Differential geometry of surfacesIn mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface.
Surface (topology)In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Gauss–Bonnet theoremIn the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology. In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. The Gauss–Bonnet theorem extends this to more complicated shapes and curved surfaces, connecting the local and global geometries. The theorem is named after Carl Friedrich Gauss, who developed a version but never published it, and Pierre Ossian Bonnet, who published a special case in 1848.
Growth factorA growth factor is a naturally occurring substance capable of stimulating cell proliferation, wound healing, and occasionally cellular differentiation. Usually it is a secreted protein or a steroid hormone. Growth factors are important for regulating a variety of cellular processes. Growth factors typically act as signaling molecules between cells. Examples are cytokines and hormones that bind to specific receptors on the surface of their target cells. They often promote cell differentiation and maturation, which varies between growth factors.
Biological processBiological processes are those processes that are vital for an organism to live, and that shape its capacities for interacting with its environment. Biological processes are made of many chemical reactions or other events that are involved in the persistence and transformation of life forms. Metabolism and homeostasis are examples. Biological processes within an organism can also work as bioindicators. Scientists are able to look at an individual's biological processes to monitor the effects of environmental changes.
Epidermal growth factorEpidermal growth factor (EGF) is a protein that stimulates cell growth and differentiation by binding to its receptor, EGFR. Human EGF is 6-kDa and has 53 amino acid residues and three intramolecular disulfide bonds. EGF was originally described as a secreted peptide found in the submaxillary glands of mice and in human urine. EGF has since been found in many human tissues, including platelets, submandibular gland (submaxillary gland), and parotid gland. Initially, human EGF was known as urogastrone.
Economic growthEconomic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of increase in the real and nominal gross domestic product (GDP). Growth is usually calculated in real terms – i.e., inflation-adjusted terms – to eliminate the distorting effect of inflation on the prices of goods produced. Measurement of economic growth uses national income accounting.
Dual graphIn the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each pair of faces in G that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Thus, each edge e of G has a corresponding dual edge, whose endpoints are the dual vertices corresponding to the faces on either side of e.
Endogenous growth theoryEndogenous growth theory holds that economic growth is primarily the result of endogenous and not external forces. Endogenous growth theory holds that investment in human capital, innovation, and knowledge are significant contributors to economic growth. The theory also focuses on positive externalities and spillover effects of a knowledge-based economy which will lead to economic development. The endogenous growth theory primarily holds that the long run growth rate of an economy depends on policy measures.
Nerve growth factorNerve growth factor (NGF) is a neurotrophic factor and neuropeptide primarily involved in the regulation of growth, maintenance, proliferation, and survival of certain target neurons. It is perhaps the prototypical growth factor, in that it was one of the first to be described. Since it was first isolated by Nobel Laureates Rita Levi-Montalcini and Stanley Cohen in 1956, numerous biological processes involving NGF have been identified, two of them being the survival of pancreatic beta cells and the regulation of the immune system.
Post-growthPost-growth is a stance on economic growth concerning the limits-to-growth dilemma — recognition that, on a planet of finite material resources, extractive economies and populations cannot grow infinitely. The term "post-growth" acknowledges that economic growth can generate beneficial effects up to a point, but beyond that point (cited as $25,000 GDP/capita by Richard Wilkinson and Kate Pickett in their book The Spirit Level) it is necessary to look for other indicators and techniques to increase human wellbeing.
