In the study of systems’ dynamics presence symmetry dramatically reduces complexity, while in chemistry, plays a central role analysis structure, bonding, and spectroscopy molecules. more general context, principle equivalence, local symmetry, dictated gravity, space-time itself. certain instances, especially we end up having to deal with an equation multiple roots. A variety optimal methods ha...

It is well known that, in 1829, the French mathematician Jacques Charles François Sturm (1803-1855) solved the problem of finding the number of real roots of a polynomial equation f(x) = 0, with rational coefficients and without multiple roots, over a given interval, say ]a, b[. As a byproduct, he also solved the related problem of isolating the real roots of f(x). In 1835 Sturm published anoth...

Shoot–root systemic defense signaling of hybrid poplar (Populus trichocarpa Torr. & A. Gray Populus deltoides Bartr. ex Marsh.) was investigated with molecular techniques to extend existing knowledge of poplar defense. Treatment of roots with methyl jasmonate demonstrated that transcripts of PtdTI3, a poplar trypsin inhibitor and marker of poplar defense responses, can be induced in poplar root...

We estimated a wholesale demand system for beef, pork, lamb, chicken, and turkey using quarterly U.S. data and a dynamic, CBS system (Keller and Van Driel). The CBS system is a differential system, which means that it might be more appropriately applied in those situations where the data have unit roots. If there are unit roots, differencing the data can improve the properties of the estimates....