Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.     

High‐molar‐mass polypropene with tunable elastic properties by hafnocene/borate catalysts

Elastic polypropene has gained growing industrial and academic interest as a thermoplastic elastomer. In this study, “rac”‐ and “meso”‐dimethylsilyl(3‐benzylindenyl)(2‐methylindenyl)hafnium dichloride complexes (Hfr and Hfm, respectively), activated with [NHMe₂Ph][B(C₆F₅)₄]/triisobutyl aluminum, were used in propene polymerization. Using these catalyst systems, we obtained polymers with high molar masses, up to 550 kg/mol, and moderate isotacticities between 34 and 52%. By varying the polymerization conditions, we could modify the polymer microstructure and molar mass. ¹³C NMR was used to calculate the polymer pentad sequence distributions. The crystalline parts of the polymers were analyzed with the differential scanning calorimetry successive self‐nucleation and annealing (SSA) technique. The SSA thermograms revealed that Hfr produced polypropene with a more uniform lamellar structure than Hfm. The mechanical properties were tested with dynamic mechanical analysis creep‐recovery tests. In the series, the polymers with the lowest isotacticities and therefore lowest crystallinities showed the best elastic properties. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4743–4751, 2006     

Synthesis of Cembranoid Analogues through Ring‐Closing Metathesis of Terpenoid Precursors: A Challenge Regarding Ring‐Size Selectivity

A systematic study on ring‐closing metathesis with Grubbs II catalyst to cembranoid macrocycles is described. Acyclic terpenoids with a functional group X in the homoallylic position relative to an RCM active terminus and substituents R, R¹ directly attached to the other terminal double bond were prepared from geraniol derived trienes and fragments that are based on bromoalkenes and dimethyl malonate. Such terpenoids were suitable precursors, despite the presence of competing double bonds in their framework. The size of R and R¹ is crucial for successful macrocyclization. Whereas small alkyl substituents at the double bond directed the RCM towards six‐membered ring formation, cross metathesis leading to dimers dominated for bulkier alkyl groups. A similar result was obtained for precursors without functional group X. In the case of unsymmetrically substituted terpenoid precursor (R=Et, R¹=Me) with homoallylic OTBS or OMe group, the RCM could be controlled towards formation of macrocyclic cembranoids, which were isolated with excellent E‐selectivity. The role of the substituents was further studied by quantum chemical calculations of simplified model substrates. Based on these results a mechanistic rationale is proposed.     

Toll number of the Cartesian and the lexicographic product of graphs

Toll convexity is a variation of the so-called interval convexity. A tolled walk $T$ between two non-adjacent vertices $u$ and $v$ in a graph $G$ is a walk, in which $u$ is adjacent only to the second vertex of $T$ and $v$ is adjacent only to the second-to-last vertex of $T$. A toll interval between $u,v\in V\left(G\right)$ is a set $T_G(u,v)=\{x\in V\left(G\right):x\text{ lies on a tolled walk between }u\text{ and }v\}$. A set $S?V\left(G\right)$ is toll convex, if $T_G(u,v)?S$ for all $u,v\in S$. A toll closure of a set $S?V\left(G\right)$ is the union of toll intervals between all pairs of vertices from $S$. The size of a smallest set $S$ whose toll closure is the whole vertex set is called a toll number of a graph $G$, $tn\left(G\right)$. The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if $H$ is not isomorphic to a complete graph, $tn(G°H)\le 3?tn\left(G\right)$. We give some necessary and sufficient conditions for $tn(G°H)=3?tn\left(G\right)$. Moreover, if $G$ has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with $tn(G°H)=2$ are characterized. Finally, the formula for $tn(G°H)$ is given — it is described in terms of the so-called toll-dominating triples or, if $H$ is complete, toll-dominating pairs.     

Comparative analysis of CE‐SSCP to standard RFLP‐CE‐FLA method in quantification of known viral variants within an RNA virus quasispecies

RNA viruses display the highest replication error rate in our biosphere, leading to highly diverse viral populations termed quasispecies. The gold standard method for detection and quantification of variants in a quasispecies is cloning and sequencing, but it is expensive, laborious and time consuming. Therefore, other mutation detection approaches, including SSCP, are often used. In this study, we demonstrate development and the usage of a CE‐SSCP method for quantification of two nearly identical viral variants in heterogenic population of a mumps virus strain and its comparison to RFLP‐CE‐fragment length analysis (RFLP‐CE‐FLA). Analyzed PCR fragments were of the same size (245 bp) with one difference in their nucleotide sequence. The limit of detection of both methods was at 5% of the minor variant. When PCR amplicons of the two variants were pooled, methods' results were very similar. On the contrary, the quantification results of samples in which variants were mixed prior to PCR showed substantial difference between the two methods. Our results indicate that although both methods can be used for detection and monitoring of a specific mutation within a viral population, caution should be taken when quantitative analysis of complex samples is based solely on results of one method.     

Strategies for "wiring" redox-active proteins to electrodes and applications in biosensors, biofuel cells, and nanotechnology

In this tutorial review the basic approaches to establish electrochemical communication between redox-active proteins and electrodes are elucidated and examples for applications in electrochemical biosensors, biofuel cells and nanotechnology are presented. The early stage of protein electrochemistry is described giving a short overview over electron transfer (ET) between electrodes and proteins, followed by a brief introduction into experimental procedures for studying proteins at electrodes and possible applications arising thereof. The article starts with discussing the electrochemistry of cytochrome c, the first redox-active protein, for which direct reversible ET was obtained, under diffusion controlled conditions and after adsorption to electrodes. Next, examples for the electrochemical study of redox enzymes adsorbed on electrodes and modes of immobilization are discussed. Shortly the experimental approach for investigating redox-active proteins adsorbed on electrodes is outlined. Possible applications of redox enzymes in electrochemical biosensors and biofuel cells working by direct ET (DET) and mediated ET (MET) are presented. Furthermore, the reconstitution of redox active proteins at electrodes using molecular wire-like units in order to "wire" the proteins to the electrode surface and possible applications in nanotechnology are discussed.     

Simple rules for the understanding of Heusler compounds

Heusler compounds are a remarkable class of intermetallic materials with 1:1:1 (often called Half-Heusler) or 2:1:1 composition comprising more than 1500 members. Today, more than a century after their discovery by Fritz Heusler, they are still a field of active research. New properties and potential fields of applications emerge constantly; the prediction of topological insulators is the most recent example. Surprisingly, the properties of many Heusler compounds can easily be predicted by the valence electron count. Their extremely flexible electronic structure offers a toolbox which allows the realization of demanded but apparently contradictory functionalities within one ternary compound. Devices based on multifunctional properties, i.e. the combination of two or more functions such as superconductivity and topological edge states will revolutionize technological applications. The subgroup of more than 250 semiconductors is of high relevance for the development of novel materials for energy technologies. Their band gaps can readily be tuned from zero to ≈4 eV by changing the chemical composition. Thus, great interest has been attracted in the fields of thermoelectrics and solar cell research. The wide range of their multifunctional properties is also reflected in extraordinary magneto-optical, magnetoelectronic, and magnetocaloric properties. The most prominent example is the combination of magnetism and exceptional transport properties in spintronic devices. To take advantage of the extremely high potential of Heusler compounds simple rules for the understanding of the structure, the electronic structure and the relation to the properties are reviewed.