An adjustment scheme for nonlinear pricing problem with two buyers

We examine a contracting problem with asymmetric information in a monopoly pricing setting. Traditionally, the problem is modeled as a one-period Bayesian game, where the incomplete information about the buyers’ preferences is handled with some subjective probability distribution. Here we suggest an iterative online method to solve the problem. We show that, when the buyers behave myopically, the seller can learn the optimal tariff by selling the product repeatedly. In a practical modification of the method, the seller offers linear tariffs and adjusts them until optimality is reached. The adjustment can be seen as gradient adjustment, and it can be done with limited information and so that it benefits both the seller and the buyers. Our method uses special features of the problem and it is easily implementable.     

Markov Chains on Graded Posets

We consider two types of discrete-time Markov chains where the state space is a graded poset and the transitions are taken along the covering relations in the poset. The first type of Markov chain goes only in one direction, either up or down in the poset (an up chain or down chain). The second type toggles between two adjacent rank levels (an up-and-down chain). We introduce two compatibility concepts between the up-directed transition probabilities (an up rule) and the down-directed (a down rule), and we relate these to compatibility between up-and-down chains. This framework is used to prove a conjecture about a limit shape for a process on Young’s lattice. Finally, we settle the questions whether the reverse of an up chain is a down chain for some down rule and whether there exists an up or down chain at all if the rank function is not bounded.     

Heterogenization of racemic ethylenebis(1-indenyl)zirconium dichloride on trimethylaluminum vapor modified silica surface

Heterogeneous metallocene catalysts were prepared by adsorbing rac-Et(Ind)₂ZrCl₂ on a modified silica surface in solution. The modification of silica was conducted in gas phase with atomic layer chemical vapor deposition (ALCVD) technique, where the silica, preheated at either 350 or 600°C, was allowed to react with vaporized trimethylaluminum (TMA) at 250°C. Modified carriers and heterogeneous catalysts were characterized with FTIR, ¹H MAS (magic-angle spinning) NMR, ¹³C, and ²⁹Si CP (cross-polarization) MAS NMR spectroscopies and elemental analyses. In the reaction of TMA with silica, a saturated surface was formed consisting of different (---O)_4−nSi(CH₃)_n (n=1, 2 or 3) and ---AlCH₃ groups. The ratio of ---SiMe to ---AlMe groups was approximately 1.5 in the TMA/SiO₂ carriers. When the metallocene was adsorbed onto the carrier it seemed to react with the surface ---AlCH₃ groups and possibly ---ZrCH₃ groups were formed. Heterogeneous catalysts were tested in the polymerization of ethylene and propylene in the presence of methylalumoxane (MAO). And they produced similar polymer as the homogeneous rac-Et(Ind)₂ZrCl₂ catalyst, but with lower activity. A catalyst with the best activity was achieved from silica that was preheated at 600°C. Moreover, leaching of catalyst was examined whereupon a part of zirconium was observed to desorb from the carrier.     

Instability of matchings in decentralized markets with various preference structures

In any two-sided matching market, a stable matching can be found by a central agency using the deferred acceptance procedure of Gale and Shapley. But if the market is decentralized and information is incomplete then stability of the ensuing matching is not to be expected. Despite the prevalence of such matching situations, and the importance of stability, little theory exists concerning instability. We discuss various measures of instability and analyze how they interact with the structure of the underlying preferences. Our main result is that even the outcome of decentralized matching with incomplete information can be expected to be “almost stable” under reasonable assumptions.     

Congestion and cascades in payment systems

We develop a parsimonious model of the interbank payment system. The model incorporates an endogenous instruction arrival process, a scale-free topology of payments between banks, a fixed total liquidity which limits banks’ capacity to process arriving instructions, and a global market that distributes liquidity. We find that at low liquidity the system becomes congested and payment settlement loses correlation with payment instruction arrival, becoming coupled across the network. The onset of congestion is evidently related to the relative values of three characteristic times: the time for banks’ net position to return to 0, the time for a bank to exhaust its liquidity endowment, and the liquidity market relaxation time. In the congested regime settlement takes place in cascades having a characteristic length scale. A global liquidity market substantially attenuates congestion, requiring only a small fraction of the payment-induced liquidity flow to achieve strong beneficial effects.     

Confinement versus chiral symmetry

We construct an effective Lagrangian which illustrates why color deconfines when chiral symmetry is restored in hot gauge theories with quarks in the fundamental representation. For quarks in the adjoint representation we show that, while deconfinement and the chiral transition do not need to coincide, entanglement between them is still present. Extension to the chemical potential driven transition is discussed.     

New Method for Synthesis of Methacrylate-Type Polymerizable Ionic Liquids

A new method for the synthesis of polymerizable ionic liquids bearing a methacrylate moiety was developed with the aim to avoid premature polymerization of synthesized compounds. Spacer length between the imidazolium cation and the polymerizable functional group varied from 2 to 10 carbon atoms. Different 1-(n-hydroxyalkyl)-3-methylimidazolium bromides and 1-[n-(methacryloyloxy)-alkyl]-3-methylimidazolium bromides were obtained with very good yields (more than 90%).

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource: Full experimental and spectral details.]     

Synthesis of 9-Alkyl- and 9-Arylthiophenanthrenes

A simple method for the preparation of 9-alkyl- and 9-arylthio-phenanthrenes from 9-bromophenanthrene and a thiol is described.     

Determination of toxic PCB congeners in biological samples by multidimensional gas chromatography-mass spectrometry (GC/GC/MS)

Summary Multidimensional gas chromatography-mass spectrometry (GC/GC/MS) was used for the determination of coplanar PCB congeners in biological samples. A quadrupole low resolution mass spectrometer was used as the main detector in order to increase the reliability of identification and enable the use of ¹³C-labelled internal standards. The technique was capable to separate these toxic congeners from the complex matrix and decreased the need of sample purification.     

Sequence-based detection of sleeping cell failures in mobile networks

This article presents an automatic malfunction detection framework based on data mining approach to analysis of network event sequences. The considered environment is long term evolution (LTE) of Universal Mobile Telecommunications System with sleeping cell caused by random access channel failure. Sleeping cell problem means unavailability of network service without triggered alarm. The proposed detection framework uses N-gram analysis for identification of abnormal behavior in sequences of network events. These events are collected with minimization of drive tests functionality standardized in LTE. Further processing applies dimensionality reduction, anomaly detection with K-Nearest Neighbors, cross-validation, postprocessing techniques and efficiency evaluation. Different anomaly detection approaches proposed in this paper are compared against each other with both classic data mining metrics, such as F-score and receiver operating characteristic curves, and a newly proposed heuristic approach. Achieved results demonstrate that the suggested method can be used in modern performance monitoring systems for reliable, timely and automatic detection of random access channel sleeping cells.