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

Mobility of TX100 suspended multiwalled carbon nanotubes (MWCNTs) and the facilitated transport of phenanthrene in real soil columns

AbstractThe transport behavior of TX100 suspended multiwalled carbon nanotubes (MWCNTs) through different soil columns as well as their effects on the mobility of phenanthrene was systematically studied. Results showed that the mobility of MWCNTs varied with soils, which was found to be correlated positively to the average soil particle diameters and soil sand contents, while correlated negatively to soil clay contents. The retention of MWCNTs on soil columns is most likely due to surface deposition and physical straining. Co-transport of phenanthrene with MWCNTs was tested in three selected soils (soil HB, DX and BJ), where MWCNTs could act as carriers of phenanthrene and enhance the mobility of phenanthrene in soils. However, during passing through the soil columns phenanthrene initially adsorbed onto MWCNTs could be partially “stripped” off. In soil with the lowest phenanthrene sorption affinity and highest water velocity (soil HB), only 8.5% phenanthrene was desorbed during transport, suggesting that a strong MWCNT-associated phenanthrene mobile may occur in this soil. More than 80% of phenanthrene was stripped off in soils with higher sorption affinity (soil DX and BJ), indicating the limitation of the co-transport of phenanthrene and MWCNTs in such soils

Observational constraints on cosmic neutrinos and dark energy revisited

Using several cosmological observations, i.e. the cosmic microwave background anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the HST prior, we impose constraints on the sum of neutrino masses (\mnu), the effective number of neutrino species (\neff) and dark energy equation of state ($w$), individually and collectively. We find that a tight upper limit on \mnu can be extracted from the full data combination, if \neff and $w$ are fixed. However this upper bound is severely weakened if \neff and $w$ are allowed to vary. This result naturally raises questions on the robustness of previous strict upper bounds on \mnu, ever reported in the literature. The best-fit values from our most generalized constraint read \mnu=0.556^{+0.231}_{-0.288}\rm eV, \neff=3.839\pm0.452, and $w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on total neutrino mass, favors an extra light degree of freedom, and supports the cosmological constant model. The current weak lensing data are already helpful in constraining cosmological model parameters for fixed $w$. The dataset of Hubble parameter gains numerous advantages over supernovae when $w=-1$, particularly its illuminating power in constraining \neff. As long as $w$ is included as a free parameter, it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints.Comment: 39 pages, 15 figures, 7 tables, accepted to JCA

Fabrication of micro-scale radiation shielding structures using tungsten nanoink through electrohydrodynamic inkjet printing

Electronics components used in space and strategic missions are exposed to harsh radiation environments, which could cause operational malfunction of the system through lattice displacement or ionization effects. One potential solution is to use tungsten as radiation shielding. Tungsten is a very effective material in shielding electronic components and manufacturing gratings for x-ray imaging. However, intrinsic properties of tungsten (e.g. density, chemical/thermal inertness and hardness) post a significant challenge of fabricating the material into micro-scale and delicate structures, especially in electronic device fabrication. To address the problem, we designed a new tungsten nanoink and developed a straightforward approach to create tungsten micro-structures by 3D printing. Various microstructures down to 10 µm resolution have been patterned and fabricated by electrohydrodynamic inkjet (e-jet) printing using tungsten nanoink. By optimizing process parameters (voltage modality) and materials properties (ink formulation), the dimension and morphology of the structures can be precisely controlled. An AC-modulated voltage was employed during the e-jet printing process to make the patterns much more controllable and stable. Multi-layer tungsten lines were characterized by x-ray imaging and exhibited excellent absorption of x-ray radiation. With the same thickness, printed lines showed nearly 1/3 absorptivity of x-ray radiation of bulk tungsten, leading to significant radiation attenuation effectiveness. Tungsten nanoink is a new material used in e-jet printing that has not been reported in the literature to the best of authors\u27 knowledge. The study establishes a new methodology of manufacturing micro-nano scale shielding components for electronic devices and rapid prototyping of gratings and collimators in radiography for medical and inspection applications. The research also provides practical guidance to fabricate high melting-point metals via nanoink and micro/nano scale 3D printing