Solving the perspective-three-point problem using comprehensive Gröbner systems

A complete solution classification of the perspective-three-point (P3P) problem is given by using the Gröbner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gröbner system. Combining with properties of the generalized discriminant sequences, the authors give the explicit conditions to determine the number of distinct real positive solutions of the P3P problem. Several examples are provided to illustrate the effectiveness of the proposed conditions.     

Effect of Ni addition on the glass-forming ability and soft-magnetic properties of FeNiBPNb metallic glasses

The effect of Ni addition on the glass-forming ability (GFA) and soft-magnetic properties of an (Fe1-xNix)75.5B14.5P7Nb3 (x=0-0.6) alloy system were investigated. We found that the addition of Ni was effective in allowing the alloy to approach a eutectic point as well as increasing the thermal stability of the supercooled liquid. By increasing the amount of Ni,the supercooled liquid region (ΔTx),the reduced glass transition temperature Trg (Tg/Tl) and the Y parameter [Tx/(Tg+Tl)] increased from 49 to 75 K,0...     

Rapid reductive degradation of azo dyes by a unique structure of amorphous alloys

An Fe-based amorphous alloy was found to significantly enhance the reductive degradation of an azo dye in aqueous solution. The surface-area normalized rate constant was up to 2.0 L m-2 min-1 at room temperature,an order of magnitude larger than any previously reported value. The activation energy of the degradation process was calculated according to the Arrhenius equation,and a much lower value than those previously reported was obtained. Valence band measurement indicated that a depressed valence band maximum and a widened empty band were established in the amorphous ribbon. The unique structure of the amorphous alloy is important-it may reduce the activation energy of the degradation process and enhance the activity of the electrons,thus accelerating the degradation process.     

Lipids of sulfate-reducing bacteria and sulfur-oxidizing bacteria found in the Dongsheng uranium deposit

U-bearing sandstones from the Dongsheng deposit in Ordos Basin contain abundant C15-C18 fatty acids. The fatty acids may have been derived from modern and ancient organisms including organisms from the intervals of U mineralization. A certain amount of i15:0, a15:0, a17:0 fatty acids coexist with small amounts of i17:1ω7c and 10me16:0, characteristic biomarkers of Desulfovibrio and Desulfobacter sp., respectively. This indicates the existence of sulfate-reducing bacteria (SRB) in the sandstones. The presence of sulfur-oxidizing bacteria (SOB), such as Beggiatoa and Thioploca, is indicated by significant amounts of 16:1ω7c and 18:1ω7c fatty acids. The existence of the SRB in the deposit, as inferred from the fatty acids, is consistent with results from fossilized microorganisms and isotopic compositions of ore-stage pyrite. This suggests that the environment may have been favorable for the SRB to grow since ore formation (9.8-22 Ma). The bacteria may have degraded hydrocarbons directly, or indirectly utilized hydrocarbons degraded by oxic microbes in the deposits. This process may have produced 12C-rich calcite and prominent baseline humps of unresolved complex mixtures (UCM), and 25-demethylated hopanes and tricyclic terpanes. The existence of sulfur-oxidizing bacteria and sulfate-reducing bacteria in the deposit may have resulted in bacterial sulfate reduction to sulfide, re-oxidization of the sulfide to sulfate and subsequent reduction of the sulfate to sulfide. This assertion is supported by ore-stage pyrite with δ34S values as low as-39.2‰, and the lightest sulfate (about 11‰) measured during the Phanerozoic, a difference of more than 46‰.     

Scale Relativity and Fractal Space-Time: Theory and Applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology.     

Spatial prisoner’s dilemma games with increasing size of the interaction neighborhood on regular lattices

We studied the evolution of cooperation in the prisoner’s dilemma game on a square lattice where the size of the interaction neighborhood is considered. Firstly, the effects of noise and the cost-to-benefit ratio on the maintenance of cooperation were investigated. The results indicate that the cooperation frequency depends on the noise and cost-to-benefit ratio: cooperation reaches a climax as noise increases, but it monotonously decreases and even vanishes with the ratio increasing. Furthermore, we investigated how the size of the interaction neighborhood affects the emergence of cooperation in detail. Our study demonstrates that cooperation is remarkably enhanced by an increase in the size of the interaction neighborhood. However, cooperation died out when the size of the interaction neighborhood became too large since the system was similar to the mean-field system. On this basis, a cluster-forming mechanism acting among cooperators was also explored, and it showed that the moderate range of the neighborhood size is beneficial for forming larger cooperative clusters. Finally, large-scale Monte Carlo simulations were carried out to visualize and interpret these phenomena explicitly.     

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system with one constant coefficient is considered in this paper. Adaptive control law are obtained by Lyapunov redesign method. The energy method for parabolic systems and the Agmon’s inequality are applied in the analysis, which leads to a stronger result than that of Hong and Bentsman (Automatica, 1994).     

Fairness of extra-gain guilty in performance of supply chain and contract design

Considering a one-supplier and two-retailer supply chain setting in which the supplier makes contacts with retailers in sequence based on FCFS(first–come–first-service) principle, the authors investigate the marginal effect of extra-gain guilty fairness concerns of supply chain members on the contract design, supply chain's profit and profit distribution. When the supplier considers distributional fairness of loss aversion and extra-gain guilty, extra-gain guilty concern reduces the optimal wholesale and retail price, and improves supply chain performance. When the first or the second retailer considers distributional fairness and peer-induced fairness, extra-gain guilty concerns decrease the optimal wholesale and retail price but increase the profit of all supply chain members only when the level of loss aversion is large enough and the level of extra-gain guilty is less than 1/2. However, when the level of loss aversion is small and the level of extra-gain guilty is less than 1/2, extra-gain guilty has no influence on supply chain performance. The analysis reveals that the supply chain performance can be further improved by considering fairness of extra-gain guilty.     

Temporal and spatial distribution of tropospheric CO<Subscript>2</Subscript> over China based on satellite observations

Mid-troposphere CO₂ data retrieved by the AIRS (atmospheric infrared sounder) were validated with five ground-based stations and aircraft measurements in the Northern Hemisphere. AIRS CO₂ products show good agreement with ground and aircraft observations. The data had a monthly average accuracy better than 3 ppmv. In this study, the spatial and temporal distribution of mid-troposphere CO₂ from January 2003 to December 2008 was analyzed based on this satellite product. The average concentration of atmospheric CO₂ was higher in the Northern Hemisphere than in the Southern Hemisphere. The yearly average results show a gradual increase from 2003 to 2008. In China, the annual growth rate was about 2 ppmv/a, similar to the United States, Europe, Australia and India, but was slightly lower than Canada and Russia. Mid-troposphere CO₂ concentrations were higher over northern China than over southern areas, due to differences in natural conditions and industrial layout. There were four centers of high CO₂ concentration between 35° and 45°N over China, with low concentrations over Yunnan Province. There was a significant seasonal CO₂ variation with peak concentration in spring and the lowest concentration in autumn.     

Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

<正> Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.