The soliton connection

It is pointed out that the linear scattering problem for a non-linear evolution equation which admits soliton solutions may be described in terms of a linear connection on a principal SL(2, ). The equation in question is satisfied if and only if the curvature of this connection vanishes. Some other properties of the curvature are identified. The sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations are treated explicitly.On leave of absence. Visit supported by NSF Grant 36217 and by the Norman Foundation.     

Positivity and monotonicity properties ofC 0-semigroups. I

If exp {?tH}, exp {?tK}, are self-adjoint, positivity preserving, contraction semigroups on a Hilbert space ?=L ²(X;dμ) we write (*) $$e^{ - tH} \succcurlyeq e^{ - tK} \succcurlyeq 0$$ whenever exp {?tH}-exp {?tK} is positivity preserving for allt≧0 and then we characterize the class of positive functions for which (*) always implies $$e^{ - tf(H)} \succcurlyeq e^{ - tf(K)} \succcurlyeq 0.$$ This class consists of thef∈C ^∞(0, ∞) with $$( - 1)^n f^{(n + 1)} (x) \geqq 0,x \in (0,\infty ),n = 0,1,2, \ldots .$$ In particular it contains the class of monotone operator functions. Furthermore if exp {?tH} isL ^p (X;dμ) contractive for allp∈[1, ∞] and allt>0 (or, equivalently, forp=∞ andt>0) then exp {?tf(H)} has the same property. Various applications to monotonicity properties of Green's functions are given.     

Optimal Synthetic Glycosylation of a Therapeutic Antibody

Glycosylation patterns in antibodies critically determine biological and physical properties but their precise control is a significant challenge in biology and biotechnology. We describe herein the optimization of an endoglycosidase‐catalyzed glycosylation of the best‐selling biotherapeutic Herceptin, an anti‐HER2 antibody. Precise MS analysis of the intact four‐chain Ab heteromultimer reveals nonspecific, non‐enzymatic reactions (glycation), which are not detected under standard denaturing conditions. This competing reaction, which has hitherto been underestimated as a source of side products, can now be minimized. Optimization allowed access to the purest natural form of Herceptin to date (≥90 %). Moreover, through the use of a small library of sugars containing non‐natural functional groups, Ab variants containing defined numbers of selectively addressable chemical tags (reaction handles at Sia C1) in specific positions (for attachment of cargo molecules or “glycorandomization”) were readily generated.     

Synthesis and characterization of Schiff bases derived from 5-aminouracil and N-heterocyclic aldehydes

New Schiff bases of 5-aminouracil have been synthesized by the 1: 1 condensation with N-heterocyclic aldehydes. The new compounds were characterized by elemental analyses and ¹H NMR spectroscopy. Under similar conditions, the condensation of 6-aminouracil with aldehydes failed to yield the desired Schiff base. Interestingly, the reaction of 6-aminouracil with 6-methylpyridine-2-carbaldehyde resulted in an unusual compound, 2-methyl-6-[7-(6-methylpyridin-2-yl)-2,4-dioxo-1,2,3,4-tetrahydropyrimido[4,5-d]pyrimidin-5-yl]-pyridinium methanesulfonate, whose crystal structure was elucidated by X-ray crystallography.     

Electrochemical Characterization of Vertically Aligned Carbon Nanofiber Arrays Prepared by Hole‐mask Colloidal Lithography

Nanoelectrode arrays consisting of vertically aligned carbon nanofibers were prepared through plasma enhanced chemical vapor deposition and patterned using hole‐mask colloidal lithography (HCL), a simple fabrication method employed as a cost‐effective patterning alternative to the conventional electron beam lithography. The density of the carbon nanofibers was easily altered by changing the concentration of the polystyrene spheres employed in HCL. Cyclic voltammetry and chronoamperometry were used to electrochemically characterize the arrays of different density. Results indicate that the density of the carbon nanofibers leads to differences in the macro/micro electroactive surface areas.     

Low‐Temperature Solution Synthesis of Few‐Layer 1T ′‐MoTe2 Nanostructures Exhibiting Lattice Compression

Molybdenum ditelluride, MoTe₂, is emerging as an important transition‐metal dichalcogenide (TMD) material because of its favorable properties relative to other TMDs. The 1T ′ polymorph of MoTe₂ is particularly interesting because it is semimetallic with bands that overlap near the Fermi level, but semiconducting 2H‐MoTe₂ is more stable and therefore more accessible synthetically. Metastable 1T ′‐MoTe₂ forms directly in solution at 300 °C as uniform colloidal nanostructures that consist of few‐layer nanosheets, which appear to exhibit an approx. 1 % lateral lattice compression relative to the bulk analogue. Density functional theory calculations suggest that small grain sizes and polycrystallinity stabilize the 1T ′ phase in the MoTe₂ nanostructures and suppress its transformation back to the more stable 2H polymorph through grain boundary pinning. Raman spectra of the 1T ′‐MoTe₂ nanostructures exhibit a laser energy dependence, which could be caused by electronic transitions.     

Multiutility service companies: A complex systems model of increasing resource efficiency

Domestic households account for a significant portion of energy consumption and carbon emissions in the United Kingdom. Gains in energy and resource efficiency are undermined by the continuing rise in consumption. A multiutility service company (MUSCo) could enable households to make efficiency improvements through energy technologies and demand management, thus reducing overall consumption. We present a system dynamics model for the domestic energy demand and supply system in the United Kingdom, in which MUSCos compete with traditional utility providers. The market transition toward a leasing contracted service is examined and various potential business models explored. © 2015 Wiley Periodicals, Inc. Complexity 21: 23–33, 2016