In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation.
The diesel engine, named after the German engineer Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is called a compression-ignition engine. This contrasts with engines using spark plug-ignition of the air-fuel mixture, such as a petrol engine or a gas engine.
Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.
Linear algebra is the branch of mathematics concerning linear equations such as:
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors, dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix.
In mathematics and physics, a vector space is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field.
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
A testicle or testis is the male gonad in all bilaterians, including humans. It is homologous to the female ovary. The functions of the testicles are to produce both sperm and androgens, primarily testosterone. Testosterone release is controlled by the anterior pituitary luteinizing hormone, whereas sperm production is controlled both by the anterior pituitary follicle-stimulating hormone and gonadal testosterone.
Cafedrine, sold under the brand name Akrinor among others, is a chemical linkage of norephedrine and theophylline and is a cardiac stimulant and antihypotensive agent used to increase blood pressure in people with hypotension. It has been marketed in Europe, South Africa, and Indonesia.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them also work with special relativity.
The Planck constant, or Planck's constant, denoted by , is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum. The closely related reduced Planck constant, equal to and denoted is commonly used in quantum physics equations.
Penmesterol, or penmestrol, also known as 17α-methyltestosterone 3-cyclopentyl enol ether, is a synthetic, orally active anabolic-androgenic steroid (AAS) that was developed in the early 1960s. It is the 3-cyclopentyl enol ether of methyltestosterone.
Nilestriol, also known as nylestriol, is a synthetic estrogen which was patented in 1971 and is marketed in China. It is the 3-cyclopentyl ether of ethinylestriol, and is also known as ethinylestriol cyclopentyl ether (EE3CPE). Nilestriol is a prodrug of ethinylestriol, and is a more potent estrogen in comparison. It is described as a slowly-metabolized, long-acting estrogen and derivative of estriol. Nilestriol was assessed in combination with levonorgestrel for the potential treatment of postmenopausal osteoporosis, but this formulation ultimately was not marketed.
Stenbolone acetate, also known as 2-methyl-4,5α-dihydro-δ1-testosterone 17β-acetate or as 2-methyl-5α-androst-1-en-17β-ol-3-one 17β-acetate, is a synthetic, injected anabolic–androgenic steroid (AAS) and derivative of dihydrotestosterone (DHT) which has been marketed in Spain.
Miproxifene (INN) is a nonsteroidal selective estrogen receptor modulator (SERM) of the triphenylethylene group that was never marketed. It is a derivative of afimoxifene (4-hydroxytamoxifen) in which an additional 4-isopropyl group is present in the β-phenyl ring. The drug has been found to be 3- to 10-fold more potent than tamoxifen in inhibiting breast cancer cell growth in in vitro models. Miproxifene is the active metabolite of miproxifene phosphate (TAT-59), a phosphate ester and prodrug of miproxifene that was developed to improve its water solubility. Miproxifene phosphate was under development for the treatment of breast cancer and reached phase III clinical trials for this indication but development was discontinued.
Miproxifene phosphate is a nonsteroidal selective estrogen receptor modulator (SERM) of the triphenylethylene group that was under development in Japan for the treatment of breast cancer but was abandoned and never marketed. It reached phase III clinical trials for this indication before development was discontinued. The drug is a phosphate ester and prodrug of miproxifene (DP-TAT-59) with improved water solubility that was better suited for clinical development. Miproxifene has been found to be 3- to 10-fold as potent as tamoxifen in inhibiting breast cancer cell growth in in vitro models. It is a derivative of afimoxifene (4-hydroxytamoxifen) in which an additional 4-isopropyl group is present in the β-phenyl ring.
Androstenediol dipropionate, or 5-androstenediol 3β,17β-dipropionate, also known as androst-5-ene-3β,17β-diol 3β,17β-dipropionate, is a synthetic anabolic–androgenic steroid and an androgen ester – specifically, the dipropionate diester of 5-androstenediol (androst-5-ene-3β,17β-diol) – which has been marketed in Europe, including in Spain, Italy, and Austria.
