A hexachloro congener (Q1-hex) of the natural heptachloro-1'-methyl-1,2'-bipyrrole Q1 was recently observed as a byproduct of the Q1 synthesis. NMR investigation confirmed that Q1-hex has a proton on a carbon in beta-position to a nitrogen. Three isomers are possible that fulfill this prerequisite; unfortunately, however, the NMR data were not sufficient to distinguish among the three structura...

The terminology and notation used here are introduced in the following articles: [24], [27], [1], [3], [4], [2], [14], [12], [25], [22], [23], [11], [21], [8], [9], [6], [26], [15], [10], [18], [17], [5], [20], [19], [7], [13], and [16]. In this paper n is a natural number. We now state a number of propositions: (1) For all subsets A, B of E T such that A meets B holds proj1◦ A meets proj1◦ B. ...

We tackle the containment problem for conjunctive queries with negation, which takes two queries q1 and q2 as input and asks if q1 is contained in q2. A general approach for solving this problem consists of considering all completions of q1 (intuitively these completions represent all canonical databases that satisfy q1) and checking if each completion yields the same answer on q2. Since the to...

In this paper, we first give the maximal and minimal values of the ranks and inertias of the quadratic matrix functions q1(X) = Q1 − XP1X and q2(X) = Q2 − XP2X subject to a consistent matrix equation AX = B, where Q1, Q2, P1 and P2 are Hermitian matrices. As applications, we derive necessary and sufficient conditions for the solution of AX = B to satisfy the quadratic equality XP1X ∗ = Q1 and X...