Background: Acrylic resin ��ere �irst �sed in dentistry ��r dent�re �ases. ��e �asic kn���ledge �� acrylic resin c�ring �et��d s���ld �e kn���n �y t�e dentist, �eca�se t�e i��r�ved �er��r�ance �� acrylic resin de�ends �n t�e c�ring �et��d. Purpose: ��is st�dy ��as ai�ed t� �ind t�e ��st e��ective c�ring �et��d t� �r�d�ce t�e �ig�est transverse strengt� �� acrylic resin. Method: 18 rectag�lar ac...

Let $F$ be a non-negatively graded free module over polynomial ring $\mathbb{K}[x_1,\dots,x_n]$ generated by $m$ basis elements. $M$ submodule of elements in with degrees bounded $D$ and dim $F/M$=$r$. We prove that if is graded, the degree reduced Gr\"{o}bner for any term order $2\left[1/2((Dm)^{n-r}m+D) \right]^{2^{r-1}}$. If not bound $2\left[1/2((Dm)^{(n-r)^2}m+D) \right]^{2^{r}}$. This gen...

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

The title compound, C(26)H(32)O(11), is composed of an α,β-unsaturated cyclo-hexa-none ring (A), two cyclo-hexane rings (B and C), a six-membered lactone ring (D) and tetra-hydro-furan ring (E). Ring A exists in a half-chair conformation with a C atom displaced by 0.679 (2) Å from the mean plane through the remaining five atoms. Ring B exists in a normal chair conformation. Both rings C and D e...

The solution conformation of the homogeneous, heparin-derived tetrasaccharide delta UA2S(1-->4)-alpha-D-GlcNpS6S(1-->4)-alpha-L-IdoAp2S (1-->4)-alpha-D-GlcNpS6S (residues A, B, C and D respectively, where IdoA is iduronic acid) has been investigated by using 1H- and 13C-NMR. Ring conformations have been defined by J-coupling constants and inter-proton nuclear Overhauser effects (NOEs), and the ...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...