The Angle Defect for Odd-Dimensional Simplicial Manifolds

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that χ(link(ηⁱ, K)) = 2 for all i-simplices ηⁱ of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Evidence for a two-step mechanism in electronically selective single-walled carbon nanotube reactions

Covalent and noncovalent chemistries that are selective to single-walled carbon nanotubes of a particular electronic type have become increasingly important for electronic structure separation and on-chip modification of nanoelectronic devices. By monitoring transient Raman spectroscopy and photoluminescence (PL) during a reaction with 4-chlorobenzene diazonium in aqueous solution, evidence for a characteristic two-step mechanism with two distinct time constants is uncovered. A long-lived intermediate selectively and noncovalently binds and partially dopes the nanotube surface (tau = 2.4 min). A slower, covalent reaction is tracked using the time-dependent increase in the disorder mode in Raman (tau = 73 min). The transient Raman and PL data are well described using a series of two first-order reactions. The covalent bonding step can be deactivated by changing the structure of the surfactant adsorbed phase, further supporting the mechanism.     

Nitrogen extrusion from pyrazoline-substituted porphyrins and chlorins using long wavelength visible light

Protoporphyrin reacts with diazomethane to give pyrazolines which at long wavelength (approximately 630 nm) extrude nitrogen to give the corresponding cyclopropyl derivatives.     

Evidence for unfolding and refolding of gas-phase cytochrome <Emphasis Type="Italic">c</Emphasis> ions in a Paul trap

The folding pathways of gas-phase cytochrome c ions produced by electrospray ionization have been studied by an ion trapping/ion mobility technique that allows conformations to be examined over extended timescales (10 ms to 10 s). The results show that the +9 charge state emerges from solution as a compact structure and then rapidly unfolds into several substantially more open structures, a transition that requires 30-60 ms; over substantially longer timescales (250 ms to 10 s) elongated states appear to refold into an array of folded structures. The new folded states are less compact than those that are apparent during the initial unfolding. Apparently, unfolding to highly open conformations is a key step that must occur before +9 ions can sample more compact states that are stable at longer times.     

Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Dry Reforming of Methane on a Highly‐Active Ni‐CeO2 Catalyst: Effects of Metal‐Support Interactions on C−H Bond Breaking

Ni‐CeO₂ is a highly efficient, stable and non‐expensive catalyst for methane dry reforming at relative low temperatures (700 K). The active phase of the catalyst consists of small nanoparticles of nickel dispersed on partially reduced ceria. Experiments of ambient pressure XPS indicate that methane dissociates on Ni/CeO₂ at temperatures as low as 300 K, generating CH_x and CO_x species on the surface of the catalyst. Strong metal–support interactions activate Ni for the dissociation of methane. The results of density‐functional calculations show a drop in the effective barrier for methane activation from 0.9 eV on Ni(111) to only 0.15 eV on Ni/CeO_2?x(111). At 700 K, under methane dry reforming conditions, no signals for adsorbed CH_x or C species are detected in the C 1s XPS region. The reforming of methane proceeds in a clean and efficient way.     

Total synthesis and biochemical characterization of mirror image barnase

In this study we synthesized and characterized mirror image barnase (B. amyloliquefaciens ribonuclease). d-Barnase was identical to l-barnase, when analyzed by liquid chromatography and mass-spectrometry. Proteolysis of the mirror image enzyme revealed that in contrast to its native counterpart, d-barnase was completely stable to digestive proteases. In enzymatic assays, d-barnase had the reciprocal chiral specificity and was fully active towards mirror image substrates. Interestingly, d-barnase also hydrolyzed the substrate of the native chirality, albeit 4000 times less efficiently. This effect was further confirmed by digesting a native 112-mer RNA with the enzyme. Additional studies revealed that barnase accommodates a range of substrates with various chiralities, but the prime requirement for guanosine remains. These studies point toward using mirror image enzymes as modern agents in biotechnology.     

An ion trap-ion mobility-time of flight mass spectrometer with three ion sources for ion/ion reactions

This instrument combines the capabilities of ion/ion reactions with ion mobility (IM) and time-of-flight (TOF) measurements for conformation studies and top-down analysis of large biomolecules. Ubiquitin ions from either of two electrospray ionization (ESI) sources are stored in a three dimensional (3D) ion trap (IT) and reacted with negative ions from atmospheric sampling glow discharge ionization (ASGDI). The proton transfer reaction products are then separated by IM and analyzed via a TOF mass analyzer. In this way, ubiquitin +7 ions are converted to lower charge states down to +1; the ions in lower charge states tend to be in compact conformations with cross sections down to ～880 Ų. The duration and magnitude of the ion ejection pulse on the IT exit and the entrance voltage on the IM drift tube can affect the measured distribution of conformers for ubiquitin +7 and +6. Alternatively, protein ions are fragmented by collision-induced dissociation (CID) in the IT, followed by ion/ion reactions to reduce the charge states of the CID product ions, thus simplifying assignment of charge states and fragments using the mobility-resolved tandem mass spectrum. Instrument characteristics and the use of a new ion trap controller and software modifications to control the entire instrument are described.