On the equivalence of contact invariants in sutured Floer homology theories

We recently defined an invariant of contact manifolds with convex boundary in Kronheimer and Mrowka's sutured monopole Floer homology theory. Here, we prove that there is an isomorphism between sutured monopole Floer homology and sutured Heegaard Floer homology which identifies our invariant with the contact class defined by Honda, Kazez and Mati\'c in the latter theory. One consequence is that the Legendrian invariants in knot Floer homology behave functorially with respect to Lagrangian concordance. In particular, these invariants provide computable and effective obstructions to the existence of such concordances. Our work also provides the first proof which does not rely on the relative Giroux correspondence that the vanishing or non-vanishing of Honda, Kazez and Mati\'c's contact class is a well-defined invariant of contact manifolds.Comment: 63 pages, 13 figures; v2: corrected Lemma 3.3 and subsequent material, many other small changes; v3: accepted version, substantially revised to correct the proof of the main theore

Cationic Alkylaluminum-Complexed Zirconocene Hydrides as Participants in Olefin Polymerization Catalysis

The alkylaluminum-complexed zirconocene trihydride cation [(SBI)Zr(μ-H)_3(AliBu_2)_2]^+, which is obtained by reaction of (SBI)ZrCl_2 with [Ph_3C][B(C_6F_5)_4] and excess HAl^iBu_2 in toluene solution, catalyzes the formation of isotactic polypropene when exposed to propene at -30 °C. This cation remains the sole observable species in catalyst systems free of AlMe compounds. In the presence of AlMe_3, however, exposure to propene causes the trihydride cation to be completely converted, under concurrent consumption of all hydride species by propene hydroalumination, to the doubly Me-bridged cation [(SBI)Zr(μ-Me)_2AlMe_2]^+. The latter then becomes the resting state for further propene polymerization, which produces, by chain transfer to Al, mainly AlMe_2-capped isotactic polypropene

Alkylaluminum-complexed zirconocene hydrides: identification of hydride-bridged species by NMR spectroscopy

Reactions of unbridged zirconocene dichlorides, (R_nC_5H_5−n)_2ZrCl_2 (n = 0, 1, or 2), with diisobutylaluminum hydride (HAl^iBu_2) result in the formation of tetranuclear trihydride clusters of the type (R_nC_5H_5−n)_2Zr(μ-H)_3(Al^iBu_2)_3(μ-Cl)_2, which contain three [Al^iBu_2] units. Ring-bridged ansa-zirconocene dichlorides, Me_2E(R_nC_5H_4−n)_2ZrCl_2 with E = C or Si, on the other hand, are found to form binuclear dihydride complexes of the type Me_2E(R_nC_5H_4−n)_2Zr(Cl)(μ-H)_2Al^iBu_2 with only one [Al^iBu_2] unit. The dichotomy between unbridged and bridged zirconocene derivatives with regard to tetranuclear versus binuclear product formation is proposed to be connected to different degrees of rotational freedom of their C_5-ring ligands. Alkylaluminum-complexed zirconocene dihydrides, previously observed in zirconocene-based precatalyst systems activated by methylalumoxane (MAO) upon addition of HAl^iBu_2 or Al^iBu_3, are proposed to be species of the type Me_2Si(ind)_2Zr(Me)(μ-H)_2Al^iBu_2, stabilized by interaction of their terminal Me group with a Lewis acidic site of MAO

Industrial Waste Management through Material and Energy Recovery: The Case of Hwange Power Station, Zimbabwe

The aim of this study was to examine industrial waste minimisation through material and energy recovery at Hwange Power Station in Zimbabwe. This project is significant in that it envisages the opportunities of boosting power output through the use of industrial waste management at international and national levels. Most industries in Zimbabwe are facing challenges in the sustainable waste disposal and the nation at large is experiencing severe power shortages. A detailed descriptive study was undertaken to analyse the potential of boosting power output whilst sustainably managing industrial waste. The research administered 200 questionnaires which are approximately 30% of the entire population directly involved in the core waste generating activities. Out of the 200 questionnaires that were administered, a total of 182 were completed and returned in time for data compilation giving a response rate of 88.5%. The qualitative and quantitative research designs were used with direct field observations, interviews and questionnaires as primary sources of data. Secondary data was acquired from existing literature to boost and support the research findings. The main findings of the research divulged the types and quantities of waste from power generation activities, the effectiveness of the current methods of waste management and the definitive degree of waste management through material and energy recovery at Hwange Power Station. The study also revealed that energy and material recovery are essential methods of industrial waste management as well as opportunities for boosting power output. It was therefore recommended that Hwange Power Station needs to consider investing in energy recovery to boost power output at the same time sustainably managing waste

Instanton L-spaces and splicing

We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman, Pinzon-Caicedo, and Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner's earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2,C)-representation.Comment: 16 pages, 8 figure

Zero-surgery characterizes infinitely many knots

We prove that 0 is a characterizing slope for infinitely many knots, namely the genus-1 knots whose knot Floer homology is 2-dimensional in the top Alexander grading, which we classified in recent work and which include all $(-3,3,2n+1)$ pretzel knots. This was previously only known for $5_2$ and its mirror, as a corollary of that classification, and for the unknot, trefoils, and the figure eight by work of Gabai from 1987.Comment: 9 pages, 1 figur