On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Estimated mass and stiffness matrices of shear building from modal test data

A method that estimates mass and stiffness matrices of shear building from modal test data is presented in this paper. The method depends on only measurable points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured. So it is applicable to most of the general test. Based on this method modal data of unmeasurable points are estimated, then global mass and stiffness matrices of structure are obtained by using the first two orders of modal data. Taking advantage of iteration the optimum global mass and stiffness matrices are gained. Finally, an example is studied in this paper. Its result shows that this method is reliable. © 1998 John Wiley & Sons, Ltd.     

Biogeochemical records of paleoenvironmental changes in Nainital Lake,Kumaun Himalayas,India

Rapid urbanization and increased tourism around Nainital Lake in the Kumaun Himalayan region in north India has raised concerns about sediment and water pollution. Lead-210 dated sediment cores from the lake represent ~95 years of accumulation and yield a mean sedimentation rate of ~4.7 mm year⁻¹. Total organic carbon (TOC), percent N and S and their atomic C/N and C/S ratios, stable isotopes (δ¹³C, δ¹⁵N, and δ³⁴S), and specific biomarkers (n-alkanes and pigments) were measured in the core. Organic matter is primarily derived from in-lake algal production and TOC flux varies from 1.0 to 3.5 g m⁻² year⁻¹. Sediments are anoxic (Eh −328 to −187 mV) and have low (0.10–0.30 g m⁻² year⁻¹) N, but high (0.37–1.0 g m⁻² year⁻¹) S flux. Shifts in δ¹³C, δ¹⁵N, and δ³⁴S suggest in-lake microbial processes dominated by denitrification and sulfate reduction. The sediments are dominated by short-chain hydrocarbons with low Carbon Preference Index values. The pigments indicate a gradual shift to cyanobacterial domination of the phytoplankton community in recent years. Despite an increase in external input of nutrients, the trophic state of the lake has remained largely unchanged, and the perceived human-induced impacts are limited.     

Geochemical reconstruction of late Holocene drainage and mixing in Kluane Lake,Yukon Territory

The level of Kluane Lake in southwest Yukon Territory, Canada, has fluctuated tens of metres during the late Holocene. Contributions of sediment from different watersheds in the basin over the past 5,000 years were inferred from the elemental geochemistry of Kluane Lake sediment cores. Elements associated with organic material and oxyhydroxides were used to reconstruct redox fluctuations in the hypolimnion of the lake. The data reveal complex relationships between climate and river discharge during the late Holocene. A period of influx of Duke River sediment coincides with a relatively warm climate around 1,300 years BP. Discharge of Slims River into Kluane Lake occurred when Kaskawulsh Glacier advanced to the present drainage divide separating flow to the Pacific Ocean via Kaskawulsh and Alsek rivers from flow to Bering Sea via tributaries of Yukon River. During periods when neither Duke nor Slims river discharged into Kluane Lake, the level of the lake was low and stable thermal stratification developed, with anoxic and eventually euxinic conditions in the hypolimnion.     

Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology.     

Lateral continuity of basement seismic reflections in 15 Ma ultrafast-spreading crust at ODP Site 1256

The Ocean Drilling Program (ODP) initiated drilling at Site 1256D in the Guatemala Basin, about 1,000 km off the East Pacific Rise to penetrate plutonic rocks, anticipated to be relatively shallow in this region, formed at an ultra-fast spreading rate. IODP Expedition E312 successfully drilled into gabbros at ~1,150 m in basement. Multi-channel seismic traces show weak laterally coherent sub-basement reflections at borehole depths. Synthetic reflectivity seismograms were computed using a Ricker wavelet and impedance profiles from borehole sonic logs. These seismograms show significant sub-basement amplitude peaks. A zero-offset vertical seismic profile, shot on E312, was processed to investigate the authenticity of these reflections and their relationship to borehole geology. A dual scheme of the median filtering and F–K dip filtering was used. Tests with synthetic seismograms indicate the approach is effective at reasonable SNR levels. Downgoing energy is clearly identified but negligible upgoing energy is visible over random noise. These results indicate that lava flows and igneous contacts in upper ocean crust have significant topography on lateral scales less than the Fresnel Zone (~300 m) due to igneous and tectonic processes.     

Environmental Geochemistry and Acid Mine Drainage Evaluation of an Abandoned Coal Waste Pile at the Alborz-Sharghi Coal Washing Plant,NE Iran

In this paper, an abandoned waste coal pile, which is resulted from Alborz-Sharghi coal washing plant, NE of Iran was mineralogically and geochemically characterized to evaluate pyrite oxidation, acid mine drainage (AMD) generation, and trace element mobility. After digging ten trenches and vertical sampling, a quantitative method including the atomic absorption test, and the quality-based methods including optical study were carried out for determination of pyrite fractions in the waste pile. The geochemical results revealed that the fraction of remaining pyrite increased with depth, indicating that pyrite oxidation is limited to the shallower depths of the pile which were confirmed by variations of sulfate, pH, EC, and carbonate with depth of the pile. To evaluate the trend of trace elements and mineralogical constituents of the waste particles, the samples were analyzed by using XRD, ICP-MS, and ICP-OES methods. The results showed the secondary and neutralizing minerals comprising gypsum have been formed below the oxidation zone. Besides, positive values of net neutralization potential indicated that AMD generation has not taken in the waste pile. In addition, variations of trace elements with depth reveal that Pb and Zn exhibited increasing trends from pile surface toward the bottom sampling trenches while another of them such as Cu and Ni had decreasing trends with increasing depth of the waste pile.     

Methane hydrate formation comparisons in media with and without a water source supply

Water is a necessary element during gas hydrate formations. Therefore, by analyzing water depletion changes in media, the reaction characteristics of methane hydrate in media can be studied. In this study, two water sources supplying some liquid water which may be consumed by the methane hydrate formation reactions were designed and assembled. Using them, the full formation processes of methane hydrate was studied. Experimental results show the following： If heat released from nucleation reaction of methane hydrate is diffused rapidly, the nucleation ratios will be enhanced discernibly. While the hydrate is formed, a force is generated that sucks fresh water from the source into the vicinity of the hydrate, slowing down the cementation process and causing some hydrate grain dissociation. As a result of cementation differences, the hydrate reaction processes with different water sources present linear or quadratic equation characteristics. After a few repeated dissociation and formation processes of some hydrate grains caused by the fresh water, the gas amounts contained in hydrate will be significantly enhanced.     

STUDIES ON TERRACES AND RIVER SYSTEM CHANGES OF THE UPPER YELLOW RIVER

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