Related papers: Note on the Chen-Lin result with Li-Zhang method
We prove some new results related to Tanaka's formula.
We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove a celebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also allows us to prove…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
We present in this work a new and simple proof of the false centre theorem.
We extend a new uniqueness result recently proved by Q. Chen, C. Miao and Z. Zhang.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
In this paper, we prove a conjecture of Schnell in the surface case.
We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
We prove a result on the existence of linear forms of a given Diophantine type.
In this note we give a detailed proof of a theorem of Aubin.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
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.
In this note we shall give a new proof to a quadrature formulae due to Newton.