Related papers: Stevin numbers and reality
We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's…
This paper attributes the sudden emergence of mathematical probability and statistics in the second half of the seventeenth century to Calvin's Reformed theology. Calvin accommodated Epicurean chance with Stoic determinism and synthesised…
Many scholars have called for raising statistical hurdles to guard against false discoveries in academic publications. I show these calls may be difficult to justify empirically. Published data exhibit bias: results that fail to meet…
Statistics experiences a storm around the perceived misuse and possible abuse of its methods in the context of the so-called reproducibility crisis. The methods and styles of quantification practiced in mathematical modelling rarely make it…
Much recent progress has been made concerning the probable existence of Odd Perfect Numbers, forming part of what has come to be known as Sylvester's Web Of Conditions. This paper proves some results concerning certain properties of the…
The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling…
Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…
The philosophical foundations of statistics involve issues in theoretical statistics, such as goals and methods to meet these goals, and interpretation of the meaning of inference using statistics. They are related to the philosophy of…
This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…
Size bias occurs famously in waiting-time paradoxes, undesirably in sampling schemes, and unexpectedly in connection with Stein's method, tightness, analysis of the lognormal distribution, Skorohod embedding, infinite divisibility, and…
In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical…
The use of statistical software in academia and enterprises has been evolving over the last years. More often than not, students, professors, workers, and users, in general, have all had, at some point, exposure to statistical software.…
There are growing uncertainties surrounding the classical model of computation established by G\"odel, Church, Kleene, Turing and others in the 1930s onwards. The mismatch between the Turing machine conception, and the experiences of those…
The aim of this paper is to prove conjectures concerning $p$-adic valuations of Stirling numbers of the second kind $S(n,k)$, $n,k\in\mathbb{N}_+$, stated by Amdeberhan, Manna and Moll and Berrizbeitia et al., where $p$ is a prime number.…
Let $p$ be a prime and $b$ a primitive root of $p^2$. In this paper, we give an explicit formula for the number of times a value in ${0,1,...,b-1}$ occurs in the periodic part of the base $b$ expansion of $1/p^m$. As a consequence of this…
The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all…
Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$.…
While the ``hierarchy of science'' has been widely analysed, there is no corresponding study of the status of subfields within a given scientific field. We use bibliometric data to show that subfields of mathematics have a different…
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and even directly in model inference. Over the past decades, the application areas and overall potential of…