Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

3-D KINETIC CHARACTERISTICS OF OBESE CHILDREN AND NORMAL WEIGHT CHILDREN DURING NORMAL WALKING

Previous researches on obese children walking gait have been mainly focused on the kinematic characteristics, and little focused on the kinetic characteristics. The aim of this study is to identify and compare the kinetic characteristics of the walking gait of obese children with those of normal weight children

GeV {\gamma}-ray Emission Detected by Fermi-LAT Probably Associated with the Thermal Composite Supernova Remnant Kesteven 41 in a Molecular Environment

Hadron emission from supernova remnant (SNR)-molecular cloud (MC) association systems has been widely regarded as a probe of the shock-accelerated cosmic-ray protons. Here, we report on the detection of a {\gamma}-ray emission source, with a significance of 24{\sigma} in 0.2-300 GeV, projected to lie to the northwest of the thermal composite SNR Kesteven 41, using 5.6 years of Fermi-Large Area Telescope (LAT) observation data. No significant long-term variability in the energy range 0.2--300 GeV is detected around this source. The 3{\sigma} error circle, 0.09 degree; in radius, covers the 1720MHz OH maser and is essentially consistent with the location of the V_{LSR} ~-50 km/s MC with which the SNR interacts. The source emission has an exponential cutoff power-law spectrum with a photon index of 1.9+/-0.1 and a cutoff energy of 4.0+/-0.9 GeV, and the corresponding 0.2-300 GeV luminosity is ~1.3*10^36 erg/s at a distance of 12 kpc. There is no radio pulsar in the 3{\sigma} circle responsible for the high {\gamma}-ray luminosity. While the inverse Compton scattering scenario would lead to a difficulty in the electron energy budget, the source emission can naturally be explained by the hadronic interaction between the relativistic protons accelerated by the shock of SNR Kesteven 41 and the adjacent northwestern MC. In this paper, we present a list of Galactic thermal composite SNRs detected at GeV {\gamma}-ray energies by Fermi-LAT is presented