Related papers: Differentiation in Bundles with a Hyperspace Base
An action of a Lie algebra $\frak g$ on a manifold $M$ is just a Lie algebra homomorphism $\zeta:\frak g\to \frak X(M)$. We define orbits for such an action. In general the space of orbits $M/\frak g$ is not a manifold and even has a bad…
In this paper we introduce hyperations and cohyperations, which are forms of transfinite iteration of ordinal functions. Hyperations are iterations of normal functions. Unlike iteration by pointwise convergence, hyperation preserves…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…
The ability of deep networks to learn superior representations hinges on leveraging the proper inductive biases, considering the inherent properties of datasets. In tabular domains, it is critical to effectively handle heterogeneous…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…
We provide two new formulations of the separativity problem. First, it is known that separativity (and strong separativity) in von Neumann regular (and exchange) rings is tightly connected to unit-regularity of certain kinds of elements. By…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the global sections of this sheaf play an analogous role for formal…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
The differential calculus on `non-standard' $h$-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…