Total Domination in Graphs with Given Girth

A set S of vertices in a graph G without isolated vertices is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γ _t (G) of G. In this paper, we establish an upper bound on the total domination number of a graph with minimum degree at least two in terms of its order and girth. We prove that if G is a graph of order n with minimum degree at least two and girth g, then γ _t (G) ≤ n/2 + n/g, and this bound is sharp. Our proof is an interplay between graph theory and transversals in hypergraphs. Michael A. Henning: Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.     

Quantum Pieri rules for isotropic Grassmannians

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.     

Saccharometrie

Ohne Zusammenfassung     

Spectrum Slicing for Multiple Access Channels with Heterogeneous Services

Wireless mobile networks from the fifth generation (5G) and beyond serve as platforms for flexible support of heterogeneous traffic types with diverse performance requirements. In particular, the broadband services aim for the traditional rate optimization, while the time-sensitive services aim for the optimization of latency and reliability, and some novel metrics such as Age of Information (AoI). In such settings, the key question is the one of spectrum slicing: how these services share the same chunk of available spectrum while meeting the heterogeneous requirements. In this work we investigated the two canonical frameworks for spectrum sharing, Orthogonal Multiple Access (OMA) and Non-Orthogonal Multiple Access (NOMA), in a simple, but insightful setup with a single time-slotted shared frequency channel, involving one broadband user, aiming to maximize throughput and using packet-level coding to protect its transmissions from noise and interference, and several intermittent users, aiming to either to improve their latency-reliability performance or to minimize their AoI. We analytically assessed the performances of Time Division Multiple Access (TDMA) and ALOHA-based schemes in both OMA and NOMA frameworks by deriving their Pareto regions and the corresponding optimal values of their parameters. Our results show that NOMA can outperform traditional OMA in latency-reliability oriented systems in most conditions, but OMA performs slightly better in age-oriented systems.     

In situ ion beam sputter deposition and X‐ray photoelectron spectroscopy (XPS) of multiple thin layers under computer control for combinatorial materials synthesis

Deposition of ultra‐thin layers under computer control is a frequent requirement in studies of novel sensors, materials screening, heterogeneous catalysis, the probing of band offsets near semiconductor junctions and many other applications. Often large‐area samples are produced by magnetron sputtering from multiple targets or by atomic layer deposition (ALD). Samples can then be transferred to an analytical chamber for checking by X‐ray photoelectron spectroscopy (XPS) or other surface‐sensitive spectroscopies. The ‘wafer‐scale’ nature of these tools is often greater than is required in combinatorial studies, where a few square centimetres or even millimetres of sample is sufficient for each composition to be tested. The large size leads to increased capital cost, problems of registration as samples are transferred between deposition and analysis, and often makes the use of precious metals as sputter targets prohibitively expensive. Instead we have modified a commercial sample block designed to perform angle‐resolved XPS in a commercial XPS instrument. This now allows ion‐beam sputter deposition from up to six different targets under complete computer control. Ion beam deposition is an attractive technology for depositing ultra‐thin layers of great purity under ultra‐high vacuum conditions, but is generally a very expensive technology. Our new sample block allows ion beam sputtering using the ion gun normally used for sputter depth‐profiling of samples, greatly reducing the cost and allowing deposition to be done (and checked by XPS) in situ in a single instrument. Precious metals are deposited cheaply and efficiently by ion‐beam sputtering from thin metal foils. Samples can then be removed, studied and exposed to reactants or surface treatments before being returned to the XPS to examine and quantify the effects. Copyright © 2016 The Authors Surface and Interface Analysis Published by John Wiley & Sons Ltd.     

Use of monomer fraction data in the parametrization of association theories

Association theories such as the CPA (cubic-plus-association), NRHB (non-random hydrogen bonding) equations of state and the various variants of SAFT (statistical associating fluid theory) have been extensively applied to phase equilibrium calculations. Such models can also be used for estimating the monomer fraction of hydrogen bonding compounds and their mixtures. Monomer fraction data are obtained from spectroscopic measurements and they are available for a few compounds such as pure water and alcohols as well as for some alcohol–alkane and similar mixtures. These data are useful for an understanding of the capabilities and limitations of association models. The purpose of this work is two-fold: (i) to compare the performance of three models, CPA, NRHB and sPC-SAFT, in predicting the monomer fraction of water, alcohols and mixtures of alcohol-inert compounds and (ii) to investigate whether “improved” model parameters can be obtained if monomer fraction data are included in the parameter estimation together with vapor pressures and liquid densities. The expression “improved” implies parameters which can represent several pure compound properties as well as monomer fraction data for pure compounds and mixtures. The accuracy of experimental monomer fraction data is discussed, as well as the role of monomer fraction data in clarifying which association scheme should be used in these equations of state. The results reveal that the investigated association models (CPA, sPC-SAFT and NRHB) can predict, at least qualitatively correct, monomer fractions of associating compounds and mixtures. Only, small differences are observed between the models. In addition, it has been shown that, using a suitable association scheme, a single set of parameters can describe satisfactorily vapor pressures, liquid densities and monomer fractions of water and alcohols. The 4C scheme is the best choice for water, while for methanol there is small difference between the 2B and 3B association schemes.     

Understanding the effect of cobalt particle size on Fischer-Tropsch synthesis: surface species and mechanistic studies by SSITKA and kinetic isotope effect

Co/γ-Al(2)O(3) catalysts with particle sizes in the range of 4-15 nm were investigated by isothermal hydrogenation (IH), temperature programmed hydrogenation (TPH), and steady-state isotopic transient kinetic analysis (SSITKA). Kinetic isotope effect experiments were used to probe possible mechanisms on Co/γ-Al(2)O(3) with different particle size. It was found that CO dissociated on Co/γ-Al(2)O(3) catalysts at 210 °C. The total amount of CO(2) formed following the dissociation depends on the cobalt crystal size. O-Co binding energy was found to be highly dependent on the Co metal particle size, whereas similar C-Co binding energy was found on catalysts with different Co particle size. Very strongly bonded carbon and oxygen surface species increased with decreasing particle size and acted as site blocking species in the methanation reaction. SSITKA experiments showed that the intrinsic activity (1/τ(CH(x))) remained constant as the particle size increased from 4 to 15 nm. The number of surface intermediates (N(CH(x))) increased with increasing particle size. The apparent activation energies were found similar for these catalysts, about 85 kJ/mol. D(2)-H(2) switches further confirmed that the particle size did not change the kinetically relevant steps in the reaction. The reactivity of the active sites on the 4 nm particles was the same as those on the 8, 11, and 15 nm particles, and only the number of total available surface active sites was less on the 4 nm particles than on the others.     

Synthesis of a small library of non-symmetric cyclic sulfamide HIV-1 protease inhibitors

A set of 11 non-symmetric cyclic sulfamide HIV-1 protease inhibitors were synthesized and evaluated. The use of a key microwave-assisted silver(I) oxide mediated selective mono N-benzylation reaction enabled fast and straightforward synthesis. The K_i values of the new inhibitors ranged between 0.28 μM and >20 μM.     

Slow dynamics of a colloidal lamellar phase

We used x-ray photon correlation spectroscopy to study the dynamics in the lamellar phase of a platelet suspension as a function of the particle concentration. We measured the collective diffusion coefficient along the director of the phase, over length scales down to the interparticle distance, and quantified the hydrodynamic interaction between the particles. This interaction sets in with increasing concentration and can be described qualitatively by a simplified model. No change in the microscopic structure or dynamics is observed at the transition between the fluid and the gel-like lamellar phases.     

Accelerated 18O-labeling in urinary proteomics

Proteolytic (18)O-labeling of peptides has been studied and optimized in order to improve the labeling efficiency and to accelerate the process without increasing the degree of incomplete labeling. Using peptides generated from tryptic digested bovine serum albumin (BSA) and cytochrome c as model proteins, it was shown that complete labeling was achieved after 2 h at pH 6. To increase the sample throughput in a bottom-up proteomic setup, tryptic digestion of proteins in-solution was replaced with tryptic digestion using immobilized trypsin. As a result, an integrated approach was made possible, where both digestion (pH 8) and (18)O/(16)O-labeling of the resulting peptides (pH 6) were done using immobilized trypsin beads. This simplified the sample handling and reduced the overall reaction time significantly: the setup enabled tryptic digestion and (18)O/(16)O-labeling without sample transfer steps within 3.5 h with average (18)O/(16)O-ratios of 0.96±0.13 in aqueous buffer. The initial results were confirmed with a more complex matrix, by spiking urine with the model proteins, yielding results comparable with the ratios obtained in buffer. Satisfying ratios were also achieved regarding urinary proteins identified in a full scale bottom-up experiment. Average (18)O/(16)O-peptide ratios of 0.83±0.13 and 0.91±0.27 indicated good performance in a highly relevant matrix for biomarker discovery.