Dinuclear complexes with a μ-cyano ligand. Part XI(1). Synthesis and characterization of several derivatives ofcis-[Co(NH3)(en)2(H2O)]3+

Summary The new complex double saltscw-[Co(NH₃)(en)₂(H₂O)]₂ [M(CN)₄]₃ (en = ethylenediamine; M = Ni, Pd or Pt),cis-[Co(NH₃(en)₂(H₂O)]₂[FeNO(CN)₅]₃ andcis-[Co(NH₃)(en)₂(H₂O)][Co(CN)₆] have been synthesized and by anation in the solid state the corresponding new dinuclear complexes with a cyano bridgecis- ortrans-[(NH₃)(en)₂Co-NC-M(CN)₃]₂ [M(CN)₄] (M = Ni, Pd or Pt);cis-, trans-[(NH₃)(en)₂Co-NC-FeNO(CN)₄]₂[FeNO(CN)₅] andcis-[(NH₃)(en)₂Co-NC-Co(CN)₅ have been prepared. The complexes have been characterized by chemical analysis, t.g. measurements, and by i.r. and electronic spectroscopy. With [Ni(CN)₄][^2– and [Co(CN)in]₆ ^3– only thecis-isomer is produced; with [Pd(CN)₄]^2–, [Pt(CN)₄]^2– and [FeNO(CN)₅]^2– thetrans- isomer is the dominant species. The dinuclear complex derived from [Pt(CN)₄]^2– shows strong Pt-Pt interactions both in the solid state and in solution.     

Boundary Regularity of Rotating Vortex Patches

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C ^∞, provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C ² norm. Our proof is based on Burbea’s approach to V-states.     

Some Evidence on the Polymerization of Phenylglycidylether Using AIP/ZnCl2 as Initiator System

Abstract

The influence of the composition of the initiator system used in the polymerization of PGE is studied. Structural studies of intermediate species by NMR and IR spectroscopies are made which allow confirmation of some characteristics on the previously proposed mechanism and clarification of the mechanism leading to the chlorinated insoluble polymer fraction. This can be explained by the formation of halogenated oligomers in the first stage of the reaction which interchange with different aluminum alkoxides to give another type of initiator system.     

An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Rings with x(yz)=z(yx)

In non-associative rings the associative law is replaced by various weaker identities. In this paper the identity x.yz = z.yx is considered. Let R be a ring satisfying this identity. It is obvious that if R has an identity element, then R is both commutative and associative. It is shown that if R is prime, third power associative, 2-torsion free, and has a nonzero idempotent, then this idempotent must be an identity and hence R must be commutative and associative.     

Access to Enantiopure Advanced Intermediates en Route to Madangamines

The synthesis of enantiopure ABCE and ABCD tetracyclic advanced intermediates en route to madangamine alkaloids and studies for the construction of the triunsaturated 15-membered D ring of madangamine B and the saturated 13-membered D ring of madangamine E are reported.