let $mathfrak{a}$ be an algebra. a linear mapping $delta:mathfrak{a}tomathfrak{a}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{a}$. given two derivations $delta$ and $delta'$ on a $c^*$-algebra $mathfrak a$, we prove that there exists a derivation $delta$ on $mathfrak a$ such that $deltadelta'=delta^2$ if and only if either $delta'=0$...

The scattering of elastic waves in a medium with damage from microcracking is discussed. The influence of damage from penny-shaped microcracks within a homogeneous medium is considered. The microcracks are assumed to be randomly oriented and uniformly distributed. Explicit expressions are derived for the attenuation of longitudinal and shear elastic waves in terms of the damage parameter and th...

Cellular automata are discrete agent-based models, generally used in cell-based applications. There is much interest in obtaining continuum models that describe the mean behaviour of the agents in these models. Previously, continuum models have been derived for agents undergoing motility and proliferation processes, however, these models only hold under restricted conditions. In order to narrow...

Under the assumptions that SU(3)c × U(1)Y ×G ′ with G simple is a local symmetry group at high energies, that color is parity-conserving, and the Ycharges are irreducible, we show that anomaly constraints imply the minimal set of fermions is fifteen in number. Given this minimal set, we further show that G must be SU(2) and the unbroken gauge symmetry is either color or the product of color wit...

We show a very simple yet rigorous derivation of the invariance of the space-time interval (and hence the whole special relativity) just from the isotropy, homogeneity and a principle of relativity, without the need of the speed of light axiom. This article is intended as a textbook explanation of the special relativity.

If pi: A-->B is a surjective morphism between separable C(*)-algebras, then for each derivation delta of B there is a derivation [unk]delta of A such that pi([unk]delta(a)) for each a in A.