相关论文: Pedagogical Introduction to Extra Dimensions
I here conduct an exploration of programming language extensibility, making an argument for an often overlooked component of conventional language design. Now, this is not a technical detailing of these components, rather, I attempt to…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
This article briefly summarizes and reviews the motivations for - and the present status of - the proposal that the small size of the observed Dark Energy density can be understood in terms of the dynamical relaxation of two large extra…
This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…
This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be…
An extension of the Standard Model by extra scalar singlets was considered. Theoretical (unitarity, vacuum stability, triviality) and cosmological (dark matter relic abundance, direct detection experiments, constraints on dark matter…
Ces notes de cours visent a decrire de maniere pedagogique certaines extensions populaires du modele standard des interactions fortes et electrofaibless. Les sujets abordes comprennent le secteur de Higgs, le modele symetrique gauche-droit,…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
In this paper, the second of two companion pieces, we explore novel philosophical questions raised by recent progress in large language models (LLMs) that go beyond the classical debates covered in the first part. We focus particularly on…
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Computer science education has evolved extensively; however, systemic barriers still prevent students with visual impairments from fully participating. While existing research has developed specialized programming tools and assistive…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
Contribution: A flipped classroom approach to teaching empirical software engineering increases student learning by providing more time for active learning in class. Background: There is a need for longitudinal studies of the flipped…
In these lectures, we give a pedagogical introduction to the superconformal index. This is the writeup of the lectures given at the Winter School "YRISW 2020" and is to appear in a special issue of JPhysA. The lectures are at a basic level…
Large Language Models (LLMs) have demonstrated their transformative potential across numerous disciplinary studies, reshaping the existing research methodologies and fostering interdisciplinary collaboration. However, a systematic…