Related papers: The Marker-Steinhorn Theorem
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.
We prove that the quiver problem is NP complete.
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
In this paper the circulant Hadamard conjecture is proved.
The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
We prove a conjecture due to Y. Last on Jacobi matrices.
In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
We give a new proof of Markov's classical theorem relating any two closed braid representations of the same knot or link. The proof is based upon ideas in a forthcoming paper by the authors, "Stabilization in the braid groups". The new…
This is an exposition of Gauss's proof of Descartes's rule of signs.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.
We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.