Related papers: Did Hypatia Know about Negative Numbers?
I review some of the past and current methods for retrieval of literature and other published information, excluding commercial services. Much of this is a personal view and based on experience made at various institutions, some of them…
These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
We answer a question of Zadrozny.
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.
In this short note, we give an affirmative answer to Wu's conjecture on practical numbers, which was posed in [X.-H. Wu, {\it Special forms and the distribution of practical numbers}, Acta Math. Hungar., {\bf 160}(2020), 405-411].
A few remarks on hep-ph/9612213 are given.
In a recent letter (PRL 95, 190601 (2005)), T.M. Rocha Filho and coworkers address the very interesting issue of the entropic form to be used for Hamiltonians with long-range interactions. In our opinion the letter misses several points…
A long-standing problem of theoretical physics is the exceptionally small value of the cosmological constant $\Lambda \sim 10^{-120}$ measured in natural Planckian units. Here we derive this tiny number from a toroidal string cosmology…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…
The riddle of the sigma is recast in a way that tries to differentiate fact from fiction as a basis for future/further discussion. By doing this, it is hoped that the role of the sigma as dominating the ubiquitous $\pi\pi$ interactions…
What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the…
Recently, authors studied the unsigned degenerate r-Stirling number of the first kind and the degenerate r-Stirling number of the second kind, respectively of which are the degenerate versions of the unsigned r-Stirling numbers of the first…
First, dark matter is introduced. Next, the Dirac negative energy state is rediscussed. It is a negative matter with some new characteristics, which are mainly the gravitation each other, but the repulsion with all positive matter. Such the…
We review briefly some well known facts about trace anomaly and then concentrate on its 'infrared' manifestation. Among other things we show by means of dispersion relations that dilatations and translations are conflicting symmetries. We…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
In this paper, we chronologically recount several situations that have contributed to the development and formalization of the objects known as imaginary or complex numbers. We will begin by introducing the earliest documented knowing for…