关于除数函数d_k(n)的一个注记

设dk(n)为k重除数函数 (k≥ 2 )。证明了 :对充分大正数x ,同时使等式组 {dk(n) =dk(n + 1) ,k≥ 2 }成立且不超过x的n的个数为 x(loglogx) -2 .5。

Molecular Evolution of the Cytochrome b Gene in Geographically Isolated Populations of Oryzias Latipes

The mitochondrial cytochrome b gene was isolated from the caudal fin of Oryzias latipes and PCR was undertaken to determine phylogeny. The nucleotide sequence of the complete cytochrome b gene including the 5＇ and 3＇ ends was 1,143 base pairs （bp） and 1,137 bp encoding 380 and 378 amino acids in the K-11 strain and HS strain, respectively. In addition, higher substitutions both in base and amino acid residues occurred more frequently between the former control （Hd-rR strain） and HS strains than the K-I 1 strain. Approximately similar values in polymorphism, as assessed by restriction endonuclease digestion, were detected when utilizing 20 different enzymes. Therefore, the evolutionary processes were unlikely to involve common ancestors, especially between the K-11 strain and HS strains, in O. latipes populations in Japan. The sequence had been deposited in GenBank Data Base under accession number AB480878 （K-I I strain） and AB480879 （HS strain）.

Behavior of Vacuum Polarization of Gauge-Boson and Wavefunction Renormalization Factor of Fermion in Different Phases of QED3

We investigate the behavior of the vacuum polarization of the gauge-boson Ⅱ and the wave-function renormalization factor of the fermion A in QEDs, using the coupled Dyson-Schwinger equations for the gauge-boson and fermion propagator. Using several different ansatze for the fermion-gauge-boson vertex, we find that the wave-function renormalization factor .4 and especially the vacuum polarization Ⅱ have different behaviors in the dynamical chiral symmetry breaking phase and in the chiral symmetric phase and hence in the phenomenological applications of QED3 one should choose different forms of gauge-boson propagator for these two phases. We also find that when adopting a specific ansatze of the fermion-gauge-boson vertex （ansatze （3）） the vacuum polarization function equals its one-loop perturbative result in the chiral symmetric phase. This fact suggests that in QEDs the Wigner vacuum corresponds to the perturbative vacuum.

Water Quality, Climatic and Plant Traits as Predictors on Abundance of Insects in Paddy Field, Tanjung Karang, Selangor, Malaysia

The abundance of beneficial insects in the paddy field can be influenced by the abundance of insect pests, water parameters, climatic factors and plant traits. This study was conducted to determine effects of water parameters, climatic factors and plant traits on abundant insects. Findings of the studies showed that there were significant correlations between all beneficial insects in paddy field and water parameters tested, namely, water temperature, salinity, turbidity, pH, dissolved oxygen, biological oxygen demand, chemical oxygen demand, ammonia and total suspended solids. Moreover, the selected water parameters of water temperature, dissolved oxygen, biological oxygen demand and chemical oxygen demand were good predictors for abundant beneficial insects in paddy field at Sungai Burong, specifically for insects of sub-orders Anisoptera and Zygoptera, and insects from families Gerridae and Coccinellidae. The plant height, insect pest, temperature, rainfall and humidity were found to be good predictors on the abundance of beneficial insects; nevertheless, the R2 value of multiple regression models was relatively low due to significant relationship between water parameters and insects. Consideration factors of water parameters, climatic factors and plant traits were strongly correlated with those parameters and abundance of insects in the paddy field at Sungai Burong, Tanjung Karang, Selangor.

Congruent elliptic curves with non-trivial Shafarevich-Tate groups： Distribution part

Given a large positive number x and a positive integer k, we denote by Qk(x) the set of congruent elliptic curves E(n): y2= z3- n2 z with positive square-free integers n x congruent to one modulo eight,having k prime factors and each prime factor congruent to one modulo four. We obtain the asymptotic formula for the number of congruent elliptic curves E(n)∈ Qk(x) with Mordell-Weil ranks zero and 2-primary part of Shafarevich-Tate groups isomorphic to(Z/2Z)2. We also get a lower bound for the number of E(n)∈ Qk(x)with Mordell-Weil ranks zero and 2-primary part of Shafarevich-Tate groups isomorphic to(Z/2Z)4. The key ingredient of the proof of these results is an independence property of residue symbols. This property roughly says that the number of positive square-free integers n x with k prime factors and residue symbols(quadratic and quartic) among its prime factors being given compatible values does not depend on the actual values.

Dynamics of a Function Related to the Primes

Let n = p1p2 ··· pk, where pi(1 ≤ i ≤ k) are primes in the descending order and are not all equal. Let Ωk(n) = P(p1 + p2)P(p2 + p3) ··· P(pk-1+ pk)P(pk+ p1), where P(n) is the largest prime factor of n. Define w0(n) = n and wi(n) = w(wi-1(n)) for all integers i ≥ 1. The smallest integer s for which there exists a positive integer t such thatΩs k(n) = Ωs+t k(n) is called the index of periodicity of n. The authors investigate the index of periodicity of n.

A Barban-Davenport-Halberstam theorem for integers with fixed number of prime divisors

The purpose of this paper is to study the distribution of integers with a given number prime divisors over arithmetic progressions,via using the large-sieve inequality,Huxley-Hooley contour and the zero-density estimate,and present a Barban-Davenport-Halberstam type theorem for it.

The geometric factor of high energy protons detector on FY-3 satellite

Geometric factor is the key parameter for inversion of particle spectrum in space particle detection. Traditional geometric factor is obtained through the method of numerical calculation with the actual structure of the detector as the input condition. The degree of accuracy for data inversion is reduced since traditional geometric factor fails to take into account the physical process of interaction between the particle and substance as well as the influence of factors such as the particle interference between different energy channels on the measurement result. Here we propose an improved geometrical factor calculation method, the concept of which is to conduct actual structural modelling of the detector in the GEANT4 program, consider the process of interaction between the particle and substance, obtain the response function of the detector to particles of different energy channels through the method of Monte Carlo simulation, calculate the influence of contaminated particle on the geometrical factor, and finally get the geometrical factors for different energy channels of the detector. The imrpoved geometrical factor obtained through the method has carried out inversion for the data of high energy protons detector on China's FY-3 satellite, the energy spectrum after which is more in line with the power law distribution recognized by space physics. The comparison with the measured result of POES satellite indicates that the FY-3 satellite data are in good accordance with the satellite data, which shows the method may effectively improve the quality of data inversion.

Impact analysis of the Journal of Geographical Sciences during 2009–2015

Based on Journal Citation Reports^(TM), Web of Science, Springer data and manuscript statistical data, we analyzed the citation indices of the Journal of Geographical Sciences(JGS) from 2009 to 2015. The main indices include the number and proportion of international manuscripts, published articles, downloads, impact factors, total cites, cited journals, citing journals, and highly cited papers. Up to 2015, the JGS had received manuscripts from authors in 80 countries and published papers from authors in 32 countries. The citation indices of JGS show increasing trends in the last seven years. The impact factor of the JGS increased from 0.518 in 2009 to 1.923 in 2015. Total cites increased from 157 in 2009 to 1276 in 2015. The international full-text downloads of the JGS increased year by year, and the number of downloads in 2015 was about three times that of 2009. The published papers were considered to be influential. The results of this study provide scientific guidance for the development of the Journal of Geographical Sciences and can be used to improve the quality of other Chinese geographical journals.