In this chapter, we report the concept and results of an empirical study that explored the effects of immersion and pictorial realism on the sense of presence in a virtual environment (VE). The VE used was similar to a typical industrial application. Seventy-seven participants each experienced one of four settings with varied combinations of immersion and pictorial realism, displayed in a proje...

‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

Subbarao and Andrews have observed that the combinatorial technique used by F. Franklin to prove Eulers famous partition identity (l-x)(l-x)(l-x)(l-x*) ••• = 1-x-x +x +x -x -x + ••• can be applied to prove the more general formula l-x-xy(l-xy) -xy(±-xy)(±-xy) xy (1 xy) (1 xy) (1 xy) = 1 -x-xy+xy+xy -xy -xy + • •• which reduces to Eulers when y = 1. This note shows that several finite versions o...

It is impossible to have quantum Hall effect without breaking the time-reversal symmetry. xy  xy. If we want xy to be invariant under , xy  xy, xy must be zero. Q: Can we have other type of topological insulators, in the presence of -symmetry? By saying topological insulator, I mean an insulator with a protected metallic edge. By protected, I mean no matter what we do, we cannot tu...

We present a complete description of $2$-dimensional equations that arise as symmetry reductions fourf $3$-dimensional Lax-integrable equations: (1) the universal hierarchy equation~$u_{yy}=u_zu_{xy}-u_yu_{xz}$; (2) 3D rdDym equation $u_{ty}=u_xu_{xy}-u_yu_{xx}$; (3) The basic Veronese web $u_{ty}=u_tu_{xy}-u_yu_{tx}$; (4) Pavlov's $u_{yy}=u_{tx}+u_yu_{xx}-u_xu_{xy}$.

This curve has the points (1 : 0 : 0) and (0 : 1 : 0) at infinity over any field. The affine equation is XY +Y +X = 0. The origin is a point of this curve. If (x, y) ∈ F8 is a point of this curve with nonzero coordinates, then x = 1. So 0 = xy + y + x = xy + xy + x = x[(xy) + (xy) + 1]. Let t = xy. Then t + t+ 1 = 0. So the Klein quartic has 3.7 = 21 rational points over F8 with nonzero coordin...

You should do problems involving the exact equation. Here is one example. Solve (2xy + y + 1) + (3xy + 4xy + 3y) dy dx = 0. Solution: Let M(x, y) = 2xy + y + 1 and N(x, y) = 3xy + 4xy + 3y, We have have My = 6xy 2 + 4y and Nx = 6xy 2 + 4y. So My = Nx and the given equation is exact. Thus there is a function φ(x, y) such that φx = M = 2xy +y+1 and φy = N = 3x y+4xy+3y. Integrating the first equa...

In 45,X/46,XY DSDs, the proportion of the two cell lineages is uneven in different organs and tissues, and 45,X and 46,XY cells can be found throughout the body. The gonadal development of 45,X/46,XY patients depends on the population of 46,XY cells in the gonads and the clinical features are variable. We had a 45,X/46,XY DSD patient whose 46,XY population in peripheral blood was extremely low,...