Uniform convergenceIn the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .
Recursion (computer science)In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement.
UniformA uniform is a variety of costume worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects.
RecursionRecursion occurs when the definition of a concept or process depends on a simpler version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur.
Course-of-values recursionIn computability theory, course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion, the value of f(n) is computed from the sequence . The fact that such definitions can be converted into definitions using a simpler form of recursion is often used to prove that functions defined by course-of-values recursion are primitive recursive.
Uniform spaceIn the mathematical field of topology, a uniform space is a topological space with additional structure that is used to define uniform properties, such as completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate the weakest axioms needed for most proofs in analysis. In addition to the usual properties of a topological structure, in a uniform space one formalizes the notions of relative closeness and closeness of points.
Military uniformA military uniform is a standardised dress worn by members of the armed forces and paramilitaries of various nations. Military dress and styles have gone through significant changes over the centuries, from colourful and elaborate, ornamented clothing until the 19th century, to utilitarian camouflage uniforms for field and battle purposes from World War I (1914–1918) on. Military uniforms in the form of standardised and distinctive dress, intended for identification and display, are typically a sign of organised military forces equipped by a central authority.
Pointwise convergenceIn mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A net or sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as if (and only if) The function is said to be the pointwise limit function of the Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
Full dress uniformFull dress uniform, also known as a ceremonial dress uniform or parade dress uniform, is the most formal type of uniforms used by military, police, fire and other public uniformed services for official parades, ceremonies, and receptions, including private ones such as marriages and funerals. Full dress uniforms typically include full-size orders and medals insignia. Styles tend to trace back to uniforms used during the 19th century, although the 20th century saw the adoption of mess dress-styled full-dress uniforms.
Combat uniformA combat uniform, also called field uniform, battledress or military fatigues, is a casual type of uniform used by military, police, fire and other public uniformed services for everyday fieldwork and combat duty purposes, as opposed to dress uniforms worn in functions and parades. It generally consists of a jacket, trousers and shirt or T-shirt, all cut to be looser and more comfortable than more formal uniforms. Design may depend on regiment or service branch, e.g. army, navy, air force, marines, etc.
Compact convergenceIn mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology. Let be a topological space and be a metric space. A sequence of functions is said to converge compactly as to some function if, for every compact set , uniformly on as . This means that for all compact , If and with their usual topologies, with , then converges compactly to the constant function with value 0, but not uniformly.
Sobel operatorThe Sobel operator, sometimes called the Sobel–Feldman operator or Sobel filter, is used in and computer vision, particularly within edge detection algorithms where it creates an image emphasising edges. It is named after Irwin Sobel and Gary M. Feldman, colleagues at the Stanford Artificial Intelligence Laboratory (SAIL). Sobel and Feldman presented the idea of an "Isotropic 3 × 3 Image Gradient Operator" at a talk at SAIL in 1968. Technically, it is a discrete differentiation operator, computing an approximation of the of the image intensity function.
Binary heapA binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: Shape property: a binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right.
CorecursionIn computer science, corecursion is a type of operation that is to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data.
Prewitt operatorThe Prewitt operator is used in , particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical directions and is therefore relatively inexpensive in terms of computations like Sobel and Kayyali operators.
Well-founded relationIn mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is, an element m ∈ S not related by s R m (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.
Binary codeA binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits (which is also called a byte) can represent any of 256 possible values and can, therefore, represent a wide variety of different items.
Connected-component labelingConnected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with . Connected-component labeling is used in computer vision to detect connected regions in s, although s and data with higher dimensionality can also be processed.
Feature (computer vision)In computer vision and , a feature is a piece of information about the content of an image; typically about whether a certain region of the image has certain properties. Features may be specific structures in the image such as points, edges or objects. Features may also be the result of a general neighborhood operation or feature detection applied to the image. Other examples of features are related to motion in image sequences, or to shapes defined in terms of curves or boundaries between different image regions.
Binary search algorithmIn computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found.
