Related papers: Generalized Subdifferentials of the Sign Change Co…

The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…

Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…

Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…

This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…

We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use it to derive new results in quite high generality including:…

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…

Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…

We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound…

For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of the functional CUSUM process…

This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution…

We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of…

We define a switch function to be a function from an interval to $\{1,-1\}$ with a finite number of sign changes. (Special cases are the Walsh functions.) By a topological argument, we prove that, given $n$ real-valued functions, $f_1,…

The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.

The $F$-signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties. For example, this invariant detects (non)singularity and strong $F$-regularity. However, it is very difficult to…

This note addresses the signed-digit representation of nonnegative binary integers. Popular literature methods for the conversion into the canonical signed-digit representation are reviewed and revisited. A method based on string…

Object counting models suffer when deployed across domains with differing density variety, since density shifts are inherently task-relevant and violate standard domain adaptation assumptions. To address this, we propose a theoretical…

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…

The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…

We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gon\c{c}alves in 2019. In our setup, the signs of a function and…