相关论文: Philipp Reis's telephone in Aberdeen
The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.
In 1874, Mertens famously proved an asymptotic formula for the product $p/(p-1)$ over all primes $p$ up to $x$. On the other hand, one may expand Mertens' prime product into series over numbers $n$ with only small prime factors. It is…
Mermin states in a recent paper that his nontechnical version of Bell's theorem stands and is not invalidated by time and setting dependent instrument parameters as claimed in one of our previous papers. We identify a number of…
Recently, there has been a flurry of research on the use of Reconfigurable Intelligent Surfaces (RIS) in wireless networks to create dynamic radio environments. In this paper, we investigate the use of an RIS panel to improve bi-directional…
The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau…
We give a transcription of a letter from Eisenstein's parents to Gauss, and an unpublished proof of the quadratic reciprocity law by Eisenstein using the tangent function.
In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of…
Riemann's hypothesis, formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin…
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze…
On April 30th 2008, the journal Nature announced that the missing circuit element, postulated thirty-seven years before by Professor Leon O. Chua has been found. Thus, after the capacitor, the resistor and the inductor, the existence of a…
In 1866 Gregor Mendel published a seminal paper containing the foundations of modern genetics. In 1936 Ronald Fisher published a statistical analysis of Mendel's data concluding that "the data of most, if not all, of the experiments have…
For several decades a portrait of Johannes Kepler has been widely circulating among professional astronomers, scientific and academic institutions, and the general public. Despite its provenance and identification having been questioned in…
This is a prelude to a book which I intend to publish. This paper describes my temporary thoughts on Einstein's pathway to the special theory of relativity. See my papers on my thoughts on Einstein's pathway to his general theory of…
In a previews paper we introduced the quantitative method named Reference Publication Year Spectroscopy (RPYS). With this method one can determine the historical roots of research fields and quantify their impact on current research. RPYS…
Intelligent reflecting surface (IRS) has emerged as a promising technology to realize smart radio environment for future wireless communication systems. Existing works in this line of research have mainly considered the conventional passive…
Reconfigurable Intelligent Surfaces (RISs) exhibit promising enhancements in coverage and data rates for wireless communication systems, particularly in the context of 5G and beyond. This paper introduces a novel approach by focusing on the…
Empirical, theoretical and historical aspects of Post's "problem of tag" from 1921 are explored. Evidence of strong computational irreducibility is found. Despite their deterministic origin, the lengths of successive sequences generated…
Roger Apery's seminal method for proving irrationality is "turned on its head" and taught to computers, enabling a one second redux of the original proof of zeta(3), and many new irrationality proofs of many new constants, alas, none of…
In this paper, we systematically study the electromagnetic (EM) and communication aspects of an RIS through EM simulations, system-level and ray-tracing simulations, and finally measurements. We simulate a nearly perfect, lossless RIS, and…
I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identity to prove Andrews' result along with a variety of new…