Related papers: On Erd\"os--Szekeres problem and related problems
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We introduce and study a new kind of congruent number problem on the right trapezoid.
We give a short survey of recent LHC experiments and related theory topics concerning the Odderon problem.
We survey the classical results of the Dirichlet Approximation Theorem.
This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.
We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.
This is a survey article in algebraic logic, where we take a magical tour from old concepts due to Henkin, Monk and Tarski like neat embeddings, to modern views and perspectives, culminating in the use of Erdos graphs in settling important…
We respond to invalid criticism in the recent Comment by Schneider et al. [arXiv:1407.4127v1]
We prove an abstract linking theorem that can be used to show existence of solutions to various types of variational elliptic equations, including Schr\"{o}dinger--Poisson--Slater type equations.
We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.
In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…
This is a survey of old and new problems and results in additive number theory.
We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, defined by polynomials with integer coefficients, and on their reductions modulo sufficiently large primes to study congruences with products…
In this paper, using the compression method, we recover the lower bound for the Erd\H{o}s unit distance problem and provide an alternative proof to the distinct distance conjecture. In particular, in $\mathbb{R}^k$ for all $k\geq 2$, we…
A brief report on recent work on the sphere-packing problem.
A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…