Planetary boundary layerIn meteorology, the planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL) or peplosphere, is the lowest part of the atmosphere and its behaviour is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface radiative forcing in an hour or less. In this layer physical quantities such as flow velocity, temperature, and moisture display rapid fluctuations (turbulence) and vertical mixing is strong.
Triple productIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
SeizureAn epileptic seizure, informally known as a seizure, is a period of symptoms due to abnormally excessive or synchronous neuronal activity in the brain. Outward effects vary from uncontrolled shaking movements involving much of the body with loss of consciousness (tonic-clonic seizure), to shaking movements involving only part of the body with variable levels of consciousness (focal seizure), to a subtle momentary loss of awareness (absence seizure). Most of the time these episodes last less than two minutes and it takes some time to return to normal.
Orthogonal transformationIn linear algebra, an orthogonal transformation is a linear transformation T : V → V on a real inner product space V, that preserves the inner product. That is, for each pair u, v of elements of V, we have Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them. In particular, orthogonal transformations map orthonormal bases to orthonormal bases. Orthogonal transformations are injective: if then , hence , so the kernel of is trivial.
Matrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .
Seizure typesIn the field of neurology, seizure types are categories of seizures defined by seizure behavior, symptoms, and diagnostic tests. The International League Against Epilepsy (ILAE) 2017 classification of seizures is the internationally recognized standard for identifying seizure types. The ILAE 2017 classification of seizures is a revision of the prior ILAE 1981 classification of seizures. Distinguishing between seizure types is important since different types of seizures may have different causes, outcomes, and treatments.
Focal seizureFocal seizures (also called partial seizures and localized seizures) are seizures which affect initially only one hemisphere of the brain. The brain is divided into two hemispheres, each consisting of four lobes – the frontal, temporal, parietal and occipital lobes. A focal seizure is generated in and affects just one part of the brain – a whole hemisphere or part of a lobe. Symptoms will vary according to where the seizure occurs. When seizures occur in the frontal lobe the patient may experience a wave-like sensation in the head.
Vector calculusVector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Generalized tonic–clonic seizureA generalized tonic–clonic seizure, commonly known as a grand mal seizure or GTCS, is a type of generalized seizure that produces bilateral, convulsive tonic and clonic muscle contractions. Tonic–clonic seizures are the seizure type most commonly associated with epilepsy and seizures in general and the most common seizure associated with metabolic imbalances. It is a misconception that they are the sole type of seizure, as they are the main seizure type in approximately 10% of those with epilepsy.
Product (mathematics)In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together). When one factor is an integer, the product is called a multiple. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication.
Absence seizureAbsence seizures are one of several kinds of generalized seizures. These seizures are sometimes referred to as petit mal seizures (from the French for "little illness", a term dated in the late 18th century). Absence seizures are characterized by a brief loss and return of consciousness, generally not followed by a period of lethargy (i.e. without a notable postictal state). Absence seizures are most common in children. They affect both sides of the brain. Absence seizures affect between 0.7 and 4.
