Related papers: Cranks in Ramanujan's Lost Notebook
The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand.…
The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures concerning the…
We demonstrate that quotients of septic theta functions appearing in S. Ramanujan's Notebooks and in F. Klein's work satisfy a new coupled system of nonlinear differential equations with interesting symmetric form. This differential system…
In this paper, we investigate the arithmetic properties of the difference between the number of partitions of a positive integer $n$ with even crank and those with odd crank, denoted $C(n)=c_e(n)-c_o(n)$. Inspired by Ramanujan's classical…
We prove that the non-backtracking random walk on Ramanujan graphs with large girth exhibits the fastest possible cutoff with a bounded window.
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
This is a chapter of a recently published book entitled Atom Chips, edited by Jakob Reichel and Vladan Vuletic. The contents of this chapter include: Basic Principles; Atomic-Fountain versus Trapped-Atom Clocks; Optical-Transition Clocks…
In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.
These notes are based on the lectures given by the author during Winter Braids IX in Reims in March 2019. We discuss slice knots and why they are interesting, as well as some ways to decide if a given knot is or is not slice. We describe…
Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of Baudh\=ayana's approximate quadrature of the circle, have shown that it is useful to submit mathematical texts to a form of literary analysis. Several passages…
We make a few comments on some misleading statements in the above paper.
In experimental physics, lab notebooks play an essential role in the research process. For all of the ubiquity of lab notebooks, little formal attention has been paid to addressing what is considered `best practice' for scientific…
This is intended to appear as the introduction to "The CBM Physics Book: compressed baryonic matter in laboratory experiments" (ed. B. Friman, C. H\"ohne, S. Leupold, J. Knoll, J. Randrup, R. Rapp, P. Senger), to be published by Springer.…
A desktop keyboard has several sections like character key section, navigation key section, numeric key section, and function key section etc. each consisting of several number of keys. However, a laptop computer does not have so much of…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers-Ramanujan type and identities of false theta functions.
To provide a survey on the existing tasks and models in Machine Reading Comprehension (MRC), this report reviews: 1) the dataset collection and performance evaluation of some representative simple-reasoning and complex-reasoning MRC tasks;…
We present two practical and widely applicable methods, including some criteria and a general procedure, for detecting Brunnian property of a link, if each component is known to be unknot. The methods are based on observation and handwork.…
In this paper, we prove inequalities for ranks, cranks, and partitions among different classes modulo 11. These were conjectured by Borozenets.
This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.