arXiv subjects
Publications and source records attributed to Francesco D'Agostino.
We analyze weighted $L^p$ convergence for the truncated reconstruction operator in the rank-one non-symmetric Heckman--Opdam setting. After localization at the mirror, the operator admits a rigid structural decomposition and reduces, up to bounded terms, to a rank-one functional. Boundedness on $L^p(w)$ is characterized by the mirror-local integrability of $w^{-\frac{1}{p-1}}$.
I propose a mathematical framework for embedding an unshaped discrete lattice $L$ on a smooth manifold $M$. This framework simplifies complex concepts in pure mathematics and physics by connecting discrete lattice structures with continuous geometric interpretations through practical embeddings.
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding of a Discrete Lattice Structure in a Smooth Manifold," this work investigates the existence and solvability of partial differential equations (PDEs) governing the embedding process. The primary aim is to derive and analyze solutions to these PDEs while preserving the geometric and topological properties of $L$ and $M$. The solutions are shown to exist under initial boundary conditions, with the geometric structure of $M$ and the discrete topology of $L$ playing crucial roles in ensuring well-posedness and regularity. This paper provides a detailed exposition of the mathematical interplay between discrete and continuous spaces, offering novel insights into embedding theory and the geometry of manifolds interacting with discrete substructures.
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat such sectors separately, requiring ad hoc regularizations near singularities and failing at capturing inter-sector interactions under renormalization group flow. Therefore, the scope of this study aims at resolving these limitations through the construction of a unified orbifold algebra $\mathcal{A}(X/G)$ that decomposes into idempotent-projected components corresponding to conjugacy classes of the finite group $G$ acting on the target space $X$. The formalism is shown to recover conventional sigma model results in the smooth limit where $G$ approaches the trivial group, with the internal renormalization group derivation reducing to the standard one-loop beta function proportional to the Ricci tensor. Examples demonstrate the applicability, including explicit calculations for the $\mathbb{C}/\mathbb{Z}_2$ orbifold that exhibit the decomposition into untwisted and twisted field contributions.
This paper introduces a unified theoretical framework for modeling temporal memory dynamics, combining concepts from temporal logic, memory decay models, and hierarchical contexts. The framework formalizes the evolution of propositions over time using linear and branching temporal models, incorporating exponential decay (Ebbinghaus forgetting curve) and reactivation mechanisms via Bayesian updating. The hierarchical organization of memory is represented using directed acyclic graphs to model recall dependencies and interference. Novel insights include feedback dynamics, recursive influences in memory chains, and the integration of entropy-based recall efficiency. This approach provides a foundation for understanding memory processes across cognitive and computational domains.
The concept of super-resolution refers to various methods for improving the angular resolution of an optical imaging system beyond the classical diffraction limit. Although several techniques to narrow the central lobe of the illumination Point Spread Function have been developed in optical microscopy, most of these methods cannot be implemented on astronomical telescopes. A possible exception is represented by the variable transmittance filters, also known as "Toraldo Pupils" (TPs) since they were introduced for the first time by G. Toraldo di Francia in 1952. In the microwave range, the first successful laboratory test of TPs was performed in 2003. These first results suggested that TPs could represent a viable approach to achieve super-resolution in Radio Astronomy. We have therefore started a project devoted to a more exhaustive analysis of TPs and how they could be implemented on a radio telescope. In the present work we report on the results of extensive microwave measurements, using TPs with different geometrical shapes, which confirm the correctness of the first experiments in 2003. We have also extended the original investigation to carry out full-wave electromagnetic numerical simulations and also to perform planar scanning of the near-field and transform the results into the far-field.