Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Complication (medicine)A complication in medicine, or medical complication, is an unfavorable result of a disease, health condition, or treatment. Complications may adversely affect the prognosis, or outcome, of a disease. Complications generally involve a worsening in the severity of the disease or the development of new signs, symptoms, or pathological changes that may become widespread throughout the body and affect other organ systems. Thus, complications may lead to the development of new diseases resulting from previously existing diseases.
Connection (vector bundle)In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport must be linear. A linear connection is equivalently specified by a covariant derivative, an operator that differentiates sections of the bundle along tangent directions in the base manifold, in such a way that parallel sections have derivative zero.
Corneal opacityThe human cornea is a transparent membrane which allows light to pass through it. The word corneal opacification literally means loss of normal transparency of cornea. The term corneal opacity is used particularly for the loss of transparency of cornea due to scarring. Transparency of the cornea is dependent on the uniform diameter and the regular spacing and arrangement of the collagen fibrils within the stroma. Alterations in the spacing of collagen fibrils in a variety of conditions including corneal edema, scars, and macular corneal dystrophy is clinically manifested as corneal opacity.
Type theoryIn mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.
Centimetre or millimetre of waterA centimetre or millimetre of water (US spelling centimeter or millimeter of water) are less commonly used measures of pressure based on the pressure head of water. A centimetre of water (US spelling centimeter of water) is a unit of pressure. It may be defined as the pressure exerted by a column of water of 1 cm in height at 4 °C (temperature of maximum density) at the standard acceleration of gravity, so that 1 cmH2O (4°C) = 999.9720 kg/m3 × 9.80665 m/s2 × 1 cm = 98.063754138 Pa ≈ 98.
Millimetre of mercuryA millimetre of mercury is a manometric unit of pressure, formerly defined as the extra pressure generated by a column of mercury one millimetre high, and currently defined as exactly 133.322387415 pascals or exactly 133.322 pascals. It is denoted mmHg or mm Hg. Although not an SI unit, the millimetre of mercury is still routinely used in medicine, aviation, and many other scientific fields. One millimetre of mercury is approximately 1 Torr, which is 1/760 of standard atmospheric pressure (101325/760 ≈ 133.
Levi-Civita connectionIn Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection.
Type safetyIn computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors.
Complications of diabetesComplications of diabetes mellitus include problems that develop rapidly (acute) or over time (chronic) and may affect many organ systems. The complications of diabetes can dramatically impair quality of life and cause long-lasting disability. Overall, complications are far less common and less severe in people with well-controlled blood sugar levels. Some non-modifiable risk factors such as age at diabetes onset, type of diabetes, gender and genetics may influence risk.
