On defining partition entropy by inequalities

Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets.We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies

Preliminary experimental comparison and feasibility analysis of CO2/R134a mixture in Organic Rankine Cycle for waste heat recovery from diesel engines

This paper presents results of a preliminary experimental study of the Organic Rankine Cycle (ORC) using CO2/R134a mixture based on an expansion valve. The goal of the research was to examine the feasibility and effectiveness of using CO2 mixtures to improve system performance and expand the range of condensation temperature for ORC system. The mixture of CO2/R134a (0.6/0.4) on a mass basis was selected for comparison with pure CO2 in both the preheating ORC (P-ORC) and the preheating regenerative ORC (PR-ORC). Then, the feasibility and application potential of CO2/R134a (0.6/0.4) mixture for waste heat recovery from engines was tested under ambient cooling conditions. Preliminary experimental results using an expansion valve indicate that CO2/R134a (0.6/0.4) mixture exhibits better system performance than pure CO2. For PR-ORC using CO2/R134a (0.6/0.4) mixture, assuming a turbine isentropic efficiency of 0.7, the net power output estimation, thermal efficiency and exergy efficiency reached up to 5.30 kW, 10.14% and 24.34%, respectively. For the fitting value at an expansion inlet pressure of 10 MPa, the net power output estimation, thermal efficiency and exergy efficiency using CO2/R134a (0.6/0.4) mixture achieved increases of 23.3%, 16.4% and 23.7%, respectively, versus results using pure CO2 as the working fluid. Finally, experiments showed that the ORC system using CO2/R134a (0.6/0.4) mixture is capable of operating stably under ambient cooling conditions (25.2–31.5 °C), demonstrating that CO2/R134a mixture can expand the range of condensation temperature and alleviate the low-temperature condensation issue encountered with CO2. Under the ambient cooling source, it is expected that ORC using CO2/R134a (0.6/0.4) mixture will improve the thermal efficiency of a diesel engine by 1.9%

Evidence of slow-light effects from rotary drag of structured beams

Self-pumped slow light, typically observed within laser gain media, is created by an intense pump field. By observing the rotation of a structured laser beam upon transmission through a spinning ruby window, we show that the slowing effect applies equally to both the dark and bright regions of the incident beam. This result is incompatible with slow-light models based on simple pulse-reshaping arising from optical bleaching. Instead, the slow-light effect arises from the long upper-state lifetime of the ruby and a saturation of the absorption, from which the Kramers–Kronig relation gives a highly dispersive phase index and a correspondingly high group index

LATEST DEVONIAN (FAMENNIAN) TO EARLIEST CARBONIFEROUS (TOURNAISIAN) BRACHIOPODS FROM THE BACHU FORMATION OF THE TARIM BASIN, XINJIANG PROVINCE, NORTHWEST CHINA

Brachiopods are described from two horizons of the Bachu Formation from the Bachu area of the Tarim Basin, Xinjiang Province, northwest China. We assign the brachiopods from the basal Bachu Formation to late Famennian and correlate those from its upper part to the Eochoristites-Martiniella Assemblage of South China, of early Tournaisian age. The brachiopod fauna of the Bachu Formation exhibits strong generic and specific links with coeval South Chinese faunas, suggesting a close biogeographical affinity with the South China block. Eleven species are described, including one new species, Ptychomaletoechia bachuensis sp. nov.&nbsp

Microstructure and Fe-vacancy ordering in the KFexSe2 superconducting system

Structural investigations by means of transmission electron microscopy (TEM) on KFexSe2 with 1.5 \leq x \leq 1.8 have revealed a rich variety of microstructure phenomena, the KFe1.5Se2 crystal often shows a superstructure modulation along the [310] zone-axis direction, this superstructure can be well interpreted by the Fe-vacancy order within the a-b plane. Increase of Fe-concentration in the KFexSe2 materials could not only result in the appearance of superconductivity but also yield clear alternations of microstructure. Structural inhomogeneity, the complex superstructures and defect structures in the superconducting KFe1.8Se2 sample have been investigated based on the high-resolution TEM.Comment: 13 pages, 4 figure

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

Atomically precise lateral modulation of a two-dimensional electron liquid in anatase TiO2 thin films

Engineering the electronic band structure of two-dimensional electron liquids (2DELs) confined at the surface or interface of transition metal oxides is key to unlocking their full potential. Here we describe a new approach to tailoring the electronic structure of an oxide surface 2DEL demonstrating the lateral modulation of electronic states with atomic scale precision on an unprecedented length scale comparable to the Fermi wavelength. To this end, we use pulsed laser deposition to grow anatase TiO2 films terminated by a (1 x 4) in-plane surface reconstruction. Employing photo-stimulated chemical surface doping we induce 2DELs with tunable carrier densities that are confined within a few TiO2 layers below the surface. Subsequent in-situ angle resolved photoemission experiments demonstrate that the (1 x 4) surface reconstruction provides a periodic lateral perturbation of the electron liquid. This causes strong backfolding of the electronic bands, opening of unidirectional gaps and a saddle point singularity in the density of states near the chemical potential

Ground State Degeneracy in the Levin-Wen Model for Topological Phases

We study properties of topological phases by calculating the ground state degeneracy (GSD) of the 2d Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always non-degenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.Comment: 8 pages, 2 figures. v2: reference added; v3: two appendices adde

A new solution algorithm for solving rule-sets based bilevel decision problems

Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd. Bilevel decision addresses compromises between two interacting decision entities within a given hierarchical complex system under distributed environments. Bilevel programming typically solves bilevel decision problems. However, formulation of objectives and constraints in mathematical functions is required, which are difficult, and sometimes impossible, in real-world situations because of various uncertainties. Our study develops a rule-set based bilevel decision approach, which models a bilevel decision problem by creating, transforming and reducing related rule sets. This study develops a new rule-sets based solution algorithm to obtain an optimal solution from the bilevel decision problem described by rule sets. A case study and a set of experiments illustrate both functions and the effectiveness of the developed algorithm in solving a bilevel decision problem