A galaxy at a redshift z = 6.96

When galaxy formation started in the history of the Universe remains unclear. Studies of the cosmic microwave background indicate that the Universe, after initial cooling (following the Big Bang), was reheated and reionized by hot stars in newborn galaxies at a redshift in the range 6 < z < 14 (ref. 1). Though several candidate galaxies at redshift z > 7 have been identified photometrically, galaxies with spectroscopically confirmed redshifts have been confined to z < 6.6 (refs 4-8). Here we report a spectroscopic redshift of z = 6.96 (corresponding to just 750 Myr after the Big Bang) for a galaxy whose spectrum clearly shows Lyman-alpha emission at 9,682 A, indicating active star formation at a rate of approximately 10M(o) yr(-1), where M(o) is the mass of the Sun. This demonstrates that galaxy formation was under way when the Universe was only approximately 6 per cent of its present age. The number density of galaxies at z approximately 7 seems to be only 18-36 per cent of the density at z = 6.6.     

A luminous quasar at a redshift of z = 7.085

The intergalactic medium was not completely reionized until approximately a billion years after the Big Bang, as revealed by observations of quasars with redshifts of less than 6.5. It has been difficult to probe to higher redshifts, however, because quasars have historically been identified in optical surveys, which are insensitive to sources at redshifts exceeding 6.5. Here we report observations of a quasar (ULAS?J112001.48+064124.3) at a redshift of 7.085, which is 0.77 billion years after the Big Bang. ULAS?J1120+0641 has a luminosity of 6.3 × 10(13)L(⊙) and hosts a black hole with a mass of 2 × 10(9)M(⊙) (where L(⊙) and M(⊙) are the luminosity and mass of the Sun). The measured radius of the ionized near zone around ULAS?J1120+0641 is 1.9?megaparsecs, a factor of three smaller than is typical for quasars at redshifts between 6.0 and 6.4. The near-zone transmission profile is consistent with a Lyα damping wing, suggesting that the neutral fraction of the intergalactic medium in front of ULAS?J1120+0641 exceeded 0.1.     

Spectroscopic confirmation of a galaxy at redshift z = 8.6

Galaxies had their most significant impact on the Universe when they assembled their first generations of stars. Energetic photons emitted by young, massive stars in primeval galaxies ionized the intergalactic medium surrounding their host galaxies, cleared sightlines along which the light of the young galaxies could escape, and fundamentally altered the physical state of the intergalactic gas in the Universe continuously until the present day. Observations of the cosmic microwave background, and of galaxies and quasars at the highest redshifts, suggest that the Universe was reionized through a complex process that was completed about a billion years after the Big Bang, by redshift z?≈?6. Detecting ionizing Lyman-α photons from increasingly distant galaxies places important constraints on the timing, location and nature of the sources responsible for reionization. Here we report the detection of Lyα photons emitted less than 600?million years after the Big Bang. UDFy-38135539 (ref. 5) is at a redshift of z = 8.5549?±?0.0002, which is greater than those of the previously known most distant objects, at z = 8.2 (refs 6 and 7) and z = 6.96 (ref. 8). We find that this single source is unlikely to provide enough photons to ionize the volume necessary for the emission line to escape, requiring a significant contribution from other, probably fainter galaxies nearby.     

A short gamma-ray burst apparently associated with an elliptical galaxy at redshift z = 0.225

Gamma-ray bursts (GRBs) come in two classes: long (> 2 s), soft-spectrum bursts and short, hard events. Most progress has been made on understanding the long GRBs, which are typically observed at high redshift (z approximately 1) and found in subluminous star-forming host galaxies. They are likely to be produced in core-collapse explosions of massive stars. In contrast, no short GRB had been accurately (< 10') and rapidly (minutes) located. Here we report the detection of the X-ray afterglow from--and the localization of--the short burst GRB 050509B. Its position on the sky is near a luminous, non-star-forming elliptical galaxy at a redshift of 0.225, which is the location one would expect if the origin of this GRB is through the merger of neutron-star or black-hole binaries. The X-ray afterglow was weak and faded below the detection limit within a few hours; no optical afterglow was detected to stringent limits, explaining the past difficulty in localizing short GRBs.     

An 84-microG magnetic field in a galaxy at redshift z = 0.692

The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars. The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, that is, Faraday rotation, yield an average value for the magnetic field of B approximately 3 microG (ref. 2). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain. Here we report a measurement of a magnetic field of B approximately 84 microG in a galaxy at z = 0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 microG in the neutral interstellar gas of our Galaxy. This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past rather than stronger.     

Molecular gas in the host galaxy of a quasar at redshift z = 6.42

Observations of molecular hydrogen in quasar host galaxies at high redshifts provide fundamental constraints on galaxy evolution, because it is out of this molecular gas that stars form. Molecular hydrogen is traced by emission from the carbon monoxide molecule, CO; cold H2 itself is generally not observable. Carbon monoxide has been detected in about ten quasar host galaxies with redshifts z > 2; the record-holder is at z = 4.69 (refs 1-3). Here we report CO emission from the quasar SDSS J114816.64 + 525150.3 (refs 5, 6) at z = 6.42. At that redshift, the Universe was only 1/16 of its present age, and the era of cosmic reionization was just ending. The presence of about 2 x 1010 M\circ of H2 in an object at this time demonstrates that molecular gas enriched with heavy elements can be generated rapidly in the youngest galaxies.     

High velocity dispersion in a rare grand-design spiral galaxy at redshift z = 2.18

Although grand-design spiral galaxies are relatively common in the local Universe, only one has been spectroscopically confirmed to lie at redshift z?>?2 (HDFX 28; z = 2.011); and it may prove to be a major merger that simply resembles a spiral in projection. The rarity of spirals has been explained as a result of disks being dynamically 'hot' at z?>?2 (refs 2-5), which may instead favour the formation of commonly observed clumpy structures. Alternatively, current instrumentation may simply not be sensitive enough to detect spiral structures comparable to those in the modern Universe. At z?相似文献   

An optical spectrum of the afterglow of a gamma-ray burst at a redshift of z = 6.295

The prompt gamma-ray emission from gamma-ray bursts (GRBs) should be detectable out to distances of z > 10 (ref. 1), and should therefore provide an excellent probe of the evolution of cosmic star formation, reionization of the intergalactic medium, and the metal enrichment history of the Universe. Hitherto, the highest measured redshift for a GRB has been z = 4.50 (ref. 5). Here we report the optical spectrum of the afterglow of GRB 050904 obtained 3.4 days after the burst; the spectrum shows a clear continuum at the long-wavelength end of the spectrum with a sharp cut-off at around 9,000 A due to Lyman alpha absorption at z approximately 6.3 (with a damping wing). A system of absorption lines of heavy elements at z = 6.295 +/- 0.002 was also detected, yielding the precise measurement of the redshift. The Si ii fine-structure lines suggest a dense, metal-enriched environment around the progenitor of the GRB.     

A large population of 'Lyman-break' galaxies in a protocluster at redshift z approximately 4.1

The most massive galaxies and the richest clusters are believed to have emerged from regions with the largest enhancements of mass density relative to the surrounding space. Distant radio galaxies may pinpoint the locations of the ancestors of rich clusters, because they are massive systems associated with 'overdensities' of galaxies that are bright in the Lyman-alpha line of hydrogen. A powerful technique for detecting high-redshift galaxies is to search for the characteristic 'Lyman break' feature in the galaxy colour, at wavelengths just shortwards of Lyalpha, which is due to absorption of radiation from the galaxy by the intervening intergalactic medium. Here we report multicolour imaging of the most distant candidate protocluster, TN J1338-1942 at a redshift z approximately 4.1. We find a large number of objects with the characteristic colours of galaxies at that redshift, and we show that this excess is concentrated around the targeted dominant radio galaxy. Our data therefore indicate that TN J1338-1942 is indeed the most distant cluster progenitor of a rich local cluster, and that galaxy clusters began forming when the Universe was only ten per cent of its present age.     

Evidence against a redshift z > 6 for the galaxy STIS123627+621755

The identification of galaxies at extreme distances provides the most direct information about the earliest phases of galaxy formation. But at redshifts z > 5 even the most luminous galaxies appear faint; the interpretation of low signal-to-noise ratio data is difficult and misidentifications do occur. Here we report optical and near-infrared observations of the source STIS123627+621755, which was previously suggested to be at a redshift of 6.68 (ref. 1). At that redshift, and with the reported spectral energy distribution, the galaxy should be essentially invisible at wavelengths less than 9,300 A, because the intervening intergalactic medium absorbs almost all light energetic enough to ionize neutral hydrogen--that is, with wavelengths less than the redshifted Lyman limit of lambda = (1 + z) x 912A. At near-infrared wavelengths, however, the galaxy should be relatively bright. Here we report a detection of the galaxy at 6,700 A and a non-detection at a wavelength of 1.2 microm, contrary to expectations for z approximately 6.68. The data conservatively require that STIS123627+621755 has a redshift z < 6.     

关于不定方程组{x2-2y2=1 {2y2-3z2=4和{x2-2y2=1 {2y2-5z2=7

对于不定方程组{x^2-2y^2=1 2y^2-3z^2=4和{x^2-2y^2=1 2y^2-5z^2=7，证明了它们没有整数解．     

二阶微分方程f″(z) A(z)f(z)=0解的性质

本文讨论了当A(z)为亚纯函数时,二阶微分方程f″(z) A(z)f(z)=0的两个线性独立解的性质,得到一些结果.     

The formation and assembly of a typical star-forming galaxy at redshift z approximately 3

Recent studies of galaxies approximately 2-3 Gyr after the Big Bang have revealed large, rotating disks, similar to those of galaxies today. The existence of well-ordered rotation in galaxies during this peak epoch of cosmic star formation indicates that gas accretion is likely to be the dominant mode by which galaxies grow, because major mergers of galaxies would completely disrupt the observed velocity fields. But poor spatial resolution and sensitivity have hampered this interpretation; such studies have been limited to the largest and most luminous galaxies, which may have fundamentally different modes of assembly from those of more typical galaxies (which are thought to grow into the spheroidal components at the centres of galaxies similar to the Milky Way). Here we report observations of a typical star-forming galaxy at z = 3.07, with a linear resolution of approximately 100 parsecs. We find a well-ordered compact source in which molecular gas is being converted efficiently into stars, likely to be assembling a spheroidal bulge similar to those seen in spiral galaxies at the present day. The presence of undisrupted rotation may indicate that galaxies such as the Milky Way gain much of their mass by accretion rather than major mergers.     

关于不定方程3x4-2y2=z4

利用初等方法给出了不定方程3x^4-2y^2=z^4的全部正整数解．从而推广了cohn关于3x^4-2y^2=1的结果．     

关于不定方程组x2-2y2=1,y2-54z2=4

运用了一种初等的方法,证明了当D=54时,不定方程组x^2-2y^2=1,y^2-Dz^2=4有整数解（x,y,z）=（&#177;3,&#177;2,0）。     

关于不定方程组y~2-10x~2=9，z~2-17x~2=16

文章运用初等证明方法,证明了标题所述的不定方程组只有x=0的整数解。从而证明了只有一个整数N=1使得1,10,17,N的任意两数之积减去1后均为平方数。     

The discovery of a galaxy-wide superwind from a young massive galaxy at redshift z approximately 3

High-velocity galactic outflows, driven by intense bursts of star formation and black hole accretion, are processes invoked by current theories of galaxy formation to terminate star formation in the most massive galaxies and to deposit heavy elements in the intergalactic medium. From existing observational evidence (for high-redshift galaxies) it is unclear whether such outflows are localized to regions of intense star formation just a few kiloparsecs in extent, or whether they instead have a significant impact on the entire galaxy and its surroundings. Here we present two-dimensional spectroscopy of a star-forming galaxy at redshift z = 3.09 (seen 11.5 gigayears ago, when the Universe was 20 per cent of its current age): its spatially extended Lyalpha line emission appears to be absorbed by H i in a foreground screen covering the entire galaxy, with a lateral extent of at least 100 kpc and remarkable velocity coherence. This screen was ejected from the galaxy during a starburst several 10(8) years earlier and has subsequently swept up gas from the surrounding intergalactic medium and cooled. This demonstrates the galaxy-wide impact of high-redshift superwinds.     

关于方程组x2-Dy2=1-D和x2=2z2-1的正整数解

设D是可使D-1是奇素数方幂的正整数，给出了确定方程组x^2 Dy^2=1-D和x^2=2z^2-1的全部正整数解(x，y，z)的一般方法．     

关于丢番图方程px4-(p-1)y2=z4

利用初等方法给出了丢番图方程px4-(p-1)y2=z4当p-1=Q2时的全部正整数解,从而推广了张跃辉关于3x4-2y2=z4的结果.