in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

the exposure of workers to magnetic field that occur in aluminum reduction potrooms has been studied. the pattern of magnetic field intensity has been demonstrated along the shop. it has clearly been shown that the personnel working near the pots are exposed to 20-to 1000-gauss magnetic field. to set limits of exposure to magnetic fields, the literature on the biological effects of stationary m...

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG...

Ferrofluid instabilities in DC magnetic fields for an Isopar-M based ferrofluid with saturation magnetization of about 400 Gauss. a) 1200 Gauss 5 mm diameter magnet behind small ferrofluid droplet surrounded by propanol to prevent ferrofluid wetting of 1 mm gap glass plates; Peak pattern with magnetic field perpendicular to ferrofluid layer. The peaks initiate in a hexagonal array when the magn...