Homogeneous spaceIn mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action of a group. Homogeneous spaces occur in the theories of Lie groups, algebraic groups and topological groups. More precisely, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively. The elements of G are called the symmetries of X.
Fracture mechanicsFracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip.
DentinDentin (ˈdɛntᵻn) (American English) or dentine (ˈdɛnˌtiːn or ˌdɛnˈtiːn) (British English) (substantia eburnea) is a calcified tissue of the body and, along with enamel, cementum, and pulp, is one of the four major components of teeth. It is usually covered by enamel on the crown and cementum on the root and surrounds the entire pulp. By volume, 45% of dentin consists of the mineral hydroxyapatite, 33% is organic material, and 22% is water. Yellow in appearance, it greatly affects the color of a tooth due to the translucency of enamel.
Strength reductionIn compiler construction, strength reduction is a compiler optimization where expensive operations are replaced with equivalent but less expensive operations. The classic example of strength reduction converts strong multiplications inside a loop into weaker additions – something that frequently occurs in array addressing. Examples of strength reduction include replacing a multiplication within a loop with an addition and replacing exponentiation within a loop with a multiplication.
CementumCementum is a specialized calcified substance covering the root of a tooth. The cementum is the part of the periodontium that attaches the teeth to the alveolar bone by anchoring the periodontal ligament. The cells of cementum are the entrapped cementoblasts, the cementocytes. Each cementocyte lies in its lacuna, similar to the pattern noted in bone. These lacunae also have canaliculi or canals. Unlike those in bone, however, these canals in cementum do not contain nerves, nor do they radiate outward.
Sports injurySports injuries are injuries that occur during sport, athletic activities, or exercising. In the United States, there are approximately 30 million teenagers and children who participate in some form of organized sport. Of those, about three million athletes age 14 years and under experience a sports injury annually. According to a study performed at Stanford University, 21 percent of the injuries observed in elite college athletes caused the athlete to miss at least one day of sport, and approximately 77 percent of these injuries involved the knee, lower leg, ankle, or foot.
Puiseux seriesIn mathematics, Puiseux series are a generalization of power series that allow for negative and fractional exponents of the indeterminate. For example, the series is a Puiseux series in the indeterminate x. Puiseux series were first introduced by Isaac Newton in 1676 and rediscovered by Victor Puiseux in 1850. The definition of a Puiseux series includes that the denominators of the exponents must be bounded. So, by reducing exponents to a common denominator n, a Puiseux series becomes a Laurent series in an nth root of the indeterminate.
Enamel hypoplasiaEnamel hypoplasia is a defect of the teeth in which the enamel is deficient in quantity, caused by defective enamel matrix formation during enamel development, as a result of inherited and acquired systemic condition(s). It can be identified as missing tooth structure and may manifest as pits or grooves in the crown of the affected teeth, and in extreme cases, some portions of the crown of the tooth may have no enamel, exposing the dentin. It may be generalized across the dentition or localized to a few teeth.
