Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.

COMPLEX ISOCHRONICITY OF A SIXTH DEGREE SYSTEM

In this paper, we discuss the complex isochronicity of a sixth degree polynomial system. We first adopt a new algorithm to find necessary conditions for complex isochronicity, then prove the sufficient conditions using effective methods.

Quantification of radiation damage in natural and synthetic zircon by Raman spectroscopy:application to low-temperature thermochronology

Due to its ubiquitous occurrence in igneous,metamorphic,and sedimentary rocks and its wide application in geochronology and geochemistry,zircon has become the most widely used accessory mineral in the geological community.Nevertheless,the decay of U and Th causes radiation damage to the zircon structure,resulting in various degrees of metamictization,which can affect the accuracy of U–Pb dates and Hf and O isotope results.If the degree of zircon radiation damage can be quantified,the influence on geochemical analyses can be evaluated,and the results can be corrected more precisely.In this paper,synthetic and natural zircon crystals with different crystallization ages were selected for Raman spectroscopy analysis,cathodoluminescence imaging,and determination of the U and Th concentrations.The results show that Raman FWHM(full width at half bandmaximum)and Raman shift correlate with alpha dose(Da)ofzirconsfollowingtheseequations,FWHM=44.36(±2.32)×[1-exp(-2.74×Da)]-+1.7(±0.19),Raman Shift=-6.53×Da+1007.69.Analysis of synthetic zircon crystals shows that doped REEs(rare earth elements and P)can also lead to an increase in the FWHM.However,this effect can be ignored for natural zircon samples with REE contents at a normal level of hundreds to a few thousand ppm.The FWHM and Raman shift can be used as proxies to measure the degree of zircon radiation damage.Using the updated equations to calculate the latest age when zircon began to accumulate radiation damage,a more accurate and more meaningful“radiation damage age”can be obtained.

Petrogenesis and Rb-Sr Isotopic Characteristics of Paleo-Mesoproterozoic Mirgarani Granite Sonbhadra Uttar Pradesh India:Geodynamics Implication for Supercontinent Cycle

The Rb-Sr whole-rock isochron,age 1636±66 Ma of Mirgarani granite,is the one of the oldest granite dated in the northwestern part of the Chhotanagpur Granite Gneiss Complex(CGGC).The initial Sr ratio is 0.715±0.012(MSWD=0.11),showing an S-type affinity.The Mirgarani granite has intruded the migmatite complex of the Dudhi Group and forms the Mirgarani formation comparable to the granites of the Bihar Mica Belt around Hazaribagh(1590±30 Ma).The present studies have established the chronostratigraphy of the Dudhi Group and adjoining areas in CGGC.Petro-graphic and geochemical studies revealed that the granite is enriched in Rb(271 ppm),Pb(77 ppm),Th(25 ppm),and U(33 ppm)and depleted in Sr(95 ppm),Nb(16 ppm),Ba(399 ppm)and Zr(143 ppm)contents as compared to the normal granite.The Mirgarani granite is a peraluminous(A/CNK=1.23),high potassic(K_(2)O 6.42%),Calc-Alkalic to Alkali-Calcic{(Na_(2)O+K_(2)O)-CaO=6.29}S-Type granite,a feature supported by the presence of modal garnet and normative corundum(2.68%).The Mirgarani granite is considered to have been formed by the anatexis of a crustal sedimentary protolith at a depth of approximately 30 km with temperatures ranging from 685-700℃ during the Co-lumbian-Nuna Supercontinent.

Age and Tectonic Significance of the Mafic Dyke Swarm in the Kuruktag Region, Xinjiang

The mafic dykes are composed of a series of northwest-trending diabase in Kuokesu of the Kuruktag region, Xinjiang. Four whole-rock samples of the mafic dykes in the region give an 40Ar/36Ar–40K/36Ar isochron age of 282 Ma with the initial 40Ar/36Ar = 507. The characteristics of the major, trace and rare earth elements of the dyke rocks indicate that they belong to the calc-alkaline series and were emplaced in extensional structures at an intermediate depth of the crust. This shows that there was a large-scale extension in the Permian Period, which might be associated with the post-collisional extension of the ancient Tianshan Mountains.

Metallogenic Chronology of Boron Deposits in the Eastern Liaoning Paleoproterozoic Rift Zone

Lead isotopic analytic data of 30 ores gathered from the Zhuanmiao boron deposit, Wengquangou boron (iron) deposit and its Dongtaizi Ore Member constitute three isochrons, the corresponding ages of which are 1902 ± 12 Ma, 1852 ± 9 Ma and 1917 ± 48 Ma. Lead isotopic analyses of marble from the Xiquegou Member of the Qingchenzi orefield yield a Pb-Pb isochron age of 1844 ± 27 Ma. 40Ar-39Ar quick neutron activation dating of phlogopites and microclines coexisting with ore minerals in the Wengquangou boron (iron) and Zhuanmiao boron deposits shows that: (1) the phlogopite from the Wengquangou has a plateau age of 1923 ± 1.5 Ma and an isochron age of 1924 ± 2.5 Ma; (2) the microcline from the Wengquangou has the plateau age of 1407 ± 5.4 Ma and 220 ± 12 Ma and an isochron age of 1403 ± 19 Ma; (3) the phlogopites from the Zhuanmiao yield a plateau age 1918 ± 1.3 Ma and an isochron age of 1918 ± 2.9 Ma; (4) the microclines from the Zhuanmiao yield the plateau age of 1420 ± 16 Ma and 250 ± 8 Ma and an isochron age of 1425 ± 19 Ma and 269 ± 16 Ma. These ages indicate that the eastern Liaoning area happened around 1900 Ma, an important tectonomagmatic event, which is consistent with the worldwide Mid-Proterozoic tectonomagmatic event. During this period, the Proterozoic Liaohe Group was folded and underwent strong normal metamorphism, and the (hydrothermal) sedimentary boron deposits (or source beds) formed earlier were strongly superimposed by mineralization, resulting in enrichment of boron; later regional geological processes made little contribution to the formation of the boron deposits. Lead isotopic components show that the U-Pb and Th-Pb isotopic system reached homogenization in the ores whereas only the U-Pb isotopic system reached homogenization in the marble from the Xiquegou district, which indicates that the boron deposits superimposed in the studied area endured a relatively strong process of hydrothermal migmatization during the end phase of early Proterozoic metamorphism.

Re–Os geochronology of the Cambrian stage-2 and-3 boundary in Zhijin County, Guizhou Province, China

The black shale series that formed in the Edi- acaran-Cambrian transition are important stratigraphic records of the co-evolution of the paleo-ocean, -climate, and -biology. In this study, we measured Re-Os isotopic compositions of the black shale in the Niutitang Formation from the Gezhongwu section in Zhijin, Guizhou Province. The samples had high Re and Os contents, with Re ranging from 21.27 to 312.78 ng/g and Os ranging from 0.455 to 7.789 ng/g. The Re-Os isotope isochron age of 522.9 ± 8.6 Ma implies deposition of the Niutitang black shale predated the Chengjiang Fauna, providing an age constraint for the expansion of oceanic anoxia in the study area. The initial ^187Os/^188Os ratio of 0.826 ± 0.026 indi- cates that enhanced continental weathering might have triggered the expansion of the oceanic anoxia.

Rb-Sr and Sm-Nd Isochron Ages of the Dongmozhazhua and Mohailaheng Pb-Zn Ore Deposits in the Yushu area, southern Qinghai and Their Geological Implications

Located on the northeast margin of the Qiangtang terrane between the Jinshajiang suture zone and Bangonghu-Nujiang suture zone,the Dongmozhazhua and Mohailaheng Pb-Zn deposits in the Yushu area of Qinghai Province are representative Pb-Zn deposits of the Pb-Zn-Cu polymetallic mineralization belt in the northern part of the Nujiang-Lancangjiang-Jinshajiang area,which are in the front belt of the Yushu thrust nappe system.The formed environments of these two deposits are different from those of sediment-hosted base metal deposits elsewhere in the world.The authors hold that they were formed during the Indian-Asian continental collision and developed within the fold-thrust belt combined with thrust and strike-slip-related Cenozoic basins in the interior of the collisional zone.Studying on the metallogenic epochs of these two deposits is helpful to the understanding of ore-forming regularity of the regional Pb-Zn-Cu mineralization belt and also to the search for new deposits in this region.The age of the Dongmozhazhua deposit has been determined by the Rb-Sr isochron method for sphalerite residues,whereas the age of the Mohailaheng deposit has been determined by the Rb-Sr isochron method for sphalerite residues and the Sm-Nd isochron method for fluorite.The age of the Dongmozhazhua deposit is 35.0-±0.0 Ma （（87Sr/86Sr）0=0.708807） for sphalerite residues.The age of the Mohailaheng deposit is 32.2±0.4 Ma （（87Sr/86Sr）o=0.708514） for sphalerite residues and 31.8±0.3 Ma （（143Nd/144Nd）o=0.512362） for fluorite with an average of 32.0 Ma.Together with the regional geological setting during mineralization,a possible tectonic model for metallogeny of the Dongmozhazhua and Mohailaheng Pb-Zn deposits has been established.These two ages are close to the ages of the Pb-Zn deposits in the Lanping and Tuotuohe basins,indicating that it is possible that the narrow 1000-kilometer-long belt controlled by a thrust nappe system on the eastern and northern margins of the Tibetan plateau could be a giant Pb-Zn mineralized belt.

ISOCHRONOUS STRESS-STRAIN CURVES OF LOW ALLOY STEEL CROSS-WELD-SPECIMEN AT HIGH TEMPERATURE

In this work, a parametric approach is presented and utilized to determine the creep properties of weldments; then the model of creep strain for cross weld specimen is given. On the basis of the experimental results, attempt has been made to establish equations of the isochronous stress-strain for weld joint that can predict the function of loading and service time in use of the creep data of base metal and weld metal.

Performance Evaluation of IEEE 1394b Serial Bus with Deterministic and Stochastic Petri Nets

IEEE 1394b is a high-speed data bus that is widely used in local area networks and consumer electronics. To best utilize this data bus, we need to fully understand its per- formance. To evaluate its performance for both isochronous and asynchronous data transfers, we model the IEEE 1394b bus using Deterministic and Stochastic Pelri Nets （DSPNs）, and conduct simulations using TimeNET 4.0. Using the DSPNs model, we simulate both the average waiting times of isochronous and asynchronous packets. From the simulation results, we determine the factors that influence performance, such as throughput, size of packets, arrival rate of packets, number of isochronous channels, and bus configuration.

Redefinition of Early Mesoproterozoic (1800-1600Ma) stratigraphy in the northern Kongling area,China:The nucleus of Yangtze Craton and its tectonic significance

The Wujiatai Formation, which is well exposed in Huangjiatai-Xichahe region of the northern Kongling area of central Yangtze Craton, is a suite of epimetamorphic conglomerates to pebbly sandstones to fine sandstone-dolostones deposited in littoral-carbonate platform facies. The formation has angular unconformity contacts with both the overlying Neoproterozoic Nantuo Formation and the underlying Paleoproterozoic Huanglianghe Formation complex. Detrital zircons from metafine sandstones of the lower Wujiatai Formation have ages ranging from 3377 –1828 Ma, with the youngest zircons dating to about 1828 Ma. In addition, whole-rock Pb-Pb isochron ages from dolostones in the upper Wujiatai Formation yield an age of 1718±230 Ma. These dates constrain the depositional age of the Wujiatai Formation between 1800 Ma and 1600 Ma. These are the earliest Mesoproterozoic sedimentary records reported in the Kongling region, and fill the gaps in Early Mesoproterozoic stratigraphy in Yangtze Craton. Histograms of detrital zircon ages for the Wujiatai Formation reveal four major peaks at 2039 Ma, 2691 Ma, 2966 Ma and 3377 Ma, which is consistent with the ages of the basement rocks that underlie the center of Yangtze Craton, indicating that sediment provenance is mainly from the Kongling complex. The lower Wujiatai Formation mainly consists of clastic rocks, whereas the upper Wujiatai Formation consists of dolostones. This stratigraphic change implies a deepening sequence in an expanding basin with an initial cratonic rifting tectonic setting, corresponding to the initial breakup of the Columbia supercontinent in Yangtze Craton.

Charge resolution in the isochronous mass spectrometry and the mass of ^(51)Co

Isochronous mass spectrometry(IMS)of heavyion storage rings is a powerful tool for the mass measurements of short-lived nuclei.In IMS experiments,masses are determined through precision measurements of the revolution times of the ions stored in the ring.However,the revolution times cannot be resolved for particles with nearly the same mass-to-charge(m/q)ratios.To overcome this limitation and to extract the accurate revolution times for such pairs of ion species with very close m/q ratios,in our early work on particle identification,we analyzed the amplitudes of the timing signals from the detector based on the emission of secondary electrons.Here,the previous data analysis method is further improved by considering the signal amplitudes,detection efficiencies,and number of stored ions in the ring.A sensitive Z-dependent parameter is introduced in the data analysis,leading to a better resolution of ^(34)Ar^(18+) and ^(51)Co^(27+) with A/Z=17/9.The mean revolution times of ^(34)Ar^(18+) and ^(51)Co^(27+) are deduced,although their time difference is merely 1.8 ps.The uncorrected,overlapped peak of these ions has a full width at half maximum of 7.7 ps.The mass excess of ^(51)Co was determined to be-27;332e41T keV,which is in agreement with the previous value of-27;342e48T keV.

OPERATING POINT AND STRIPPING EXTRACTION CALCULATIONS FOR CYCLONE 10/5

By using the magnetic field map, equilibrium orbit, operating point of v r and v z and beam trajectories after stripper for Cyclone 10/5 have been calculated. The positions of two strippers and two targets have been determined. The numerical simulation is consistent with experimental tests.

The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center

The number of the limit cycles bifurcating in small quadratic perturbations of quadratic systems with an ischronous center is studied, it turns out that the cyclicity of the period annulus around one kind of quadratic isochronous center is two.

Discussion on Rb-Sr Isochron Ages of Granitoids in the Hengduan Mountains

Based on the Rb-Sr isotopic study of the granitoids in the Hengduan Mountains, the classification andgeologic significance of whole-rock Rb-Sr isochrons as well as the factors influencing homogenization of theisotopic systems are discussed. Usually. there is no good linear correlation of isochrons for diorites andalkali-rich intrusive rocks (including alkaline rock and alkalic granite). But by means of the external isochron ofmonominerals from the rocks. isochrons with good linear correlation as well as ages and Sr initial ratios with ahigh confidence can be obtained. In order to obtain a satisfactory isochron, the discriminant parameters shouldbe calculated from the Rb/Sr ratios and estimated ages of samples. Only those that meet the requirements canbe used as the Rb-Sr isochrons. The quality of an isochron should be judged from three factors, i.e. correlationcoefficient. MSWD and homogenization degree.

Dating Model of Illite Grain Rb-Sr Isochron and Its Application to Precambrian Stratigraphy

This paper discusses the Rb-Sr geochemical behaviour of illites in the sedimentary process, and points out that illites of the lmd and lm types could reach Sr-isotopic equilibrium with its environmental medium during the sedimentary process and initial stage of diagenesis, and illite grains of different sizes have various Rb contents. A new dating method for sedimentary rocks----a dating model of illite grain Rb-Sr isochron----is established, in consideration of the geochemical process of Sr-isotopic homogenization and differentiation in the course of their formation and evolution. In addition, the paper concerns the application of the dating model to the Precambrian unmetamorphosed sedimentary rocks in western Henan Province, which gives satisfactory results coincident with the geological facts.

Design flood of ungauged basins based on DEM

In this paper,the northern mountainous area of Fuzhou City which is an ungauged basin has been taken for example to discuss the method of design flood calculation by means of combining the DEM(digital elevation model) and the Xin'anjiang Model(three components).The problem of estimating the parameters of the runoff model has been solved by using the parameters of the reference station.In the conflux calculation,the isochrones are obtained by DEM which helps to avoid the cumbersome work of drawing them on the map.With the establishment of the digital elevation model throughout the country,it is practically significant to use it in the hydrological estimation.

Sm-Nd ISOTOPIC AGE OF LAMPRO PHYRES IN THE GEZHEN GOLD BEARING SHEAR ZONE ON HAINAN ISLAND AND ITS GEOLOGICAL IMPLICATIONS

Sm Nd isotopic compositions of eight lamprophyre samples, which come from the Gezhen gold bearing shear zone on western Hainan Island, are measured. The Sm Nd isochron age is 495.98±13.14 Ma, (143Nd/144Nd)0=0.512094, εNd(t) ranges from +1.80 to +2.00 and TDM from 982 Ma to 1196 Ma (average: 1060 Ma). The authors point out that the whole rock Sm Nd isochron age (495.98±13.14 Ma) really represents the petrogenetic age of lamprophyre and the time of magmatism during subsequent subduction.

Effects of Solution Atoms and Precipitates on Isochronal Annealing Behavior of Cold-Rolled Squeeze-Cast SiCw/Al Composites

SiCw/Al and SiCw/6061Al composites, which contained 15 vol pct of whiskers, were fabricated through a squeeze cast route followed by cold rolling and isochronal annealing. Effects of whicker, solution atoms and precipitates on isochronal annealing behavior of cold rolled composites were investigated by comparing the isochronal annealing behavior between pure Al, SiCw/Al, solution-treated SiCw/6061Al and aged SiCw/6061Al. It was found that the recrystallization of SiCw/Al composite occurs earlier than that of pure Al, indicating SiCw has a role of particle stimulated nucleation. Solution atoms have no significant influence on the isochronal annealing behavior of SiCw/6061Al composite, while precipitates have such a strong retarding effect on the recrystallization of SiCw/6061Al composite that the isochronal annealing curve of aged SiCw/6061 composite loses the definable recrystallization step.

Adaptive Isochronal Synchronization in Mutually Coupled Chaotic Systems

This paper studies the problem of isochronal synchronization of chaotic systems with time-delayed mutual coupling. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed for the stability of isochronal synchronization between two identical chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to isochronally synchronize two identical chaotic systems with delay-coupled, so this scheme is analytical, and simple to implement in practice. Simulation results show that the isochronal synchronization behavior is determined by time delay.