Related papers: A Note on McGee's {\omega}-Inconsistency Result
We prove omega results for the central value of $L$-functions with the further condition that the angle is also constrained.
Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if the theory is consistent; however, they could be refutable.…
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
We show that the existence of a homeomorphism between $\omega_0^*$ and $\omega_1^*$ entails the existence of a non-trivial autohomeomorphism of $\omega_0^*$.
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 proof of G\"odel's incompleteness theorem is given. With this new proof a transfinite extension of G\"odel's theorem is considered. It is shown that if one assumes the set theory ZFC on the meta level as well as on the object level, a…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We investigate the violation of Leggett-Garg (LG) inequalities inquantum dots with the stationarity assumption. By comparing two types of LG inequalities, we find a better one which is easier to be tested in experiment. In addition, we show…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
Morrey's classical inequality implies the H\"older continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequality $$ \lambda\biggl\|\frac{u}{d_\Omega^{1-n/p}}\biggr\|_{\infty}^p\le…
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
In this note we prove a weighted version of the Khintchine inequalities.
We derive a number of inequalities involving L\^e numbers of non-isolated hypersurface singularities. In particular, we derive L\^e-Iomdine formulas with inequalities and use these, together with Teissier's Minkowski inequalities for…