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The Last Glacial Maximum (LGM, c. 26-16 ka) and the Holocene Optimum (HO, c. 9-5 ka) were characterized by cold-dry and warm-wet climates respectively in the recently geological Earth. How Chinese deserts and sand fields responded to these distinctive climatic changes is still not clear, however. To reconstruct environments of the deserts and sand fields during the LGM and HO is helpful to understand the forcing mechanisms of environment change in this arid region, and to test paleoclimatic modeling results. Through our long-term field and laboratory investigations, 400 optically stimulated luminescence (OSL) ages and more than 100 depositional records in the Chinese deserts and sand fields were obtained; on the basis of these data, we reconstruct spatial distributions of the deserts and sand fields during the LGM and HO. Our results show that the sand fields of Mu Us, Hunshandake, Horqin and Hulun Buir in northern and northeastern China had expanded 25%, 37%, 38% and 270%, respectively, during the LGM; the sand fields of Gonghe in the northeastern Qinghai-Tibetan Plateau had expanded 20%, and the deserts of Badain Jaran, Tengger in central northern China had expanded 39% and 29% separately during the LGM; the deserts of Taklimakan, Gurbantunggut and Kumtag in northwestern China had expanded 10%–20% respectively, compared to their modern areas. On the other hand, all of the sand fields were nearly completely covered by vegetation during the HO; the deserts in northwestern and central northern China were reduced by around 5%–20% in area during this time. Lakes in this arid region were probably expanded during the HO but this conclusion needs more investigation. Compared with the geological distributions of deserts and sand fields, human activity has clearly changed (expanded) the area of active sand dunes at the present time. Our observations show that environmental conditions of Chinese deserts and sand fields are controlled by regional climate together with human activity.

We obtain an estimate on the rate of convergence of Durrmeyer-Bezier operaters for functions of bounded variation by means of some probabilistic methods and inequality techniques. Our estimate improves the result of Zeng and Chen (2000).