ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Real-time queueing theory: A tutorial presentation with an admission control application

Real-time scheduling, or scheduling with respect to a deadline, is critical in many application areas such as telecommunications, control systems, and manufacturing. This paper presents a novel approach to real-time scheduling based on a queueing theory model. Using real-time queueing theory (RTQT), one can analytically determine the distribution of the lead-time profile (i.e., the time until the deadline is reached) of customers waiting for service. Emphasis is placed on the development of the equations used to determine the lead-time profile distribution. The development of the GI/G/1 case is presented and confirmed using simulation. Simulation results confirm prior research for the M/M/1 and GI/M/1 case. As a practical application, RTQT is used to implement a packet admission control algorithm for a telecommunications network. Using this algorithm, packet lateness was reduced by up to 31%. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Parameters of Bipartite Q-polynomial Distance-Regular Graphs

Let denote a bipartite distance-regular graph with diameter D 3 and valency k 3. Suppose ₀, ₁, ..., _D is a Q-polynomial ordering of the eigenvalues of . This sequence is known to satisfy the recurrence _{i – 1} – _i + _{i + 1} = 0 (0 > i > D), for some real scalar . Let q denote a complex scalar such that q + q ^–1 = . Bannai and Ito have conjectured that q is real if the diameter D is sufficiently large.We settle this conjecture in the bipartite case by showing that q is real if the diameter D 4. Moreover, if D = 3, then q is not real if and only if ₁ is the second largest eigenvalue and the pair (, k) is one of the following: (1, 3), (1, 4), (1, 5), (1, 6), (2, 4), or (2, 5). We observe that each of these pairs has a unique realization by a known bipartite distance-regular graph of diameter 3.     

Absolute quantitation of host cell proteins in recombinant human monoclonal antibodies with an automated CZE‐ESI‐MS/MS system

We report the first use of CZE for absolute characterization of host cell proteins (HCPs) in recombinant human monoclonal antibodies. An electrokinetically pumped nanoelectrospray interface was used to couple CZE with a tandem mass spectrometer. Three isotopic‐labeled peptides (LSFDKDAMVAR, VDIVENQAMDTR, and LVSDEMVVELIEK) were synthesized by direct incorporation of an isotope‐labeled lysine or arginine. The heavy‐labeled peptides were spiked in the HCP digests at known concentrations. After CZE‐ESI‐MS/MS analysis, the peaks of native and isotopic‐labeled peptides were extracted with mass tolerance ≤ 5 ppm from the electropherograms, and the ratios of peak area between native and isotopic‐labeled peptides pairs were calculated. Calibration curves (the ratios of peak area versus spiked peptide amount) with R² values of 0.999, 0.997, and 0.999 were obtained for the three HCP peptides, and the absolute amounts of the three proteins present were determined to be at the picomole level in a 20 μg sample of digested HCPs. The target proteins were present at the 7–30 ppt level in the purified HCP samples.     

A New Plethysm Formula for Symmetric Functions

This paper gives a new formula for the plethysm of power-sum symmetric functions and Schur symmetric functions with one part. The form of the main result is that for b,

Application of electrospray ionization with Fourier transform ion cyclotron resonance mass spectrometry for structural screening of core oligosaccharides from lipopolysaccharides of the bacteria Proteus

Electrospray ionization with Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) was used for screening and structural elucidation of core oligosaccharides isolated from lipopolysaccharides of bacteria of the genus Proteus. Mass spectra allowed the determination of the molecular masses with high accuracy and the estimation of the chemical heterogeneity of the samples. They did not, however, provide sufficient information to identify structural details of the branched oligosaccharides. Therefore, various fragmentation techniques for determining such details were examined. Infrared multiphoton dissociation tandem mass spectrometry (IRMPD-MS/MS) experiments in negative ion mode resulted in cleavage between the structurally conserved inner core region and the variable outer core region. Positive ion capillary skimmer dissociation mass spectra showed numerous fragment ion peaks, including those corresponding to the subsequent cleavage of the glycosidic linkages starting from the non-reducing end of the oligosaccharide. Despite their complexity, these mass spectrometric studies allowed confirmation of previously determined Proteus lipopolysaccharide core structures, and identification of new related structures in other strains of these bacteria.     

Totally geodesic boundaries of knot complements

Given a compact orientable -manifold whose boundary is a hyperbolic surface and a simple closed curve in its boundary, every knot in is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of is as small as you like.