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...

We revisit the symmetry structure of integrable PDEs, looking at specific example KdV equation. identify 4 nonlocal symmetries depending on a parameter, which we call generating symmetries. explain that since these are symmetries, their commutator algebra is not uniquely determined, and present three possibilities for algebra. In first version, 3 commute; this shows it possible to add further (...

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for...

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20, respectively. To a good approximation, t...

We will mainly discuss the measurable angle (local angle) of light ray $\psi_P$ at position observer $P$ instead total deflection (global $\alpha$ in Kerr spacetime. investigate not only effect gravito-magnetic field or frame dragging but also contribution motion with a coordinate radial velocity $v^r$ and transverse $bv^{\phi}$ ($b$ is impact parameter $v^{\phi}$ angular velocity) which are co...

We study a nonstandard formulation of the Neumann initial value problem \begin{equation} \begin{array}{rl} u_t(x,t) = \Delta \phi(u(x,t)), & x \in \Omega \subseteq \mathbb{R}^k, \ t \mathbb{R} \label{abstract}\\ u(x,0) u_0(x), \Omega. \end{array} \end{equation} with boundary conditions. The function $\phi C^1(\mathbb{R})$ is assumed to be decreasing either in bounded interval $(u^-,u^+)$, or an...

Purpose This study aims to explicate the behavioral factors that determine willingness share personal health data for secondary uses. Design/methodology/approach A theoretical model is developed and tested with structural equation modeling using survey from Finland. Findings It shown attitude toward information sharing strongest factor contributing (PHI). Trust control serve as mediating betwee...