Related papers: Two encounters with the p-adic Stark conjecture
Interstellar dust forms during stellar mass-loss events, occurring either during a star's giant phase or during supernova explosions. This PhD thesis provides an in-depth investigation into the theory of dust condensation and growth,…
In these lectures I discuss cosmological phase transitions with the goal of establishing the possibility of observational consequences. I argue that the {\em only} phase transition amenable of experimental study within the foreseeable…
NGST offers unprecedented opportunities for charting the `dark ages' beyond the limits of the deep optical surveys conducted with HST. An equally important motivation, however, is a detailed physical understanding of the later stages of…
By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to $p$-Schatten classes. This generalizes the main result…
In 1986 Alex Dalgarno published a paper entitled "Is Interstellar Chemistry Useful?" By the middle 1970s, and perhaps even earlier, Alex had hoped that astronomical molecules would prove to: possess significant diagnostic utility; control…
While there is no consensus about the history of time since the beginning, in this paper I will discuss some possibilities. We have a pretty clear picture of cosmic history from the electroweak phase transition through the time of…
In this paper we review a part of the approaches that have been considered to explain the extraordinary discovery of the late time acceleration of the Universe. We discuss the arguments that have led physicists and astronomers to accept…
In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are…
The quantum nature of gravity remains one of the greatest mysteries of modern physics, with many unified theories predicting variations in fundamental constants across space and time. Here we present precise measurements of these variations…
In this short note we confirm the relation between the generalized $abc$-conjecture and the $p$-rationality of number fields. Namely, we prove that given K$/\mathbb{Q}$ a real quadratic extension or an imaginary $S_3$-extension, if the…
The notion of shuffle-compatible permutation statistics was implicit in Stanley's work on P-partitions and was first explicitly studied by Gessel and Zhuang. The aim of this paper is to prove that the triple ${\rm (udr, pk, des)}$ is…
This study reviews the advances made in inflationary theory, especially regarding the seeming disparity between inflation energy and dark energy, and their significance to cosmic evolution as a whole. I attempt to connect the two sources of…
The Einstein-Podolsky-Rosen (EPR) paradox was enunciated in 1935 and since then it has made a lot of ink flow. Being a subtle result, it has also been largely misunderstood. Indeed, if questioned about its solution, many physicists will…
We propose the formula for the number of pairs of consecutive primes $p_n, p_{n+1}<x$ separated by gap $d=p_{n+1}-p_n$ expressed directly by the number of all primes $<x$, i.e. by $\pi(x)$. As the application of this formula we formulate 7…
We present an English translation and discussion of an essay that a Japanese physicist, Torahiko Terada, wrote in 1922. In the essay, he described the waiting-time paradox, also called the bus paradox, which is a known mathematical…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical…
In recent years, the hope to confirm the existence of dark matter by experimentally detecting it has diminished significantly. After more than 30 years of experimental searches, many of the most promising candidates have since been ruled…
The link between Vandiver's conjecture and Gauss sums is well known since the papers of Iwasawa (1975), Thaine (1995-1999) and Angl{\`e}s-Nuccio (2010). This conjecture is required in many subjects and we shall give such examples of…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.