Related papers: Quantitative towers in finite difference calculus …
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We connect the well-known theory of functional forms of variational bicomplex with the theory of antiexact differential forms. We identify antiexact functional forms as an obstruction to the variationality of differential equations. The…
We give a new quantum circuit approximation of quantum multiplexors based on the idea of complexity theory oracles. As an added bonus, our multiplexor approximation immediately gives a quantum circuit approximation of diagonal unitary…
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.
Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were proposed to pursue some good space-filling…
We call attention to the intermediate constructions $\T_n F$ in Goodwillie's Calculus of homotopy functors, giving a new model which naturally gives rise to a family of towers filtering the Taylor Tower of a functor. We also establish a…
The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
This article considers quantum systems described by a finite-dimensional complex Hilbert space $H$. We first define the concept of a finite observable on $H$. We then discuss ways of combining observables in terms of convex combinations,…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…