^ d jw0j (w0) + ^ d jw1j (w1) 2 + E(jwj + 1) = d 0 (w0) + d 0 (w1) 2 so d 0 obeys the average law (without conservation). Proof.[of Theorem 19] Note the d 0 constructed in Theorem 18 is generally not conservative. We will parallel Theorem 4, by constructing a slothful two-sided quasipolynomially precise cover. The construction of a conservative cover from a slothful cover preserves two-sided qu...

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

In this work, a new compound, 2-(N-allylsulfamoyl)-N-propylbenzamide, has been synthesized via tandem one-pot reaction under sonication. The rotational orientations of the allylsulfamoyl and amide groups in title molecule, C13H18N2O3S, are partly determined by an intramolecular N—H···O hydrogen bond. crystal, layer structure is generated C—H···O bonds plus C—H···π (ring) interactions. A Hirshfe...

Three new heteroleptic copper(II) complexes, [(tmen)Cu(dike)H2O]X where tmen = N,N,N',N'-tetramethylethylenediamine, dike = 2-acetylcyclopentanone anion and X= ClO4- (1), Cl- (2) and Br- (3) are prepared and characterized by elemental analyses, molar conductance measurements and IR and UV-Vis spectroscopy techniques. The complex 1 is fairly soluble in various organic solvents and demonstrates d...