On the Non-Trivial Zeros of Dirichlet Functions

The purpose of this research is to extend to the functions obtained by meromorphic continuation of general Dirichlet series some properties of the functions in the Selberg class, which are all generated by ordinary Dirichlet series. We wanted to put to work the powerful tool of the geometry of conformal mappings of these functions, which we built in previous research, in order to study the location of their non-trivial zeros. A new approach of the concept of multiplier in Riemann type of functional equation was necessary and we have shown that with this approach the non-trivial zeros of the Dirichlet function satisfying a Reimann type of functional equation are either on the critical line, or they are two by two symmetric with respect to the critical line. The Euler product general Dirichlet series are defined, a wide class of such series is presented, and finally by using geometric and analytic arguments it is proved that for Euler product functions the symmetric zeros with respect to the critical line must coincide.

Conversion Margins for the Major Uses of Agricultural Land and Their Variations in Shandong Province, China

It is of practical significance for the decision-making on country food security and farmland protection to analyze the conversion margins for the major uses of agricultural land and their variations. Based on the panel data of wheat, corn, vegetable, fruit, and forests productions from 520 investigated farmer households of 13 investigated villages in Shandong Province from 2003 to 2009, and using Cobb-Douglas production function, the revenue conversion margins can be obtained separately, between different grain-crops （wheat, corn） and different non-grain crops （vegetable, fruit, forests）, and the conversion relationship between growing grain（ wheat, corn） and going out for non-farm work. The results show that from 2003 to 2009, growing wheat and corn are more economically and reasonably for farmers, compared with growing vegetable, but growing wheat and corn are becoming less economically and less reasonably day by day, compared with planting forests. Moreover, the conversion margin between wheat and fruit shows obvious scissors difference. Just from 2007, farm- ers＇ growing fruit became economically and reasonably, but until 2009, compared with going out to work after abandoning farm- land, growing wheat had no economic rationality. From 2003 to 2009, farmers＇ growing corn is more profitable than growing fruit and going out for non-farm work after abandoning farmland. The subsidies for wheat and corn have increased farmers＇ comparative income from food production remarkably, but the subsidies cannot change the general tendency that farmers transform food （wheat, corn） production into non-food （especially forests） production. The revenue difference between growing wheat, corn and vegetable and growing fruit and forests is being pulled ceaselessly bigger, and the tendency that farmers transform wheat, corn and vegetable growing lands into fruit and forests growing lands has become increasingly apparent.

An Empirical Analysis on the Relationship betweenExports and Economic Growth in China

This paper investigates the relationship between exports and economic growth in Chinafor the reform and open-door period 1978-1996. The estimations presented indicate a positive andsignificant relation between the two variables. Also, the statistical adequacy of the models used issupported by several diagnostic test. The results provide support for the export-led growth (ELG)hypothesis.

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.