BIBO stabilityIn signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is For discrete-time signals: For continuous-time signals: For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.
Time-invariant systemIn control theory, a time-invariant (TI) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends only indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant.
Linear time-invariant systemIn system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).
ArtArt is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas. There is no generally agreed definition of what constitutes art, and its interpretation has varied greatly throughout history and across cultures. In the Western tradition, the three classical branches of visual art are painting, sculpture, and architecture.
Outsider artOutsider art is art made by self-taught or supposedly naïve artists with typically little or no contact with the conventions of the art worlds. In many cases, their work is discovered only after their deaths. Often, outsider art illustrates extreme mental states, unconventional ideas, or elaborate fantasy worlds. The term outsider art was coined in 1972 as the title of a book by art critic Roger Cardinal. It is an English equivalent for art brut (aʁ bʁyt, "raw art" or "rough art"), a label created in the 1940s by French artist Jean Dubuffet to describe art created outside the boundaries of official culture.
Public artPublic art is art in any media whose form, function and meaning are created for the general public through a public process. It is a specific art genre with its own professional and critical discourse. Public art is visually and physically accessible to the public; it is installed in public space in both outdoor and indoor settings. Public art seeks to embody public or universal concepts rather than commercial, partisan, or personal concepts or interests.
Medieval artThe medieval art of the Western world covers a vast scope of time and place, with over 1000 years of art in Europe, and at certain periods in Western Asia and Northern Africa. It includes major art movements and periods, national and regional art, genres, revivals, the artists' crafts, and the artists themselves. Art historians attempt to classify medieval art into major periods and styles, often with some difficulty.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Exact differential equationIn mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering. Given a simply connected and open subset D of R2 and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, so that and An exact equation may also be presented in the following form: where the same constraints on I and J apply for the differential equation to be exact.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Transfer functionIn engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. They are widely used in electronic engineering tools like circuit simulators and control systems. In some simple cases, this function can be represented as two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve.
Cellular differentiationCellular differentiation is the process in which a stem cell changes from one type to a differentiated one. Usually, the cell changes to a more specialized type. Differentiation happens multiple times during the development of a multicellular organism as it changes from a simple zygote to a complex system of tissues and cell types. Differentiation continues in adulthood as adult stem cells divide and create fully differentiated daughter cells during tissue repair and during normal cell turnover.
Automatic differentiationIn mathematics and computer algebra, automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational differentiation, is a set of techniques to evaluate the partial derivative of a function specified by a computer program. Automatic differentiation exploits the fact that every computer calculation, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.
Product differentiationIn economics and marketing, product differentiation (or simply differentiation) is the process of distinguishing a product or service from others to make it more attractive to a particular target market. This involves differentiating it from competitors' products as well as from a firm's other products. The concept was proposed by Edward Chamberlin in his 1933 book, The Theory of Monopolistic Competition. Firms have different resource endowments that enable them to construct specific competitive advantages over competitors.
Differentiation rulesThis is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers (R) that return real values; although more generally, the formulae below apply wherever they are well defined — including the case of complex numbers (C). For any value of , where , if is the constant function given by , then . Let and . By the definition of the derivative, This shows that the derivative of any constant function is 0.
Planetary differentiationIn planetary science, planetary differentiation is the process by which the chemical elements of a planetary body accumulate in different areas of that body, due to their physical or chemical behavior (e.g. density and chemical affinities). The process of planetary differentiation is mediated by partial melting with heat from radioactive isotope decay and planetary accretion. Planetary differentiation has occurred on planets, dwarf planets, the asteroid 4 Vesta, and natural satellites (such as the Moon).
Notation for differentiationIn differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation (and its opposite operation, the antidifferentiation or indefinite integration) are listed below.
Cluster of differentiationThe cluster of differentiation (also known as cluster of designation or classification determinant and often abbreviated as CD) is a protocol used for the identification and investigation of cell surface molecules providing targets for immunophenotyping of cells. In terms of physiology, CD molecules can act in numerous ways, often acting as receptors or ligands important to the cell. A signal cascade is usually initiated, altering the behavior of the cell (see cell signaling).
Differentiation (sociology)In system theory, "differentiation" is the increase of subsystems in a modern society to increase the complexity of a society. Each subsystem can make different connections with other subsystems, and this leads to more variation within the system in order to respond to variation in the environment. Differentiation that leads to more variation allows for better responses to the environment, and also for faster evolution (or perhaps sociocultural evolution), which is defined sociologically as a process of selection from variation; the more differentiation (and thus variation) that is available, the better the selection.
