Related papers: A new and simple proof of the false centre theorem
We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.
In the paper Compositionality of Component Fault Trees, we present a discussion of the compositionality of correctness of component fault trees. In this technical report, we present the formal proof of the central theorem of the…
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.
We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.
We prove an analogue of the prime number theorem for finite fields.
We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.
We present a simple inductive proof of the Lagrange Inversion Formula.
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.
We obtain some new inequalities of Chebyshev Type.
Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…
This paper aims at completing and clarifying a delicate step in the proof of Theorem 5.3 of our paper \cite{ST}, where it was used the differentiability of a function $F$, which a priori can appear not necessarily differentiable.
This paper has been withdrawn by the author due to a crucial error in last part of proof.
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.