This study aimed to evaluate the potential of commercial enzymes cellulase (CE), xylanase (XY) and the combination of CE + XY to improve rumen fermentation of Guinea grass ecotype ‘A’ (Panicum maximum). The experiment was carried out in a randomized complete block design. In vitro incubations were performed with four doses of individual enzymes and their combinations (1:1 from each enzyme) as 5...

‎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.

In [9], the author introduced a digital version of this theorem where the exponents appearing in (1) are viewed as sums of digits. To illustrate this, consider the binomial theorem for N = 2: (x + y) = xy + xy + xy + xy. (2) It is easy to verify that (2) is equivalent to (x+ y) = xy + xy + xy + xy, (3) where s(k) denotes the sum of digits of k expressed in binary. For example, s(3) = s(1 · 2 + ...

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...