Related papers: On Romanoff's theorem
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
We prove the Aharoni Berger Conjecture
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
In this short note we give counterexamples to several results related to extension theorems published recently.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
Let $\mathcal{A}=\{a_{n}\}_{n=1}^{\infty}$ and $\mathcal{B}=\{b_{n}\}_{n=1}^{\infty}$ be two sequences of positive integers (not necessarily distinct). Under some restrictions on $\mathcal{A}$ and $\mathcal{B}$, we obtain a lower bound for…
We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.
Considering the class of almost periodic functions in the Stepanov sense we extend and generalize the results of the first author [4]. as well as the results of L. Leindler [3] and P. Chandra [1,2].
In this note we extend a theorem from [13] about uniform circle random coverings
In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
In this short paper we review and extract some features of the Fredholm Alternative problem .
We extend a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality.
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schr\"odinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking…
In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.