On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

The Calcite Veins of the Livingston Formation

An interesting group of calcite veins occur near Livingston Montana in a zone about eight miles wide and forty miles long in the edge of the Plains region of Montana in front of the Main ranges. The zone extends from the Boulder River south of Big Timber, through Springdale and Hunters Hot Springs, to Potter's Basin just north of Wilsall in Park County. The group of veins is particularly interesting because they cut relatively flat lying strata, suggest a structural relation­ship to one another, and they are nearly pure calcite. The present investigation was to determine the position of the calcite veins by plotting them on a base map of the district. In addition, it was planned to determine the mineralogy end origin of the veins and their structural and stratigraphical relationship to the rocks of the Livingston formation which they cut.

The Livingston Formation of the South Boulder Area

The Livingston formation is a thick succession of late Cretaceous lava flows, tuffs, and bedded water-laid volcanic detritus 200 miles long and 100 miles wide lying along the eastern margin of the Rocky Mountains in western Montana from Augusta to Yellowstone Park. It differs markedly within short distances in lithologic character and sequences, and the total thickness may exceed one mile in some places.

Study of the fronts of Johnsons and Hurd Glaciers (Livingston Island, Antarctica) from 1957 to 2013, with links to shapefiles

The study of glacier fronts combines different geomatics measurement techniques as the classic survey using total station or theodolite, technical GNSS (Global Navigation Satellite System), using laser-scanner or using photogrammetry (air or ground). The measure by direct methods (classical surveying and GNSS) is useful and fast when accessibility to the glaciers fronts is easy, while it is practically impossible to realize, in the case of glacier fronts that end up in the sea (tide water glaciers). In this paper, a methodology that combines photogrammetric methods and other techniques for lifting the front of the glacier Johnsons, inaccessible is studied. The images obtained from the front, come from a non-metric digital camera; its georeferencing to a global coordinate system is performed by measuring points GNSS support in accessible areas of the glacier front side and applying methods of direct intersection in inaccessible points of the front, taking measurements with theodolite. The result of observations obtained were applied to study the temporal evolution (1957-2014) of the position of the Johnsons glacier front and the position of the Argentina, Las Palmas and Sally Rocks lobes front (Hurd glacier).