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In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered.


As in the paper of Xu Wensheng and Chen Shuping in JAMS(B), where an analogous problem in finite horizon is studied, optimal strategies are obtained via HamiltonJacobiBellman (HJB) equation which is derived from dynamic programming principle.


Discretetime stochastic equilibrium with infinite horizon incomplete asset markets


This paper examines the existence of general equilibrium in a discrete time economy with the infinite horizon incomplete markets.


The existence of general equilibrium for the infinite horizon economy is proved by taking limit of equilibria in truncated economies in which trade stops at a sequence of dates.

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 The photoelectric astrolabe type I was made in China in 1971;and several improved photoelectric astrolabes,of a second model,were constructed from 1972 to 1974.The principles and a description of the main parts of the new instruments are as follows : (1)By means of a fused quartz mirror system and mercury horizon(shown in fig.4),a telescope with a fixed glass grid,three photomultipliers with respective a.c.amplifiers and a time recorder,the astrolabe can determine the time of almu cantar transit of a... The photoelectric astrolabe type I was made in China in 1971;and several improved photoelectric astrolabes,of a second model,were constructed from 1972 to 1974.The principles and a description of the main parts of the new instruments are as follows : (1)By means of a fused quartz mirror system and mercury horizon(shown in fig.4),a telescope with a fixed glass grid,three photomultipliers with respective a.c.amplifiers and a time recorder,the astrolabe can determine the time of almu cantar transit of a star without personal error. (2)The evacuated RitcheyChrétien telescope has an aperture of 20 cm and a focal length of 2.4 m. (3)As is expected,the vacuum telescope tube with horizontal entrance window is able to eliminate astronomical refraction,the dependence of refraction on the spectral class of the star and irregular refraction in the tube.Besides,the vacuum tube provides a stable environment for optical system,especially for mercury horizon. (4)The astrolabe is equipped with high and low speed motors,as well as an automatic tracking mechanism in azimuth direction. (5)In order to reduce the heat influence from the surroundings,the astrolabe is set on the first floor of the observing building,whereas the control console,elec tronic equipments and the operator are on the ground floor. At Shanghai Observatory,observations have been carried out with the new instrument since Sep.1974.The excellent results obtained will be published later on.  我国于1972年制成Ⅰ型光电等高仪,1974年又制成Ⅱ型光电等高仪.新仪器的特点如下:(1)借助熔石英角镜组和汞地平、一架望远镜和固定的玻璃记录栅、三个光电倍增管及其交流放大器和一架计时仪,此仪器能无人差地测定星过等高圈时刻.(2)真空的 RC 望远镜的口径为20厘米,焦距2.4米.(3)有水平入射窗的真空镜筒能消除天文折射、大气色散及镜筒内的反常折射.真空镜筒还为光学系统及汞面提供了一个稳定的环境.(4)此仪器设有快、慢传动电机和自动方位跟踪机构.(5)为消除周围物体的热影响,此仪器安放在观测室楼上,而控制台、电器设备和操作者都在楼下.自1974年10月起,此仪器已在上海天文台进行了常规观测.获得的优良观测结果将在以后发表.  Eecently, Liu and Xu studied the Hawking evaporation of the Dirac particles out of the quasiextreme Kerr black holes on the foundation of the S. Chandrasekhar 's work. In this paper, Liu and Xu's work is firstly extended to the quasiextreme KerrNewman black holes, and then to general KerrNewman black holes. The Hawking thermal spectrum for fermions for general KerrNewman black holes is obtained.The Dirac equation in the spinor form of the charged particles in the KerrNewman spacetime was given by Page:... Eecently, Liu and Xu studied the Hawking evaporation of the Dirac particles out of the quasiextreme Kerr black holes on the foundation of the S. Chandrasekhar 's work. In this paper, Liu and Xu's work is firstly extended to the quasiextreme KerrNewman black holes, and then to general KerrNewman black holes. The Hawking thermal spectrum for fermions for general KerrNewman black holes is obtained.The Dirac equation in the spinor form of the charged particles in the KerrNewman spacetime was given by Page: (in this paper G= h =C=I)By means of nulltetrad and dyad, we have obtained the uncoupled Dirac equations, thatIntroducing '' Tortoise coordinates transformation''near the horizons, we haveFor the quasiextreme KerrNewman black holes, we obtainwhereK = (r2 + a2)ω am eQr. The solutions of Eq. (6) arewith Just outside the horizon, we have the outgoing waves withNow, we would exter of it. We can only e complex plane. We the radius rr+. SThe outgoing waves inside and outside the horizon can be written together as whereOutside the horizon, Eq. (9) represents an outgoing positiveenergy flux of particles coming from the horizon. But inside the horizon, Eq. (9) describes a positiveenergy flux of particles traveling backward in time out of the singularity. In other words, it describes a negativeenergy flux of antiparticles traveling forward in time for the singularity. It means that particleantiparticle pairs are created near the horizon.Apparently, from the normalization condition, we can obtain thatorwithwhere T is the temperature of the black hole, k is the Boltzmann constant, and k is the gravitational acceleration of the horizon. Eq. (10) is the Hawking thermal spectrum formula about Dirac particles for the quasiextreme KerrNewman black holes.On the other hand, the outgoing waves solutions of the Dirac equation for the quasiextreme KerrNewman black holes are also the outgoing waves solutions of the KleinGordon equation for general KerrNewman black holes. And we find these outgoing waves solutions satisfy the Dirac equation (5) for general KerrNewman black holes too. So, we can obtain the same Hawking thermal spectrum for fermions from the Dirac equation as from the KleinGordon equation for all of the KerrNewman black holes.  本文得到了KerrNewman黑洞视界附近Dirac方程的解,并与KleinGordon方程的解作了比较。把刘辽、许殿彦的工作首先从准极端Kerr黑洞推广到准极端KerrNewman黑洞,然后又进一步推广到一般KerrNewman黑洞,从而证实了一般KerrNewman黑洞辐射的Dirac粒子的能谱具有黑体辐射的形式。  An important astrophysical consequent of the experiments regarding a nonzero rest mass of neutrinos is the possible existence of selfgravitating systems of neutrinos. The masses of stable equilibrium configurations of such systems are of the order of the mass of clusters of galaxies. On the other hand, in the standard model of big bang cosmology the mass density in the universe is dominated by neutrinos if it has a nonzero mass, say, mv  1446 ev. Hence it might be expected that the clustering of matter in... An important astrophysical consequent of the experiments regarding a nonzero rest mass of neutrinos is the possible existence of selfgravitating systems of neutrinos. The masses of stable equilibrium configurations of such systems are of the order of the mass of clusters of galaxies. On the other hand, in the standard model of big bang cosmology the mass density in the universe is dominated by neutrinos if it has a nonzero mass, say, mv  1446 ev. Hence it might be expected that the clustering of matter in the early universe should be affected substantially by such neutrinos.The clustering of pure neutrinos content in expanding universe has been investigated in several works, but in which the clustering of cosmological matter has not been involved yet, Since the results of direct measures on galaxies or on clusters of galaxies, for example, the mass, the size and the velocity dispersion are always the properties of matter components themselves, it is necessary to analyse the interaction between the clustering processes of the neutrinos and the matter,1, In the case of mv=0 the clustering theory of the Jeans instability stage in the early universe can be summarized in the Figs 1 and 2.Fig 1 show the Jeans wave length λm of ionized hydrogen plus blackbody radiation as a function of cosmological radiation temperature Tr. The corresponding time of the drop in the Jeans, length is the hydrogen recombination at Tr  4000 K. Before the recombination both ionized hydrogen and radiation are in thermal equilibrium by collisions with each, other, after the recombination the matter decoupled from radiation. Dashed line Mm in Fig 2 shows the Jeans mass as a function of radiation temperature. A drop in the time of recombination occures as well. The dashed line Mhor in Fig. 2 gives the mass contained within the horizon of the cosmological model.The mass range of the Jeans instability is given by Mm < M < Mhor. Then it can be obtained from the Fig. 2 that no preferential clustering size exists in this model, i.e. all systems with mass from about 106 to 1017 M⊙ are unstable against the Jeans mechanism in the early universe and all unstable developments start from the time of recombination. That is often considered as a shortage of the theory of early clustering in the big bang model. In this work we have shown that if neutrinos have a nonzero rest mass the conclusions mentioned above should become to advantage the big bang theory.2, As the age of the universe was longer than td or the temperature dropped below Td1.3×1011 K, the neutrinos and antineutrinos decoupled from the other particles so that we might adopt the twocomponents perfectfluid to represent the contents of the universe, one of the components is the neutrinos and the other is the matter and the radiation.For the component of matter and radiation, the thermodynamieal properties are still described by the results given in section 1. The component of neutrinos is a collisionless selfgravitating gas, for which the distribution function N(t, xi pi) satisfies the Vlasov equation. In the EobertsonWalker metric, using the distribution in the time td as the initial condition, the solution of the Vlasov equation can be found as follows:where B(t) is the cosmic scale factor in the RW metric and Rd =R(td).All thermodynamieal properties of the neutrinos systems can be obtained from the distribution (1). For instance, in the nonrelativistic case the effective temperature Teff of neutrinos arewhere mv is in the unit of ev. In the same way we can derived the Jeans wave length of the neutrino system (see Fig. 1).3, The twocomponents in the early universe interact with each other through gravitational force. When we want to examine the Jeans instability, the two components system should be treated as a whole. Strictly speaking, we must deal with this problem in the relastivistic and expansive cosmological model. We can, however, safely employ classical and nonexpansive model if our interests cover only the Jeans length and mass, but not the growing rate of small fluctuations. N  本文讨论有静质量中微子对宇宙早期的Jeans不稳定性阶段的成团过程的影响。把早期宇宙作为两成分流体处理,一种成分是退耦后的中微子,另一种成分是物质及辐射,二者之间仅通过引力相耦合。主要的结论是:(1)有静质量中微子将引起复合时期之前的物质成团过程;(2)这种先复合期的物质成团的质量主要处于星系团的范围;(3)存在优先的成团尺度,它的Jeans不稳定的起始时间最早;(4)如果中微子静质量太小,则对早期的物质成团过程无影响。   << 更多相关文摘 
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