How we solve Diophantine equations
... 2 has an integer solution if and only if it has a real solution and solutions modulo all prime powers. In other words, the obvious necessary conditions are also sufficient. We say that equations of degree 2 satisfy the Hasse principle. This reduces the decision problem to a finite computation, since ...
... 2 has an integer solution if and only if it has a real solution and solutions modulo all prime powers. In other words, the obvious necessary conditions are also sufficient. We say that equations of degree 2 satisfy the Hasse principle. This reduces the decision problem to a finite computation, since ...
Astronomy Astrophysics Force-free twisted magnetospheres of neutron stars &
... This choice of constant α has been followed in several studies of the solar corona (Chiu & Hilton 1977; Seehafer 1978) or applied to the region with open field lines of the pulsar magnetosphere (Scharlemann & Wagoner 1973). The Yl (x) functions are oscillatory at large distances, and the magnetic fi ...
... This choice of constant α has been followed in several studies of the solar corona (Chiu & Hilton 1977; Seehafer 1978) or applied to the region with open field lines of the pulsar magnetosphere (Scharlemann & Wagoner 1973). The Yl (x) functions are oscillatory at large distances, and the magnetic fi ...
Midterm 1, Sec 2, Spring2005
... Q12 Read the following, and write the corresponding system of inequalities. (Write it mathematically. You do not need to solve or graph.) A furniture company manufactures tables and chairs. A table requires 2 labor-hours for assembling and 4 labor-hours for finishing. A chair requires 1 labor-hour f ...
... Q12 Read the following, and write the corresponding system of inequalities. (Write it mathematically. You do not need to solve or graph.) A furniture company manufactures tables and chairs. A table requires 2 labor-hours for assembling and 4 labor-hours for finishing. A chair requires 1 labor-hour f ...
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.