Related papers: Constructing Positive Interpolatory Cubature Formu…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
Safe stabilization is a significant challenge for quadrotors, which involves reaching a goal position while avoiding obstacles. Most of the existing solutions for this problem rely on optimization-based methods, demanding substantial…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
We introduce a method to construct general multivariate positive definite kernels on a nonempty set $X$ that employs a prescribed bounded completely monotone function and special multivariate functions on $X$.\ The method is consistent with…
We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…
We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider…
In this paper, we present a new concept of interpolative contraction mappings in $C^{\ast}$-algebra valued complete metric space and we prove the existence of fixed points and common fixed points for Kannan-Riech type contractions.
We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in…
The two-point functions in affine current algebras based on simple Lie algebras are constructed for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
Numerical evolutions of a system of equations close to null infinity in the geometric background of the inversion-Minkowski spacetime are performed. The evolved equations correspond to the linearisation of a second order metric formulation…
This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The…
A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other…
A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is…
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction.…
We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the multi-dimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new construction-free median QMC rule which can exploit the smoothness and…
We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on…