Related papers: Two different scenarios when the Collatz Conjectur…

We show that there is a contradiction between the Riemann's Hypothesis and some form of the theorem on the universality of the zeta function.

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and…

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We give an explicit formula proving Xu's Conjecture on alternating double zeta values. We also discuss the limitations of Glanois' motivic Galois descent criterion in this case, as it cannot specify the depth of the descent.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

We show that Sturm's classical comparison theorem (SCT) on the interlacing of zeros of solutions of pairs of real second order two-term ordinary differential equations necessarily fails if the usual Sturmian-type conditions on the…

Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We prove a new quaternionic and a new matrix nullstellensatz. We also show that both theories are intertwined.

A recent article claims the Lorentz force law is incompatible with special relativity. The claim is false, and the "paradox" on which it is based was resolved many years ago.

In this short note I restate and simplify the proof of the impossibility of probabilistic induction from Popper (1992). Other proofs are possible (cf. Popper (1985)).

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

The infamous 3x+1 conjecture spread by Lothar Collatz in 1952, despite its elementary formulation, remained unproved for over 60 years. From the heuristical probabilistic approach to the complex mapping of the algorithm, the scientific…

Two conjectures recently proposed by one of the authors are disproved

This paper introduces prime holdout problems, a problem class related to the Collatz conjecture. After applying a linear function, instead of removing a finite set of prime factors, a holdout problem specifies a set of primes to be…

We show that the Jacobian conjecture of the two dimensional case is true.