What are the underlying principles of how populations change over time? Two basic principles are involved, the idea of exponential growth and its ultimate control. The basics of population ecology ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

We have looked at how to solve equations with one unknown value, but what happens when there are two unknown values? An equation with two unknown values will have infinitely many solutions. or \(x=100 ...

Japanese mathematician Masaki Kashiwara wins Abel Prize for contributions to algebraic analysis and representation theory at ...

"Even the +, −, =, and x signs we take for granted only came into widespread use in the 17th century. Which means that the earlier algebraists we know of … all had expressed their equations mostly in ...

In this paper, we first establish a principle of concentration compactness in $W^{1,p(x)}({\Bbb R}^{N})$ . Then, based on this concentration compactness principle, we ...

Electronics can be seen as really just an application of physics, and you could in turn argue that physics is the application of math to the real world. Unfortunately, the way most of us were taught ...