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We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

In this note we obtain a new convergence result for the Adomian decomposition method.

A proof of Sendov's conjecture is given.

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

We prove a uniformization theorem in complex algebraic geometry.

We present a new, elementary, dynamical proof of the prime number theorem.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

We establish a Liouville type theorem for some conformally invariant fully nonlinear equations

This is an exposition of Gauss's proof of Descartes's rule of signs.

We provide a proof of the Borwein Conjecture using analytic methods.

We prove an infinitary version of the Brauer-Schur theorem.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.