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Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely…
We prove that certain sequences of finite continued fractions associated with a 2-periodic continued fraction with period a,b>0 are moment sequences of discrete signed measures supported in the interval [-1,1], and we give necessary and…
In this article we study $p$-adic properties of sequences of integers (or $p$-adic integers) that satisfy a linear recurrence with constant coefficients. For such a sequence, we give an explicit approximate twisted interpolation to $\mathbb…
For an integer $q\ge2$, a $q$-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~$q$. In this article, $q$-recursive sequences are studied and the asymptotic behavior of their summatory…
Inequality measures provide a valuable tool for the analysis, comparison, and optimization based on system models. This work studies the relation between attributes or features of an individual to understand how redundant, unique, and…
A thermal ghost imaging scheme between two distant parties is proposed and experimentally demonstrated over long-distance optical fibers. In the scheme, the weak thermal light is split into two paths. Photons in one path are spatially…
We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…
Ghost imaging is a developing imaging technique that employs random masks to image a sample. Ghost projection utilizes ghost-imaging concepts to perform the complementary procedure of projection of a desired image. The key idea underpinning…
Experimental data from second-order nonlinear optical spectroscopies (SFG, DFG, and SHG) provide parameters relevant to the physical chemistry of interfaces and thin films. We show that there are in general 2 N or 2 N-1 equivalent sets of…
The theory of thermal fluctuations in crystalline membranes is put under scrutiny. In particular, the two critical regimes of the renormalisation group diagram, which are often left out of the discussion because of their instability in one…
Meson spectra can be well approximated by a specific form of a nonlinear Regge trajectory which is consistent with a finite number of bound states. This may have important consequencies for experiment, and may be a hint for the theory.
We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous…
We discuss the presence of ghostly instabilities for metric-affine theories constructed with higher order curvature terms. We mainly focus on theories containing only the Ricci tensor and show the crucial role played by the projective…
It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite…
We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…
In this note we prove that every weak Gibbs measure for an asymptotically additive sequences is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure…
We consider a family of measures $\mu$ supported in $\br^d$ and generated in the sense of Hutchinson by a finite family of affine transformations. It is known that interesting sub-families of these measures allow for an orthogonal basis in…
The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections.…
We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order…
The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp…