Related papers: A variation of Gronwall's lemma
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
We prove the existence and uniqueness of the solution to the doubly nonlinear parabolic systems with mixed boundary conditions. Due to the unilateral constraint the problem comes as a variational inequality. We apply the penalty method and…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
A proof of Smale's mean value conjecture from 1981 is given.
New cases of the multiplicity conjecture are considered.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…
We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.
We formulate and prove a general result in spirit of hypergraph removal lemma for measurable functions of several variables.
In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random…
We use GL(2) delta method to establish the Burgess bound.
In this paper we show an index theorem for gerbes
We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.
We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…
In this note we prove an inequality involving primes and the product of consecutive primes.
We present a new, elementary, dynamical proof of the prime number theorem.
We prove a discrepancy estimate related to the sequence of fractional parts of $b^n/n$. This improves an earlier result of Cilleruelo et al.
We prove a new cross theorem for separately holomorphic functions.
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.