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In this paper we present a flexible bivariate distribution specified by a quantile function. The distribution contains as special cases new bivariate exponential, Pareto I, Pareto II, beta, power, log logistic and uniform distributions and…
Suppose $f_1(x)$ and $f_2(y)$ are given marginals for pairs $(x,y)$. I consider the construction $f_1(x)f_2(y)\{ 1+\alpha h_1(x)h_2(y) \}$, where $h_1$ and $h_2$ are seen as bounded adjustment functions, normalised to have means zero under…
The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open…
Let $\mathbb{F}_q$ denote the finite field of order $q$. For $q$ odd, we investigate the planarity over $\mathbb{F}_{q^3}$ of the family $$ f_{E,A,B,C,D}(X) := EX^2+ AX^{q+1}+ BX^{q^2+1}+CX^{2q} +DX^{2q^2}\in \mathbb{F}_{q}[X]. $$ Using…
Planar functions are mappings from a finite field $\mathbb{F}_q$ to itself with an extremal differential property. Such functions give rise to finite projective planes and other combinatorial objects. There is a subtle difference between…
For $ 1\le k <n$, we prove that for functions $F,G$ on $ {\Bbb R}^{n}$, any $k$-dimensional affine subspace $H \subset {\Bbb R}^{n}$, and $p,q,r \ge 2$ with $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1$, one has the estimate $$…
Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…
Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let $\cF$ be a bounded set of real-valued functions on $[0,1]$ with finite $q$-variation. It is proved that…
Let $q$ be an odd prime power. Let $F_1(x)=x^{d_1}$ and $F_2(x)=x^{d_2}$ be power mappings over $\mathrm{GF}(q^2)$, where $d_1=q-1$ and $d_2=d_1+\frac{q^2-1}{2}=\frac{(q-1)(q+3)}{2}$. In this paper, we study the the boomerang uniformity of…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
In this paper, we investigate the concepts of generalized twice differentiability and quadratic bundles of nonsmooth functions that have been very recently proposed by Rockafellar in the framework of second-order variational analysis. These…
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years,…
We consider a sequence $\{f(p)\}_{p\ {\rm prime}}$ of independent random variables taking values $\pm 1$ with probability $1/2$, and extend $f$ to a multiplicative arithmetic function defined on the squarefree integers. We investigate upper…
Let $G$ be the multiplicative group generated by the gamma functions $\Gamma(ax+1)$ $(a=1,2,\dots)$, and $H$ be the subgroup of all elements of $G$ that converge to nonzero constants as $x\rightarrow\infty$. The quotient group $G/H$ is the…
Let $F\in\mathbb{Z}[x,y]$ be some polynomial of degree 2. In this paper we find the asymptotic behaviour of the least common multiple of the values of $F$ up to $N$. More precisely, we consider $\psi_F(N) =…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
This paper considers permutation polynomials over the finite field $F_{q^2}$ in even characteristic by utilizing low-degree permutation rational functions over $F_q$. As a result, we obtain two classes of permutation binomials and six…
We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes.…