Related papers: A note on the representation of continuous functio…
We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpi\'nski-Pierce series (Pierce series), alternating…
The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of…
In this paper we establish a complete representation theorem for $G$-martingales. Unlike the existing results in the literature, we provide the existence and uniqueness of the second order term, which corresponds to the second order…
For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient…
The conformal crossing equation puts very stringent constraints on the conformal data. We formulate it in way that makes the conformal symmetry more transparent. This allows for generalization of the crossing equation to arbitrary Lie group…
We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…
The {\em line sum optimization problem} asks for a $(0,1)$-matrix minimizing the sum of given functions evaluated at its row and column sums. We show that the {\em uniform} problem, with identical row functions and identical column…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
We find the general form of supersymmetric invariant two point functions. By imposing supersymmetric positivity we obtain the general supersymmetric K\"allen-Lehmann representation.
We give a technical overview of our exact-real implementation of various representations of the space of continuous unary real functions over the unit domain and a family of associated (partial) operations, including integration, range…
We construct explicitly Pad\'e approximations of the second kind for a special class of G-functions. These are then applied to prove a Baker-type lower bound for linear forms in the p-adic values of these functions. Moreover, we consider…
The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $\sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=\cup_{i=1}^s…
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that…
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these…
We study the functional equation \[ \sum_{i=1}^mf_i(b_ix+c_iy)= \sum_{k=1}^nu_k(y)v_k(x) \] with $x,y\in\mathbb{R}^d$ and $b_i,c_i\in {GL}(d,\mathbb{R})$, both in the classical context of continuous complex-valued functions and in the…
Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition…
When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…