The term rare earths denotes the group of 17 chemically similar metallic elements that includes scandium, yttrium, and the lanthanides (Spedding 1978; Connelly et al. 2005). The lanthanides are the series of elements with atomic numbers 57 to 71, all of which, except promethium, occur in nature. The rare-earth elements, being chemically similar to one another, invariably occur together in minerals and behave as a single chemical entity. Thus, the discovery of the rare earths themselves occurred over a period of nearly 160 years, from 1787 to 1941 (Szabadvary 1988; Weeks 1956).

Среднее Поволжье и Прикамье включают территорию, тяготеющую к Волге в среднем ее течении и к Каме — в нижнем и среднем течении, общей площадью около 500 тыс. км2. Эта территория почти равна площади Франции и в два раза превышает площадь Англии.

The natural resources on the earth seem to be randomly distributed but their variations over space and time are not all random. They exhibit a spatial correlation. This spatial correlation can be captured by geostatistics. Geostatistics deals with the analysis and modelling of geo-referenced data. The point observations are analyzed and interpolated to create spatial maps. For geostatistical interpolation, first the spatial correlation structures of the parameter of interest are quantified and then spatial interpolation is done using the quantified spatial correlation and optimal predictions at unobserved locations to create a map.

Polymeric materials are heavily loaded with mineral fillers such as talc, calcium carbonate (CaCO3) and silica from non-renewable resources such as limestone, sand, metamorphic rocks and rock deposits. These mineral fillers are found to increase the mechanical properties, thermal stability, process ability and fire retardancy of polymer composites. However, mining of these fillers can cause adverse effects on the environment such as depletion of natural flora and fauna, erosion of soil, instability of soil and rock masses and changes in the environmental landscape. <...>

We see with maps. Using maps to create complex visual understandings of the world is an activity that most of us are so used to that we do not tend to consider how the maps we read help us form these understandings. Map use has become a thoroughly commonplace activity, whether we are navigating in a city using a smartphone, planning a journey across the country, or looking at artworks that include images of maps in an art gallery or on an artist’s website.

In this chapter, minimal prerequisites not only for classical mechanics but also for physics, in general, are introduced. Physical dimensions, SI base units, SIderived units, and significant figures are discussed. Four coordinate systems, Cartesian coordinates, plane polar coordinates, cylindrical coordinates, and spherical coordinates are concisely shown. The coordinate transformation, which will be used in later chapters, is discussed. A Taylor series expansion is often used in physics, so that it is precisely explained. <...>

To the civil engineer, soil is any uncemented or weakly cemented accumulation of mineral particles formed by the weathering of rocks, the void space between the particles containing water and/or air. Weak cementation can be due to carbonates or oxides precipitated between the particles or due to organic matter. If the products of weathering remain at their original location they constitute a residual soil. If the products are transported and deposited in a different location they constitute a transported soil, the agents of transportation being gravity, wind, water and glaciers. During transportation the size and shape of particles can undergo change and the particles can be sorted into size ranges.

The pu rpose of th is exercise is to take the student into the field to dig in soils, to appreciate the characteristics of soil differences outlined in pages 1-40 of the textbook. This exercise can consist of several short field trips, or several half-days of describing different soils according to the format given on pages 8 and 10 of the textbook.

Soil can exist as a naturally occurring material in its undisturbed state, or as a compacted material. Geotechnical engineering involves the understanding and prediction of the behavior of soil. Like other construction materials, soil possesses mechanical properties related to strength, compressibility, and permeability. It is important to quantify these properties to predict how soil will behave under field loading for the safe design of soil structures (e.g. embankments, dams, waste containment liners, highway base courses, etc.), as well as other structures that will overly the soil. Quantification of the mechanical properties of soil is performed in the laboratory using standardized laboratory tests. <...>