相关论文: Impossibility of the Existence of the Universal De…

We prove the geometric Bogomolov conjecture over a function field of characteristic zero.

For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…

The classical Universal Approximation Theorem holds for neural networks of arbitrary width and bounded depth. Here we consider the natural `dual' scenario for networks of bounded width and arbitrary depth. Precisely, let $n$ be the number…

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…

In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…

We prove generalized ABC theorems for vanishing sums of non-Archimedean entire functions of several variables in arbitrary characteristic.

We investigate the possibility of electrostatic potential saturation, which may lead to the phenomenon of effective charge saturation. The system under study is a uniformly charged infinite plane immersed in an arbitrary electrolyte made up…

It is shown that the absence of an objective existence of the results of quantum measurements cannot be proved by known experiments. There are also general arguments confirming this conclusion.

We prove Kitaoka's conjecture for all totally real number fields of degree 4 -- namely, there is no positive definite classical quadratic form in three variables which is universal. To achieve this, we study the fields (often without…

By applying Birkhoff's theorem to the problem of the general relativistic collapse of a uniform density dust, we directly show that the density of the dust $\rho=0$ even when its proper number density $n$ would be assumed to be finite! The…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…

We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When the shift is rational we prove a counting result which…

The Nielsen-Ninomiya no-go theorem asserts that chiral Weyl~(``neutrino'') fields cannot exist on lattices. However, the actual mathematical arguments advanced in the theorem fail to make that case. The theorem leaves the problem of lattice…

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.

The main result shows a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighborhood consisting entirely of univalent functions. For the particular choice of a linear function in…

Bayes classifiers for functional data pose a challenge. This is because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

We disprove a conjecture of Bombieri regarding univalent functions in the unit disk in some previously unknown cases. The key step in the argument is showing that the global minimum of the real function…

We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…