Related papers: On the McLaughlin-Rundell theorem

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions,…

In this paper, we shall prove that the irreducibility in the sense of fine topology implies the uniqueness of invariant probability measures. It is also proven that this irreducibility is strictly weaker than the strong Feller property plus…

We prove Union-Closed sets conjecture.

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in…

In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic…

In this work, we will prove a uniqueness result for Calder\'on's inverse problem via some integral representation formulas for solutions of the Vekua equation in the framework of Clifford analysis.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Let $M_n$ denote a random symmetric $n$ by $n$ matrix, whose upper diagonal entries are iid Bernoulli random variables (which take value -1 and 1 with probability 1/2). Improving the earlier result by Costello, Tao and Vu, we show that…

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

This is the second paper devoted to the numerical version of Signature-inverse Theorem in terms of the underlying joint invariants. Signature Theorem and its Inverse guarantee any application of differential invariant signature curves to…

We complete statement and proof for B. Moss\'e's unilateral recognizability theorem. We also provide an algorithm for deciding the unilateral non-recognizability of a given primitive substitution.

An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…

In this article several properties of the inverse along an element will be studied in the context of unitary rings. New characterizations of the existence of this inverse will be proved. Moreover, the set of all invertible elements along a…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.