Related papers: Divided Differences
Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were proposed to pursue some good space-filling…
The divisibility of truncated binomial series by their exponent n is analyzed. Divisibility is shown to depends on the divisibility characteristics of the integers constituting the binomials. Series division by the highest possible powers…
Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
Confusion and disagreement around the notion of time is due to the fact that we often fail to recognize that we call 'time' a variety of distinct notions, only partially related to one another. Many apparently obvious properties of time are…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.
Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical…
Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…
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…
We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and…
In this short paper, a formula for the sequence defined by the nonhomogeneous linear difference equation with variable coefficients is presented. A connection with the homogeneous case is shown.
In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been…