Related papers: Uniform approximation on ideals of multilinear map…

The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called…

We prove that every uniform approximate homomorphism from a discrete amenable group into a symmetric group is uniformly close to a homomorphism into a slightly larger symmetric group. That is, amenable groups are uniformly flexibly stable…

This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…

We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any…

We give an uniform General Neron Desingularization for one dimensional local rings with respect to morphisms which coincide modulo a high power of the maximal ideal. The result has interesting applications in the case of Cohen-Macaulay…

Multimodal Recommendation (MMR) systems are crucial for modern platforms but are often hampered by inherent noise and uncertainty in modal features, such as blurry images, diverse visual appearances, or ambiguous text. Existing methods…

We use methods of the general theory of congruence and *congruence for complex matrices--regularization and cosquares-to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices…

We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result…

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

We consider the problem of approximating a subset $M$ of a Hilbert space $X$ by a low-dimensional manifold $M_n$, using samples from $M$. We propose a nonlinear approximation method where $M_n $ is defined as the range of a smooth nonlinear…

Let $\mathcal H_c(M)$ stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold $M$. It is shown that $\mathcal H_c(M)$ is perfect and simple under mild assumptions on $M$. Next,…

The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions $\sigma$, then a standard feedforward neural network with one hidden layer is able to approximate any…

We study the problem of whether $\mathcal{P}_w(^nE)$, the space of $n$-homogeneous polynomials which are weakly continuous on bounded sets, is an $M$-ideal in the space of continuous $n$-homogeneous polynomials $\mathcal{P}(^nE)$. We obtain…

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…

By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$.…

Let $(M, g)$ be a compact real analytic Riemannian manifold and $\pi \colon \widetilde{M} \to M$ its universal cover. Assume that $\widetilde{M}$ can be realised as a manifold definable in an o-minimal structure $\Sigma$ expanding…

We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.

We establish uniform bounds for the sup-norms of modular forms of arbitrary real weight $k$ with respect to a finite index subgroup $\Gamma$ of $\mathrm{SL}_2(\mathbb{Z})$. We also prove corresponding bounds for the supremum over a compact…

We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a…