相关论文: Analysis and dynamics on the Berkovich projective …

This paper introduces the bicomplex Prabhakar derivative, extending fractional calculus to four-dimensional bicomplex spaces. Using the generalized kernel involving bicomplex Prabhakar function, we construct the bicomplex Prabhakar…

Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis,…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space $\mR^{m+1}$, including a higher dimensional generalization of the complex logarithmic function. Their…

This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…

Let $C$ be a curve over a complete discretely valued field $K$. We give tropical descriptions of the weight function attached to a pluricanonical form on $C$ and the essential skeleton of $C$. We show that the Laplacian of the weight…

We set up a new framework to study critical points of functionals defined as combinations of eigenvalues of operators with respect to a given set of parameters: Riemannian metrics, potentials, etc. Our setting builds upon Clarke's…

We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from $L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcal B_0$ are onto. We…

Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

These lecture notes develop the theory of learning in deep and recurrent neuronal networks from the point of view of Bayesian inference. The aim is to enable the reader to understand typical computations found in the literature in this…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…

As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…

This survey is meant to provide an introduction to the fundamental theorem of linear algebra and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to linear algebra. Specifically, we…

This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of…

We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…

I developed the lecture notes based on my ``Linear Model'' course at the University of California, Berkeley over the past ten years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and…

We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…