Risk averse decision making under catastrophic risk

A nonstandard probabilistic setting for modeling of the risk of catastrophic events is presented. It allows random variables to take on infinitely large negative values with non-zero probability, which correspond to catastrophic consequences unmeasurable in monetary terms, e.g. loss of human lives. Thanks to this extension, the safety-first principle is proved to be consistent with traditional axioms on a preference relation, such as monotonicity, continuity, and risk aversion. Also, a robust preference relation is introduced, and an example of a monotone robust preference relation, sensitive to catastrophic events in the sense of Chichilnisky (2002), is provided. The suggested setting is demonstrated in evaluating nuclear power plant projects when the probability of a catastrophe is itself a random variable.     

Conductivity‐Dependent Completion of Oxygen Reduction on Oxide Catalysts

The electric conductivity‐dependence of the number of electrons transferred during the oxygen reduction reaction is presented. Intensive properties, such as the number of electrons transferred, are difficult to be considered conductivity‐dependent. Four different perovskite oxide catalysts of different conductivities were investigated with varying carbon contents. More conductive environments surrounding active sites, achieved by more conductive catalysts (providing internal electric pathways) or higher carbon content (providing external electric pathways), resulted in higher number of electrons transferred toward more complete 4e reduction of oxygen, and also changed the rate‐determining steps from two‐step 2e process to a single‐step 1e process. Experimental evidence of the conductivity dependency was described by a microscopic ohmic polarization model based on effective potential localized nearby the active sites.     

Hausdorff type operators on the power weighted Hardy spaces

In this paper, we study the high‐dimensional Hausdorff type operators and establish their boundedness on the power weighted Hardy spaces for . As a consequence, we obtain that the Hausdorff type operator is bounded on if Φ is the Gauss function, or the Poisson function.     

Action of generalized symmetric groups on symmetric and exterior powers of their natural representations

We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalized symmetric groups. We adapt the methods of Savitt and Stanley from [4 Savitt, D., Stanley, R. P. (2000). A note on the symmetric powers of the standard representation of S_n. Electron. J. Combin. 7:R6. [Google Scholar]] to obtain bounds both over the complex numbers and in prime characteristic.     

Diameter of a direct power of a finite group

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gⁿ with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gⁿ such that the diameter of Gⁿ with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures.     

Geometric Design of Anode-Supported Micro-Tubular Solid Oxide Fuel Cells by Multiphysics Simulations

High volumetric power density (VPD) is the basis for the commercial success of micro-tubular solid oxide fuel cells (mtSOFCs). To find maximal VPD (MVPD) for anode-supported mtSOFC (as-mtSOFC), the effects of geometric parameters on VPD are analyzed and the anode thickness, t_an, and the cathode length, l_ca, are identified as the key design parameters. Thermo-fluid electrochemical models were built to examine the dependence of the electrical output on the cell parameters. The multiphysics model is validated by reproducing the experimental I-V curves with no adjustable parameters. The optimal l_ca and the corresponding MVPDs are then determined by the multiphysics model for 20 combinations of r_in, the inner tube radius, and t_an. And all these optimization are made at 1073.15 K. The results show that:(i) significant performance improvement may be achieved by geometry optimization, (ii) the seemingly high MVPD of 11 and 14 W/cm³ can be easily realized for as-mtSOFC with single-and double-terminal anode current collection, respectively. Moreover, the variation of the area specific power density with l_ca2(2 mm, 40 mm) is determined for three representative (r_in, t_an) combinations. Besides, it is demonstrated that the current output of mtSOFC with proper geometric parameters is comparable to that of planar SOFC.     

Hard uncertainties in multiobjective layout optimization of photovoltaic power plants

This paper describes how to treat hard uncertainties defined by so-called uncertainty maps in multiobjective optimization problems. For the uncertainty map being set-valued, a Taylor formula is shown under appropriate assumptions. The hard uncertainties are modeled using parametric set optimization problems for which a scalarization result is given. The presented new approach for the solution of multiobjective optimization problems with hard uncertainties is then applied to the layout optimization of photovoltaic power plants. Since good weather forecasts are difficult to obtain for future years, weather data are really hard uncertainties arising in the planning process. Numerical results are presented for a real-world problem on the Galapagos island Isabela.     

所有极大子群都为SMSN-群的有限群

若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.     

三项指数和四次均值的精确计算公式(2)

本文进一步深入研究了三项指数和四次均值的计算问题.运用指数和的相关性质并结合求解同余方程组的方法与技巧,利用两种不同的方法获得了两个精确的均值计算公式,揭示了三项指数和的计算与同余方程组解的个数之间的本质联系,推广了已有的结果.