Related papers: Weighted linearization of vector fields via a form…

We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…

We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…

We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.

We study the self-compactification of extra dimensions via higher curvature gravity, f(R), where f(R) is the generic function of the Ricci scalar R. First, we reduce pure f(R) theory to a scalar-tensor theory by a conformal transformation.…

A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…

A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the…

We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…

The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary…

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the…

In this paper we investigate a complex symmetric generalization of general relativity and in particular we investigate its linearized field equations. We begin by reviewing some basic definitions and structures in Moffat's symmetric complex…

I discuss progress towards "bootstrapping" a Lorentz-violating gravity theory: namely, extending a linear Lorentz-violating theory of a rank-2 tensor to a non-linear theory by coupling this field to its own stress-energy tensor.

We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincar\'e inequality, and study associated self-adjoint operators. The weighted Korn inequality compares…

A metric vector space is asymptotically metrically normable (AMN) if there exists a norm asymptotically isometric to the distance. We prove that AMN vector spaces are rigid in the class of metric vector spaces under asymptotically isometric…

We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various…

Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…

We address the problem of how to characterise when a rank-two conformal Killing tensor is the trace-free part of a Killing tensor for a metric in the conformal class. We call such a metric a Killing scale. Our approach is via differential…

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…

We investigate static cylindrical solutions within an extended theory of modified gravity. By incorporating various coupling functions through a straightforward boost symmetry approach, we establish the equations of motion in a…