CONTENTS 1 MATHEMATICAL PRELIMINARIES 1.1 Invariants 1 1.2 Some geometrical invariants 2 1.3 Elements of differential geometry 5 1.4 Gaussian coordinates and the invariant line element 7 1.5 Geometry and groups 10 1.6 Vectors 13 1.7 Quaternions 13 1
Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering { uncertainty and complexity { and in particular they ar
1. Physics in Flat Spacetime: Geometric Viewpoint 1.1 Overview 1.2 Foundational Concepts 1.3 Tensor Algebra Without a Coordinate System 1.4 Particle Kinetics and Lorentz Force Without a Reference Frame 1.5 Component Representation of Tensor Algebra
Arduino 101 houses an Intel Curie module which offers a better performance at a lower power footprint. The module has two 32-bit MCUs - an x86 Intel Quark processor and an ARC EM4 processor along with 384kB flash memory and 80kB SRAM. These onboard
interacting with data This lecture covers the basics of core concepts in probability and statistics to be used in the course. These include random variables, continuous and discrete distributions, joint and conditional distributions, the chain rule,
Nitrogen fixation of faba bean interacting with a non-legume in two contrasting intercropping systems，范分良，余常兵，A field experiment was carried out to quantify biological nitrogen fixation (BNF) using the 15N isotope natural abundance method in maize (Z
Through introducing discrete-time quantum walks on the infinite line and on circles, we present a kind of two-particle interacting quantum walk which has two kinds of interactions. We investigate the characteristics of this kind of quantum walk and t
We have recently proposed the two-particle controlled interacting quantum walks for building quantum Hash schemes (Li et al. Quantum Inf Proc, 2012. doi:10.1007/s11128-012-0421-8). In this paper, we adopt the mutual information, the measurement-induc
The evolution characteristics of quantum state fidelity in an interacting system of single-mode light field and atomic Bose-Einstein condensate have been studied and the influence of the initial light field intensity and the interaction among atoms o
Entanglement dynamics of two non-interacting atoms in a squeezed vacuum reservoir is studied. Several examples with different initial entangled states are investigated, and it is found that entangled atoms become disentangled faster in squeezed vacuu
The spontaneous emission rate of two interacting excited atoms near a dielectric interface is studied using the photon closed-orbit theory and the dipole image method. The total emission rate of one atom during the emission process is calculated as a
