We consider a new class of non–hermitian random matrices, namely the ones which have the form of sums of freely independent terms which involve unitary matrices. After deriving some general identities describing additive properties of unitary matrices, we solve three particular models: CUE plus CUE, CUE plus . . . plus CUE (i. e. the sum of an arbitrary number of CUE matrices), and CUE plus a r...

an efficient and environmentally friendly procedure for one-pot synthesis of 13-acetyl-9-methyl-11-ox-8-oxa-10,12-diazatricyclo [7.3.1. ] trideca-2,4,6-triene from salicylaldehyde, acetylaceton and urea via biginelli condensation and intramolecular michael-addition by using magnesium bromide as an expensive and easily available catalyst under solvent-free condition is desired. the structural el...

signed digit (sd) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. such carry-free addition is primarily a three-step process; adding the equally weighted sds to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the transfers to...

Does the trace language of a given vector addition system (VAS) intersect with a given context-free language? This question lies at the heart of several verification questions involving recursive programs with integer parameters. In particular, it is equivalent to the coverability problem for VAS that operate on a pushdown stack. We show decidability in dimension one, based on an analysis of a ...

The separability problem for word languages of a class C by languages of a class S asks, for two given languages I and E from C, whether there exists a language S from S that includes I and excludes E, that is, I ⊆ S and S ∩E = ∅. In this work, we assume some mild closure properties for C and study for which such classes separability by a piecewise testable language (PTL) is decidable. We chara...