Decay Constant A quantity is subject to exponential decay if it decreases at a rate proportional Proportionality, proportion or proportional may refer to: Mathematics * Proportionality (mathematics), the property of two variables being in a multiplicative relation to a constant * Ratio, of one quantity to another, especially of a part compared ... to its current value. Symbolically, this process can be expressed by the following differential equation, where ''N'' is the quantity and ''λ'' (lambda) is a positive rate called the exponential decay constant: :\frac = -\lambda N. The solution to this equation (see derivation Derivation may refer to: * Derivation (differential algebra), a unary function satisfying the Leibniz product law * Derivation (linguistics) * Formal proof or derivation, a sequence of sentences each of which is an axiom or follows from the precedi ... below) is: :N(t) = N_0 e^, where ''N''(''t'') is the quantity at time ''t'', ''N''0 = ''N''(0) is the initial quantity, t ... [...More Info...]       [...Related Items...] Scalar Multiplication In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module (mathematics), module in abstract algebra). In common geometrical contexts, scalar multiplication of a real number, real Euclidean vector by a positive real number multiplies the magnitude of the vector—without changing its direction. The term "Scalar (mathematics), scalar" itself derives from this usage: a scalar is that which uniform scaling, scales vectors. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar). Definition In general, if ''K'' is a field (algebra), field and ''V'' is a vector space over ''K'', then scalar multiplication is a function (mathematics), function from ''K'' × ''V'' to ''V''. The result of applying this function to ''k'' in ''K'' and v in ''V'' is denoted ''k''v. Prop ... [...More Info...]       [...Related Items...] picture info Poisson Process In probability Probability is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained ..., statistics and related fields, a Poisson point process is a type of random In common parlance, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. I ... mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs ... that consists of points Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland ... [...More Info...]       [...Related Items...] picture info Law Of Large Numbers In probability theory Probability theory is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are containe ..., the law of large numbers (LLN) is a theorem In mathematics, a theorem is a statement (logic), statement that has been Mathematical proof, proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the the ... that describes the result of performing the same experiment a large number of times. According to the law, the average In colloquial language, an average is a single number taken as representative of a non-empty list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divide ... of the results obtained from a large number of ... [...More Info...]       [...Related Items...] picture info Natural Science Natural science is a branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , plant biology or phytology, is the science of plant life and a branch of biology. A botanist, plant scientist or phytologist is a scientist who spe ... of science Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as an invention. ... concerned with the description, understanding and prediction of natural phenomena Nature, in the broadest sense, is the natural, physical, material world or universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and ..., based on empirical evidence Empirical evidence for a proposition In logic and linguistics, a proposition i ... [...More Info...]       [...Related Items...] picture info Modified-release Dosage Modified-release dosage is a mechanism that (in contrast to immediate-release dosage) delivers a drug A drug is any chemical substance that causes a change in an organism's physiology or psychology when consumed. Drugs are typically distinguished from food and substances that provide nutritional support. Consumption of drugs can be via insuffl ... with a delay after its administration Administration may refer to: Management of organizations * Management, the act of directing people towards accomplishing a goal ** Administration (government), management in or of government *** Administrative division ** Academic administratio ... (delayed-release dosage) or for a prolonged period of time (extended-release R, XR, XLdosage) or to a specific target in the body (targeted-release dosage). [...More Info...]       [...Related Items...] picture info Bateman Equation In nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ..., the Bateman equation is a mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environm ... describing abundances and activities in a decay chain In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". Most Radionuclide, radioisotopes do not de ... as a function of time, based on the decay rate Radioactive decay (also known as nuclear decay, radioactivity, r ... [...More Info...]       [...Related Items...] picture info Pharmacokinetics Pharmacokinetics (from Ancient Greek ''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to determine the fate of substances administered to a living organism. The substances of interest include any chemical xenobiotic such as: pharmaceutical drugs, pesticides, food additives, cosmetics, etc. It attempts to analyze chemical metabolism and to discover the fate of a chemical from the moment that it is administered up to the point at which it is completely excreted, eliminated from the body. Pharmacokinetics is the study of how an organism affects a drug, whereas pharmacodynamics (PD) is the study of how the drug affects the organism. Both together influence dosing, benefit, and adverse effects, as seen in PK/PD models. Overview Pharmacokinetics describes how the body affects a specific xenobiotic/chemical after administration through the mechanisms of absorption and distributi ... [...More Info...]       [...Related Items...] picture info Nuclear Science Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons. Discoveries in nuclear physics have led to nuclear technology, applications in many fields. This includes nuclear power, nuclear weapons, nuclear medicine and magnetic resonance imaging, industrial and agricultural isotopes, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology. Such applications are studied in the field of nuclear engineering. Particle physics evolved out of nuclear physics and the two fields are typically taught in close association. Nuclear astrophysics, the application of nuclear physics to astrophysics, is crucial in explaining the inner workings of stars and the nucleosynthesis, origin of the chemical elements. History The history o ... [...More Info...]       [...Related Items...] picture info One Half One half is the irreducible fraction An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integer An integer (from the Latin wikt:integer#Latin, ''integer'' meaning "whole") is colloquial ... resulting from dividing one 1 (one, also called unit, and unity) is a number A number is a mathematical object used to counting, count, measurement, measure, and nominal number, label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can ... by two 2 (two) is a number, numeral (linguistics), numeral and numerical digit, digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a Dualistic cosmology, duality, it ... or the fraction resulting from dividing any number by its double. Multiplication Multiplication (often denoted by the cross symbol , by the mid-li ... [...More Info...]       [...Related Items...] picture info Multiplicative Inverse In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity In mathematics, an identity element, or neutral element, is a special type of element of a set with respect to a binary operation on that set, which leaves any element of the set unchanged when combined with it. This concept is used in algebraic s ..., 1. The multiplicative inverse of a fraction A fraction (from Latin ', "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths .. ... [...More Info...]       [...Related Items...] picture info Half-life Half-life (symbol ''t''1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ... to describe how quickly unstable atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...s undergo radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ... or how long stab ... [...More Info...]       [...Related Items...]