相关论文: A higher order Weierstrass approximation theorem -…

In this short note we prove a theorem of the Stone-Weierstrass sort for subsets of the cone of non-decreasing continuous functions on compact partially ordered sets.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

In this paper we use the Vandermonde matrices and their properties to give a new proof of the classical result of Karl Weierstrass about the approximation of continuous functions $f$ on closed intervals, using a sequence of polynomials. The…

Remarks on mathematical proof and the practice of mathematics.

We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…

New cases of the multiplicity conjecture are considered.

A new generalization of the classical separate algebraicity theorem is suggested and proved.

We survey the classical results of the Dirichlet Approximation Theorem.

We prove a new cross theorem for separately holomorphic functions.

We prove several extensions of the Erdos-Fuchs theorem.

We survey recent developments on the Restriction conjecture.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We illustrate the concept of mathematical proof.

We present a self-contained development of the Weierstrass theory of those analytic functions (single-valued or multiform) which admit an algebraic addition theorem. We review the history of the theory and present detailed proofs of the…

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and…

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.