MATLAB is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
In mathematics, a frieze or frieze pattern is a design on a two-dimensional surface that is repetitive in one direction. Such patterns occur frequently in architecture and decorative art. A frieze group is the set of symmetries of a frieze pattern, specifically the set of isometries of the pattern, that is geometric transformations built from rigid motions and reflections that preserve the pattern. The mathematical study of frieze patterns reveals that they can be classified into seven types according to their symmetries.
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.
A small multiple is a series of similar graphs or charts using the same scale and axes, allowing them to be easily compared. It uses multiple views to show different partitions of a dataset. The term was popularized by Edward Tufte.
A contour line of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function f(x, y) parallel to the (x, y)-plane. In cartography, a contour line joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines.
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from Linear-Quadratic Regulator (LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.
A pole figure is a graphical representation of the orientation of objects in space. For example, pole figures in the form of stereographic projections are used to represent the orientation distribution of crystallographic lattice planes in crystallography and texture analysis in materials science.
Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK. There is also a procedural "pylab" interface based on a state machine, designed to closely resemble that of MATLAB, though its use is discouraged. SciPy makes use of Matplotlib.
The meridian circle is an instrument for timing of the passage of stars across the local meridian, an event known as a culmination, while at the same time measuring their angular distance from the nadir. These are special purpose telescopes mounted so as to allow pointing only in the meridian, the great circle through the north point of the horizon, the north celestial pole, the zenith, the south point of the horizon, the south celestial pole, and the nadir. Meridian telescopes rely on the rotation of the sky to bring objects into their field of view and are mounted on a fixed, horizontal, east–west axis.
A solar tracker is a device that orients a payload toward the Sun. Payloads are usually solar panels, parabolic troughs, fresnel reflectors, lenses or the mirrors of a heliostat.
In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or directly to another agent in the marketplace. Supply can be in currency, time, raw materials, or any other scarce or valuable object that can be provided to another agent. This is often fairly abstract. For example in the case of time, supply is not transferred to one agent from another, but one agent may offer some other resource in exchange for the first spending time doing something. Supply is often plotted graphically as a supply curve, with the quantity provided plotted horizontally and the price plotted vertically.
First developed in 1985 by RockWare Inc, RockWorks is used by the mining, petroleum, and environmental industry for subsurface visualization, borehole database management as well as the creation of grids, solid models, calculating volumetric analysis, etc.
Deformation mechanism refers to the various processes occurring at micro-scale that are responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from their original position within the crystal lattice system. These small changes are preserved in various microstructures of materials such as rocks, metals and plastics, and can be studied in depth using optical or digital microscopy.
A stereoplotter uses stereo photographs to determine elevations. It has been the primary method to plot contour lines on topographic maps since the 1930s. Although the specific devices have advanced technologically, they are all based on the apparent change in position of a feature in the two stereo photographs.
The social science of economics makes extensive use of graphs to better illustrate the economic principles and trends it is attempting to explain. Those graphs have specific qualities that are not often found in other sciences.
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.
A position representation is the parameters used to express a position relative to a reference. When representing positions relative to the Earth, it is often most convenient to represent vertical position separately, and to use some other parameters to represent horizontal position. There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars. It is a type of geographic coordinate system.
In oceanography, temperature-salinity diagrams, sometimes called T-S diagrams, are used to identify water masses. In a T-S diagram, rather than plotting each water property as a separate "profile," with pressure or depth as the vertical coordinate, potential temperature is plotted versus salinity. As long as it remains isolated from the surface, where heat or fresh water can be gained or lost, and in the absence of mixing with other water masses, a water parcel's potential temperature and salinity are conserved. Deep water masses thus retain their T-S characteristics for long periods of time, and can be identified readily on a T-S plot.
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.
