Some properties of basis invariants of the symmetry groupsG(m,p,n), B n m , D n m

Abstract

We study the properties of the basis invariants of the symmetry groups of the complex polytope ~.ym and the generalized n-cube "yn m, as well as its subgroups D~. We 9ire art explicit construction of all the basis invariants of even degree of these groups.In n-dimensional unitary space U n we introduce an orthogonal coordinate system with origin 0 and basis vectors -ei (i = 1---,-~); G is the finite irreducible group generated by reflections with respect to (n -1)-dimensional planes containing the common point 0. We define the vertices of the generalized n-cube "~ to be the following m ~ vectors aEO here a is reflection with respect to the planes of symmetry; ~ is the unit normal vector (with origin 0) of one of them, and the vector ~ is given by x" = (x~). The Pogorelov polynomials J~ belong to the algebra I c of polynomials that are invariant with respect to the group G [3]. In the present note we establish relations for the numbers m and n for which .the basis m (the generators of the algebra I ~ are representable invariants of the groups G = G (m,p, n), B~, and D n in the form (2); we construct all the generators of even degree of the algebras I ~ G = G (m,p, n), Bm~, D~. TO(ra,P,n)Theorem. The polynomials "rat are the generators of even degree mt (1 < t < n -1) of the algebra I G (ra,p,'O for any n, provided rn ~ 2 l ~ = 1, 2,...). In the case rn = 2 t the number n satisfies and n reflections of order 2 with respect to the planes with equations z~=xj+x=0, j=l,n-1; (5) zl -Oz2 = 0.

The Effect of Lesson Study for Learning Community Based Guided Inquiry Learning Model on Salt Hydrolysis Material on Student Learning Outcomes of SMAN 10 Padang

“…Model guided inquiry learning memiliki lima tahapan pembelajaran, yaitu orientasi, eksplorasi, pembentukan konsep, aplikasi, dan penutup (Hanson, 2005). Berdasarkan penelitian yang dilakukan oleh Endang Lovisia (2018) (Vermunt, 2019).…”