Inverse functionIn mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by For a function , its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.
PatientA patient is any recipient of health care services that are performed by healthcare professionals. The patient is most often ill or injured and in need of treatment by a physician, nurse, optometrist, dentist, veterinarian, or other health care provider. The word patient originally meant 'one who suffers'. This English noun comes from the Latin word patiens, the present participle of the deponent verb, patior, meaning 'I am suffering,' and akin to the Greek verb πάσχειν (paskhein, to suffer) and its cognate noun πάθος (pathos).
Inverse elementIn mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x. (An identity element is an element such that x * e = x and e * y = y for all x and y for which the left-hand sides are defined.
High-speed railHigh-speed rail (HSR) is a type of rail network utilizing trains that run significantly faster than those of traditional rail, using an integrated system of specialised rolling stock and dedicated tracks. While there is no single standard that applies worldwide, lines built to handle speeds above or upgraded lines in excess of are widely considered to be high-speed. The first high-speed rail system, the Tōkaidō Shinkansen, began operations in Japan in 1964. The system also became known by its English nickname the bullet train.
Tilting trainA tilting train is a train that has a mechanism enabling increased speed on regular rail tracks. As a train (or other vehicle) rounds a curve at speed, objects inside the train experience centrifugal force. This can cause packages to slide about or seated passengers to feel squashed by the outboard armrest, and standing passengers to lose their balance. Tilting trains are designed to counteract this by tilting the carriages towards the inside of the curve, thus compensating for the g-force.
Generalized inverseIn mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup.
Ridge regressionRidge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.
Inverse semigroupIn group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x = xyx and y = yxy, i.e. a regular semigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries. (The convention followed in this article will be that of writing a function on the right of its argument, e.g.
Doctor–patient relationshipThe doctor–patient relationship is a central part of health care and the practice of medicine. A doctor–patient relationship is formed when a doctor attends to a patient's medical needs and is usually through consent. This relationship is built on trust, respect, communication, and a common understanding of both the doctor and patients' sides. The trust aspect of this relationship goes is mutual: the doctor trusts the patient to reveal any information that may be relevant to the case, and in turn, the patient trusts the doctor to respect their privacy and not disclose this information to outside parties.
Inverse trigonometric functionsIn mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Sampling (statistics)In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.
EstimationEstimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter".
