Let S be a set with n elements. The set of all subsets of S has elements. By a partition of S we mean a disjoint set of nonempty subsets (called blocks) whose union is S. The set of all partitions of S has elements, where is the nth Bell number and where denotes the Stirling number of the second kind. For example, We have recurrences ([1,2,3]) and asymptotics where is defined by. If U and V are...

in this work, a new spectrophotometric method for the determination of trace amount of cobalt (іі) ionwas investigated and the stability constant of the related complex was evaluated 2.174 × 104. in the cobalt(іі)-piroxicam complex, the maximum absorbance wavelength is 570 nm and the linearity of calibrationcurve was investigated (5-10 ppm). the relative standard deviation for seven replicate e...

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must ...