and its corresponding Boltzmann factor. We show that the first term…

An integer composition of a nonnegative integer $n$ is a tuple $(\pi_1,\ldots,\pi_k)$ of nonnegative integers whose sum is $n$; the $\pi_i$'s are called the parts of the composition. For fixed number $k$ of parts, the number of $f$-weighted…

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…

It is well known that if a function $f$ satisfies $$\|f(x) e^{\pi \alpha |x|^2}\|_p + \| \widehat{f}(\xi) e^{\pi \alpha |\xi|^2} \|_q<\infty \qquad\qquad\qquad(*)$$ with $\alpha=1$ and $1\le p,q<\infty$, then $f\equiv 0.$ We prove that if…

We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we…

Fourier analysis on the Boolean hypercube is fundamentally defined as the orthogonal decomposition of the space of pseudo-Boolean functions with respect to the uniform probability measure. In this work, we propose an ANOVA-based…

Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding between two Bergman spaces of the upper-half plane. A question in relation with a Werhl-type entropy inequality for the affine $AX+B$ group.…