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In this short note, we improve the famous Reid Inequality related to linear operators.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We derive various inequalities involving the intersection number of the curves contained in geodesics and tight geodesics in the curve graph. While there already exist such inequalities on tight geodesics, our method applies in the setting…

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, which converges to the critical Hardy inequality. Sobolev type…

The goal of this short paper is to give a slightly different perspective on the comparison between crystalline cohomology and de Rham cohomology. Most notably, we reprove Berthelot's comparison result without using pd-stratifications,…

In this paper we will study the equivalence between super-Poincar\'e inequality and some log-Sobolev type inequalities, including weak log-Sobolev inequality and super log-Sobolev inequality. The explicit relations between associated rate…

A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…

In this short paper, a formula for the sequence defined by the nonhomogeneous linear difference equation with variable coefficients is presented. A connection with the homogeneous case is shown.

The aim of this paper is to prove a general version of Pl\"unnecke's inequality. Namely, assume that for finite sets $A$, $B_1, ... B_k$ we have information on the size of the sumsets $A+B_{i_1}+... +B_{i_l}$ for all choices of indices…

For two particles with different spin, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and 1/2; spin-1/2 and 3/2. We show that for these states Bell's inequality is violated.

We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.

In this short note, we give a simple derivation of the strong subadditivity inequalities: S(13) + S(23) \ge S(1) + S(2) and S(12) + S(23) \ge S(2) + S(123). The simplicity is due to the way we represent the quantum systems. We make a few…

We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.

In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities.

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.

In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…

In this article we present an extremely effective and relatively unknown approach to solving functional equations that appear in mathematical competitions. We aim to explain the philosophy of this novel method through numerous examples,…

For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…