Let Q be a quiver of type $\tilde {A}_n$ . Let $\alpha =\alpha _1+\alpha _2+\cdots +\alpha _s$ be the canonical decomposition. For the polynomials $M_Q(\alpha ,q)$ that count the number of isoclasses of representations of Q over ${\mathbb F}_q$ with dimension vector $\alpha $ , we obtain a precise relation between the degree of $M_Q(\alpha ,q)$ and that of $\prod _{i=1}^{s} M_Q(\alpha _i,q)$ for an arbitrary dimension vector $\alpha $ .

This work quantifies glacier variations in the Naimona’nyi area of the western Himalaya by integrating glacier spatial data from ASTER and the Landsat series of satellite imagery at four different times: 1976, 1990, 1999 and 2003. Comparison of the results from individual images with those from the integrated method indicates that the integrated approach provides a better result. Glacier variations were mapped and analyzed; discrepancies between images could be detected and removed from the integrated data using remap tables in Arc/Info grid both graphically and numerically. Our results show that glaciers in the region both retreated and advanced during the last 28 years; however, retreat dominates. The variation of glaciers in the western Himalayan region is dramatic compared with other regions in high Asia. From 1976 to 2003, glacier area decreased from 84.41 km2 to 77.29 km2. Sequential images show that glacier areas shrank by 0.17, 0.19 and 0.77 km2 a−1, on average, during the periods 1976–90, 1990–99 and 1999–2003, respectively, suggesting that glacier retreat has accelerated.

Glacier and lake variations in the Yamzhog Yumco basin in southern Tibet were studied by integrating series of spatial data from topographic maps and Landsat images at three different times: 1980, 1988/90 and 2000. The results indicate that the total glacier area has decreased from 218 km2 in 1980 to 215 km2 in 2000, a total reduction of 3 km2 (i.e. a 1.5% decrease). Glacier recession rates were clearly larger in the 1990s than the 1980s due to the warmer climate. The total lake area decreased by about 67 km2 during 1980–90 and increased by 32 km2 during 1990–2000. It is suggested that change of lake area in the basin was rapid and most likely caused primarily by the change in precipitation and evaporation in the basin, and secondarily by the increased water supply from melting glaciers.

Using Geographical Information System (GIS) and remote-sensing technologies, we describe quantitative measurements of glacier variations in the Geladandong mountain region of central Tibet. Data from Landsat images at three different times, 1973–76, 1992 and 2002, are compared with glacier areas digitized from a topographic map based on aerial photographs taken in 1969. We find that while some glaciers have advanced during the past 30 years, others have retreated. The area of retreat is much larger than that of advance. The total glacier area has decreased from 889km2 in 1969 to 847km2 in 2002, a reduction of almost 43 km2 (i.e. 4.8% decrease, or an average of 1.29km2 a–1). The variation of glacier area in the Geladandong mountain region is not as large as in other regions within the Tibetan Plateau. Glacier areas decreased 4.7km2 (i.e. an average of 0.68km2 a–1) during 1969–76, 15.4km2 (0.96km2 a–1) during 1976–92, and 22.4km2 (2.24km2 a–1) during 1992–2002, suggesting accelerated glacier retreat in recent years. The recession rates of glacier termini also increased. It is likely that the increase in summer air temperature is the major reason for glacier shrinkage in the Geladandong mountain region.

We investigate the impact of climate change on Gurenhekou glacier, southern Tibetan Plateau, which is representative of the tens of thousands of mountain glaciers in the region. We apply a three-dimensional, thermomechanically coupled full-Stokes model to simulate the evolution of the glacier. The steep and rugged bedrock geometry requires use of such a flow model. We parameterize the temperature and surface mass-balance (SMB) uncertainties using nearby automatic weather and meteorological stations, 6 year measured SMB data and an energy-balance model for a nearby glacier. Summer air temperature increased at 0.02 Ka−1 over the past 50 years, and the glacier has retreated at an average rate of 8.3 m a−1. Prognostic simulations suggest an accelerated annual average retreat rate of ~9.1 ma−1 along the central flowline for the next 25 years under continued steady warming. However, regional climate models suggest a marked increase in warming rate over Tibet during the 21st century, and this rate causes about a 0.9 ± 0.3% a−1 loss of glaciated area and 1.1 ± 0.6% a−1 shrinkage of glacier volume. These results, the rather high warming rates predicted and the small sizes of most Tibetan glaciers, suggest that significant numbers of glaciers will be lost in the region during the 21st century.

Glacier area changes on the Tibetan Plateau were studied in different drainage basins based on Landsat satellite images from three epochs: 263 in the mid-1970s, 150 in 1999–2002 and 148 in 2013/14. Three mosaics (M1976, M2001 and M2013) with minimal cloud and snow cover were constructed, and the uncertainty due to each epoch having a finite span was accounted for. Glacier outlines (TPG1976, TPG2001 and TPG2013) were digitized manually with guidance from the SRTM DEM v4.1 and Google Earth imagery. To achieve complete multi-temporal coverage in a reasonable time, only debris-free ice was delineated. Area mapping uncertainty was evaluated at three study sites, Mount Qomolangma (Everest), Mount Naimona'Nyi, Mount Geladandong, where the largest differences between present and earlier measurements were within ~±4%. Area differences with previous inventories ranged from −19.6% (TPG1976 minus the first Chinese Glacier Inventory) to −3.6% and −1.1% (TPG2013 and TPG2001, respectively minus the second Chinese Glacier Inventory), while the difference TPG2001 minus the GAMDAM Glacier Inventory was +10.4%. Glacier area on the plateau decreased from 44 366 ± 2827 km2 (1.7% of the study area) in the 1970s to 42 210 ± 1621 km2 in 2001 and 41 137 ± 1616 km2 in 2013. Shrinkage was faster in external drainage basins of the southeast than in the interior basins of the northwest, from a maximum of −0.43% a−1 (−1.60% a−1 during 1994–2013) in the Mekong catchment down to a minimum of −0.12% a−1 in the Tarim interior drainage.

The TiO2 hollow spheres (TiO2HS) were successfully prepared by a hydrothermal method and added to Vulcan XC-72 carbon black as the support materials for Pd nanoparticles. A facile approach to promote ethylene glycol (EG) electrooxidation in alkaline medium was carried out by the PdBi/TiO2HS-C catalyst. The results show that Pd and Bi nanoparticles are uniformly dispersed on the surface of carbon-doped TiO2 hollow spheres, the appropriate amount of Bi modification into Pd/TiO2HS-C catalyst can enhance remarkably the electrocatalytic activity for EG oxidation, in which the PdBi/TiO2HS-C (Pd:Bi = 1:0.1) catalyst exhibits excellent stability. The high electrochemical performance is attributed to the unique structure and high surface area of the TiO2HS, metal nanoparticles uniform distribution, the electronic effect between Pd and Bi as well as the bifunctional effect between metal nanoparticles and the support TiO2HS-C. The results obtained are significant for the development of new Pd-based TiO2HS-C electrocatalysts for alcohol fuel cells.

Arginine is a multifaceted amino acid that is critical to the normal physiology of the gastrointestinal tract. Oral arginine administration has been shown to improve mucosal recovery following intestinal injury. The present study investigated the influence of extracellular arginine concentrations on epithelial cell barrier regulation and nutrition uptake by porcine small intestinal epithelial cell line (IPEC-J2). The results show that reducing arginine concentration from 0·7 to 0·2 mm did not affect the transepithelial electrical resistance value, tight-junction proteins (claudin-1, occludin, E-cadherin), phosphorylated extracellular signal-regulated protein kinases (p-ERK) and mucin-1 expression. Furthermore, reducing arginine concentration stimulated greater expression of cationic amino acid transporter (CAT1), excitatory amino acid transporter (EAAT3) and alanine/serine/cysteine transporter (ASCT1) mRNA by IPEC-J2 cells, which was verified by elevated efficiency of amino acid uptake. Glucose consumption by IPEC-J2 cells treated with 0·2 mm-arginine remained at the same physiological level to guarantee energy supply and to maintain the cell barrier. This experiment implied that reducing arginine concentration is feasible in IPEC-J2 cells guaranteed by nutrient uptake and cell barrier function.