Related papers: Reply to W. T. Kranz on "Explicit analytical solut…
Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function $w\left(z \right)…
An error occurs in a part of the statement and proof of Proposition 2.2 in Jour. Math. Anal. and Appl., 476, (2019), 53-85 that is corrected in this erratum. The revised result reveals a new and unexpected critical phenomenon, having…
In this research, an optimal algorithm for the Collatz conjecture is presented. Properties such as the convergence of the algorithm and an equation that relates the algorithm to the classical Collatz conjecture are obtained. It is validated…
A natural analogue of the Krein--Milman theorem is shown to fail for CAT(0) spaces.
Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA*…
A shortcoming in the authors' interpretation of this beautiful new experiment is pointed out and briefly discussed.
In this article, we reduce the unsolved problem of convergence of Collatz sequences to convergence of Collatz sequences of odd numbers that are divisible by 3. We give an elementary proof of the fact that a Collatz sequence does not…
This paper has been withdrawn by the authors. There was an erroneous estimate of the degree of a transformed polynomial, making the method appear more effective than it really is. We thank an anonymous referee for pointing out this error.
We aim to fill a gap in the proof of an inequality relating two exponents of uniform Diophantine approximation stated in a paper by Bugeaud. We succeed to verify the inequality in several instances, in particular for small dimension.…
This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.
We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…
A recent paper by A. R. Lima, P. M. C. de Oliveira, and T. J. P. Penna [cond-mat/0002176; J. Stat. Phys. 99:691 (2000)], seems to contain at least two mistakes which deserve comment, one concerning the numerical data, the other being of a…
A short reply to Jarzynski's comment cond-mat/0509344 on my paper ``Flaw of Jarzynski's equality when applied to systems with several degrees of freedom'' (cond--mat/0508721) is presented.
This paper has been withdrawn due to a crucial error in the proof of the main theorem
In this work we consider an equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent…
The conditions of tests and calibrations described in the article E.E Kading et al. [Phys. Rev. Res. 2, 023279 (2020)] show striking flaws. The interpretation and extraction of quantitative results from this experiment are considered…
In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite number of lines; therefore, no formal proof is possible.
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
During my study of the iteration of functions of the form $f(z)=z^{\alpha}+c$, where $z,c \in \mathbbC$, and $\alpha$ is a rational non-integer larger than 2 (\cite{s1}), I encountered a fundamental difficulty in the exponentiation of a…
Consider critical site percolation on $\mathbb{Z}^d$ with $d \geq 2$. Cerf (2015) pointed out that from classical work by Aizenman, Kesten and Newman (1987) and Gandolfi, Grimmett and Russo (1988) one can obtain that the two-arms exponent…