FactorialIn mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book Sefer Yetzirah.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Near-death experienceA near-death experience (NDE) is a profound personal experience associated with death or impending death which researchers describe as having similar characteristics. When positive, which the great majority are, such experiences may encompass a variety of sensations including detachment from the body, feelings of levitation, total serenity, security, warmth, joy, the experience of absolute dissolution, review of major life events, the presence of a light, and seeing dead relatives.
Religious experienceA religious experience (sometimes known as a spiritual experience, sacred experience, or mystical experience) is a subjective experience which is interpreted within a religious framework. The concept originated in the 19th century, as a defense against the growing rationalism of Western society. William James popularised the concept. In some religions this may result in unverified personal gnosis. Many religious and mystical traditions see religious experiences (particularly the knowledge which comes with them) as revelations caused by divine agency rather than ordinary natural processes.
Out-of-body experienceAn out-of-body experience (OBE or sometimes OOBE) is a phenomenon in which a person perceives the world from a location outside their physical body. An OBE is a form of autoscopy (literally "seeing self"), although this term is more commonly used to refer to the pathological condition of seeing a second self, or doppelgänger. The term out-of-body experience was introduced in 1943 by G. N. M. Tyrrell in his book Apparitions, and was adopted by researchers such as Celia Green, and Robert Monroe, as an alternative to belief-centric labels such as "astral projection" or "spirit walking".
Reciprocal gamma functionIn mathematics, the reciprocal gamma function is the function where Γ(z) denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that log log grows no faster than log ), but of infinite type (meaning that log grows faster than any multiple of , since its growth is approximately proportional to log in the left-half plane).
Volume of an n-ballIn geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space. The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is where is the volume of the unit n-ball, the n-ball of radius 1.
Coordinate systemIn geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring.
SimplexIn geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices.
Barycentric coordinate systemIn geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.). The barycentric coordinates of a point can be interpreted as masses placed at the vertices of the simplex, such that the point is the center of mass (or barycenter) of these masses. These masses can be zero or negative; they are all positive if and only if the point is inside the simplex.
ExperienceExperience refers to conscious events in general, more specifically to perceptions, or to the practical knowledge and familiarity that is produced by these processes. Understood as a conscious event in the widest sense, experience involves a subject to which various items are presented. In this sense, seeing a yellow bird on a branch presents the subject with the objects "bird" and "branch", the relation between them and the property "yellow". Unreal items may be included as well, which happens when experiencing hallucinations or dreams.
Herpes simplex keratitisHerpetic simplex keratitis is a form of keratitis caused by recurrent herpes simplex virus (HSV) infection in the cornea. It begins with infection of epithelial cells on the surface of the eye and retrograde infection of nerves serving the cornea. Primary infection typically presents as swelling of the conjunctiva and eyelids (blepharoconjunctivitis), accompanied by small white itchy lesions on the corneal surface. The effect of the lesions varies, from minor damage to the epithelium (superficial punctate keratitis), to more serious consequences such as the formation of dendritic ulcers.
Psychedelic experienceA psychedelic experience (known colloquially as a trip) is a temporary altered state of consciousness induced by the consumption of a psychedelic substance (most commonly LSD, mescaline, psilocybin mushrooms, or DMT). For example, an acid trip is a psychedelic experience brought on by the use of LSD, while a mushroom trip is a psychedelic experience brought on by the use of psilocybin. Psychedelic experiences feature alterations in normal perception such as visual distortions and a subjective loss of self-identity, sometimes interpreted as mystical experiences.
Herpes simplex virusHerpes simplex virus 1 and 2 (HSV-1 and HSV-2), also known by their taxonomic names Human alphaherpesvirus 1 and Human alphaherpesvirus 2, are two members of the human Herpesviridae family, a set of viruses that produce viral infections in the majority of humans. Both HSV-1 and HSV-2 are very common and contagious. They can be spread when an infected person begins shedding the virus. As of 2016, about 67% of the world population under the age of 50 had HSV-1. In the United States, about 47.8% and 11.
Herpes simplexHerpes simplex is a viral infection caused by the herpes simplex virus. Infections are categorized based on the part of the body infected. Oral herpes involves the face or mouth. It may result in small blisters in groups often called cold sores or fever blisters or may just cause a sore throat. Genital herpes, often simply known as herpes, involves the genitalia. It may have minimal symptoms or form blisters that break open and result in small ulcers. These typically heal over two to four weeks.
Change of basisIn mathematics, an ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence of n scalars called coordinates. If two different bases are considered, the coordinate vector that represents a vector v on one basis is, in general, different from the coordinate vector that represents v on the other basis. A change of basis consists of converting every assertion expressed in terms of coordinates relative to one basis into an assertion expressed in terms of coordinates relative to the other basis.
Uniform 8-polytopeIn eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets. A uniform 8-polytope is one which is vertex-transitive, and constructed from uniform 7-polytope facets. Regular 8-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v}, with v {p,q,r,s,t,u} 7-polytope facets around each peak.
Quadratic equationIn algebra, a quadratic equation () is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.
Herpetic gingivostomatitisGingivostomatitis is a combination of gingivitis and stomatitis, or an inflammation of the oral mucosa and gingiva. Herpetic gingivostomatitis is often the initial presentation during the first ("primary") herpes simplex infection. It is of greater severity than herpes labialis (cold sores) which is often the subsequent presentations. Primary herpetic gingivostomatitis is the most common viral infection of the mouth.
OrthoherpesviridaeHerpesviridae is a large family of DNA viruses that cause infections and certain diseases in animals, including humans. The members of this family are also known as herpesviruses. The family name is derived from the Greek word ἕρπειν ( 'to creep'), referring to spreading cutaneous lesions, usually involving blisters, seen in flares of herpes simplex 1, herpes simplex 2 and herpes zoster (shingles). In 1971, the International Committee on the Taxonomy of Viruses (ICTV) established Herpesvirus as a genus with 23 viruses among four groups.
