相关论文: A Generalisation of Steenrod's Approximation Theor…

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

We extend the Colombeau algebra of generalized functions to arbitrary (infinitely differentiable, paracompact) n-dimensional manifolds M. Embedding of continuous functions and distributions is achieved with the help of a family of n-forms…

This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal…

We present necessary and sufficient conditions for a group homomorphism between spaces of smooth sections of Lie group bundles to be a weighted composition operator. These results provide new insights into a wide range of problems related…

Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E.…

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…

We prove that a connected subcartesian space admits embedding in a Euclidean space. The Whitney Embedding Theorem is then stated as a corollary of our result. Based on the above result together with the theory of distribution on smooth…

We prove a generalized vanishing theorem for certain quasi-coherent sheaves along the derived blow-ups of quasi-smooth derived Artin stacks. We give four applications of the generalized vanishing theorem: we prove a $K$-theoretic version of…

The aim of this note is to present some new explicit examples of $O(d,d)$-generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits $\mathcal{O}$ of some semi-simple Lie group $G$. Using this construction, an…

We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distributions (singular support, wavefront set, Sobolev…

There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of…

In this paper, with the aim of establishing a structure theorem for a compact K\"ahler manifold $X$ with semi-positive holomorphic sectional curvature, we study a morphism $\phi: X \to Y$ to a compact K\"ahler manifold $Y$ with…

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

This article grew out of an effort to understand the smooth mapping class groups of certain 4-manifolds in a geometric manner. We prove a smooth analog of the Birman-Hilden theorem for manifolds that admit a hyperk\"ahler structure. This…