Generalized Nonlinear Variational-Like Inequalities

This study investigates how to dynamically allocate resources with a given budget for advertising through Web portals using keyword-activated banner ads on the Internet. Identifying the factors that affect the potential number of banner ad clickthroughs in each portal, we show that the process of budget allocation between the two types of portals (generic vs specialized) that leads to the largest banner clicksthrough in the long run is an optimal control problem. Using techniques of dynamic programming, we find analytical solutions for the optimal budgeting decisions. Our analysis shows that an advertisers optimal portal budgeting depends nonlinearly on the number of visitors who type the same trigger keyword and the average clicksthrough rates, as well as on the advertiser and ad effectiveness. Further, we find that the maximal number of banner clickthroughs from both portals, at time t, depends on the remaining budget until the end of the planning period. The analytical results have useful managerial insight. One of the interesting features of our solution shows that, while a large visitor base may favor the generic portal, other parameters may affect it unfavorably: e.g., lower clickthrough rates of keyword banners from a more heterogeneous audience. Using a specificaction that is consistent with empirical observations, we show that, in the long run, an advertiser must always spend more ad money at the specialized portal.     

On the sum minimization version of the online bin covering problem

Given a set of m identical bins of size 1, the online input consists of a (potentially infinite) stream of items in (0,1]. Each item is to be assigned to a bin upon arrival. The goal is to cover all bins, that is, to reach a situation where a total size of items of at least 1 is assigned to each bin. The cost of an algorithm is the sum of all used items at the moment when the goal is first fulfilled. We consider three variants of the problem, the online problem, where there is no restriction of the input items, and the two semi-online models, where the items arrive sorted by size, that is, either by non-decreasing size or by non-increasing size. The offline problem is considered as well.     

Structure and stability of online chat networks built on emotion-carrying links

High-resolution data of online chats are studied as a physical system in the laboratory in order to quantify collective behavior of users. Our analysis reveals strong regularities characteristic of natural systems with additional features. In particular, we find self-organized dynamics with long-range correlations in user actions and persistent associations among users that have the properties of a social network. Furthermore, the evolution of the graph and its architecture with specific k$k$-core structure are shown to be related with the type and the emotion arousal of exchanged messages. Partitioning of the graph by deletion of the links which carry high arousal messages exhibits critical fluctuations at the percolation threshold.     

Optimal dynamic advertising policies in the presence of continuously distributed time lags

The Nerlove-Arrow model of optimal dynamic advertising policies is generalized by incorporating a continuously distributed lag between advertising expenditures and increases in the stock of goodwill. This leads to a control problem where the equation of motion is given by an integro-differential equation. The transitory and steady-state properties of the optimal policies are examined, both for a general lag function and for a gamma distributed lag. The dependence of the steady-state solution on the parameters of the gamma distribution is also investigated. An example is given using specific demand and cost functions.     

Online preconcentration of recombinant Arg-Gly-Asp-hirudin using dynamic pH junction for analysis in human urine samples by capillary electrophoresis-mass spectrometry

A sensitive and effort-saving method was established and validated for the quantitative determination of recombinant Arg-Gly-Asp-hirudin (rRGD-hirudin) in human urine samples. The assay was performed on a uncoated fused silica capillary of 70 cm × 50 μm I.D. and a positive voltage of 30 kV was applied. The sample was injected under pressure of 50 mbar for 300 s and the temperature of capillary was kept 25 °C. Sheath liquid consisting of 30% methanol and 70% of 0.1% formic acid aqueous solution flowing at 7 μL/min was supplied to the CE-electrospray interface. Utilizing the dynamic pH junction technique, a lower limit of quantitation of approximately 35 nM was achieved (concentration coefficiency was about 100-fold) without complex sample preprocessing procedure. CE-MS conditions and parameters were also optimized to obtain better performance. The method has been successfully applied in clinical research of rRGD-hirudin.     

Kinetics of Thermal Decomposition of Lithium Hexafluorophosphate

With on-line coupled thermo-gravimetric analyzer-Fourier transform infrared spectrometer technique, the thermal decomposition of lithium hexafluorophosphate (LiPF₆) and its gas evolution at inert environment (H₂O<10 ppm) were studied under both non-isothermal and isothermal conditions. The results showed that the LiPF₆ decomposition is a single-stage reaction with LiF as final residue and PF₅ as gas product. In addition, its decomposi-tion kinetics was determined as 2D phase boundary movement (cylindrical symmetry) under both non-isothermal and isothermal conditions. Furthermore, the activation energy of LiPF₆ decomposition was calculated as 104 and 92 kJ/mol for non-isothermal and isothermal con-ditions, respectively.     

不同推介模式下网络零售商广告策略研究

研究了不同推介模式下网络零售商的广告策略问题,通过Nash静态博弈方法求解无推介、单向推介以及双向推介三种模式下零售商均衡零售价格、广告努力水平及利润。研究发现:无推介情况下,两零售商均衡广告策略为同时投入广告。单向推介情况下,若利润分享比例较小,则两零售商同时投入广告;若利润分享比例较大,则随着广告成本系数的增大,两零售商均衡广告策略从仅有被推介零售商投入广告转变为同时投入广告。双向推介情况下,若广告成本系数较小,则两家零售商都不投入广告;若广告成本系数较大,则两家零售商同时投入广告。此外,还分析了零售商均衡广告策略下的推介动力问题。     

Heterogene Katalyse

A technically simple experiment in heterogeneous catalysis useful for student's lab classes is introduced. Ammonia is oxidized via air using manganese iron oxides close to 200 °C. The consumption of ammonia is detected online via an ion‐selective electrode. The determination of the reaction order and the activation energy is demonstrated based on lab course conditions.     

How people make friends in social networking sites—A microscopic perspective

We study the detailed growth of a social networking site with full temporal information by examining the creation process of each friendship relation that can collectively lead to the macroscopic properties of the network. We first study the reciprocal behavior of users, and find that link requests are quickly responded to and that the distribution of reciprocation intervals decays in an exponential form. The degrees of inviters/accepters are slightly negatively correlative with reciprocation time. In addition, the temporal feature of the online community shows that the distributions of intervals of user behaviors, such as sending or accepting link requests, follow a power law with a universal exponent, and peaks emerge for intervals of an integral day. We finally study the preferential selection and linking phenomena of the social networking site and find that, for the former, a linear preference holds for preferential sending and reception, and for the latter, a linear preference also holds for preferential acceptance, creation, and attachment. Based on the linearly preferential linking, we put forward an analyzable network model which can reproduce the degree distribution of the network. The research framework presented in the paper could provide a potential insight into how the micro-motives of users lead to the global structure of online social networks.