Variations of existing glaciers in the Southwestern mountain region of Xizang (Tibet)
The SW-mountain region of Xizang in this paper is taken to extend between 27° 10′ – 30° 10′N / 84° 50′–91° 30′ E, that is the vast area stretching from the Himalayas to the South Range of Xizang. The author has been in the area many times over 20 years surveying and conducting scientific investigations. In 1984 the author took part in the Sino-German Joint Expedition for further survey and the interpretation of aerial photographs and satellite images of the same area. The paper presents the data collected during this period.
Tree-ring evidence of ‘Little Ice Age’ glacier advances in southern Tibet
The history of late Holocene glacier fluctuations in eastern Tibet was studied by determining the ages of trees growing on glacier deposits. Maximum tree ages yield minimum ages of AD 1760 and 1780 for moraine formation at the maximum extent of the ‘Little Ice Age’ glacier advances in two glacier forefields. Subsequent moraines could be dated to the beginning of the nineteenth and the beginning of the twentieth century. Larch trees from a third glacier forefield in southeastern Tibet show evidence of glacier activity from 1580 to 1590, from the end of the eighteenth to the beginning of the nineteenth century and from 1860 to 1880. One glacier at Mt Gyalaperi recently advanced in both 1951 and 1987. Periods of glacier advances can partly be correlated with periods of growth reductions in chronologies of total ring width and maximum latewood density derived from trees growing on slopes above the glacier valleys. Correlation functions with meteorological data suggest that maximum latewood density of subalpine Picea balfouriana, Larix griffithii and Abies delavayi var. motouensis is positively correlated with summer temperature, while ring width of these species and of subalpine Juniperus tibetica is also sensitive to winter conditions prior to the growing season.
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.