Related papers: On Ryser's Conjecture
We settle in the affirmative the Graham-Sloane conjecture.
In this paper, we will prove some sufficient conditions for the solvability of groups.
We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.
We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.
We prove some extensions of Andrews inequality.
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\xi_1$ and $\xi_2$ satisfy Lin's condition, the same is true for their product is presented.…
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
An technically interesting proof of a known theorem.
Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…
In this paper, the abc conjecture is negated under certain conditions
A proposed solution to the Riemann Hypothesis
We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience. We show that if one of the basic assumptions is not…
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…