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H-fractal
In fractal geometry, the H tree is a fractal tree structure constructed from perpendicular line segments, each smaller by a factor of the square root of 2 from the next larger adjacent segment. It is so called because its repeating pattern resembles the letter "H". It has Hausdorff dimension 2, and comes arbitrarily close to every point in a rectangle. Its applications include VLSI design and microwave engineering. Construction An H tree can be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by \sqrt2. A variant of this construction could also be defined in which the length at each iteration is multiplied by a ratio less than 1/\sqrt2, but for this variant the resulting shape covers only part of its bounding rectangle, with a fractal boundary. An alternative process that gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H Tree
In fractal geometry, the H tree is a fractal tree structure constructed from perpendicular line segments, each smaller by a factor of the square root of 2 from the next larger adjacent segment. It is so called because its repeating pattern resembles the letter "H". It has Hausdorff dimension 2, and comes arbitrarily close to every point in a rectangle. Its applications include VLSI design and microwave engineering. Construction An H tree can be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by \sqrt2. A variant of this construction could also be defined in which the length at each iteration is multiplied by a ratio less than 1/\sqrt2, but for this variant the resulting shape covers only part of its bounding rectangle, with a fractal boundary. An alternative process that gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HTree
An HTree is a specialized tree data structure for directory indexing, similar to a B-tree. They are constant depth of either one or two levels, have a high fanout factor, use a hash of the filename, and do not require balancing. The HTree algorithm is distinguished from standard B-tree methods by its treatment of hash collisions, which may overflow across multiple leaf and index blocks. HTree indexes are used in the ext3 and ext4 Linux filesystems, and were incorporated into the Linux kernel around 2.5.40. HTree indexing improved the scalability of Linux ext2 based filesystems from a practical limit of a few thousand files, into the range of tens of millions of files per directory. History The HTree index data structure and algorithm were developed by Daniel Phillips in 2000 and implemented for the ext2 filesystem in February 2001. A port to the ext3 filesystem by Christopher Li and Andrew Morton in 2002 during the 2.5 kernel series added journal based crash consistency. With ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review B
''Physical Review B: Condensed Matter and Materials Physics'' (also known as PRB) is a peer-reviewed, scientific journal, published by the American Physical Society (APS). The Editor of PRB is Laurens W. Molenkamp. It is part of the ''Physical Review'' family of journals. About the Physical Review Journals The current Editor in Chief is . PRB currently publishes over 4500 papers a year, making it one of the largest physics journals in the world. PRB ranked by the Eigenfactor, University of Washingto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, claiming nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science ( informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoit Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation. This should not be confused with a closed manifold. Equivalent definitions By definition, a subset A of a topological space (X, \tau) is called if its complement X \setminus A is an open subset of (X, \tau); that is, if X \setminus A \in \tau. A set is closed in X if and only if it is equal to its closure in X. Equivalently, a set is closed if and only if it contains all of its limit points. Yet another equivalent definition is that a set is closed if and only if it contains all of its boundary points. Every subset A \subseteq X is always contained in its (topological) closure in X, which is denoted by \operatorname_X A; that is, if A \subseteq X then A \subseteq \oper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendroid (topology)
In mathematics, a dendroid is a type of topological space, satisfying the properties that it is hereditarily unicoherent (meaning that every subcontinuum of ''X'' is unicoherent), arcwise connected, and forms a continuum. The term dendroid was introduced by Bronisław Knaster lecturing at the University of Wrocław,. although these spaces were studied earlier by Karol Borsuk and others.. proved that dendroids have the fixed-point property: Every continuous function from a dendroid to itself has a fixed point. proved that every dendroid is ''tree-like'', meaning that it has arbitrarily fine open covers whose nerve is a tree. The more general question of whether every tree-like continuum has the fixed-point property, posed by , was solved in the negative by David P. Bellamy, who gave an example of a tree-like continuum without the fixed-point property. In Knaster's original publication on dendroids, in 1961, he posed the problem of characterizing the dendroids which can be embed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Curve
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called ''Peano curves'', but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano. Definition Intuitively, a curve in two or three (or higher) dimensions can be thought of as the path of a continuously moving point. To eliminate the inherent vagueness of this notion, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a ''curve'': In the most general form, the range of such a function may lie in an arbitrary topological space, but in the most commonly studied cases, the range will lie in a Euclidean space such as the 2-dimensional plane (a ''pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal Canopy
In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely.Bello, Ignacio; Kaul, Anton; and Britton, Jack R. (2013). ''Topics in Contemporary Mathematics'', p.511. Cengage Learning. . Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: #The angle between any two neighboring line segments is the same throughout the fractal. #The ratio of lengths of any two consecutive line segments is constant. #Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a Graph (discrete mathematics)#Connected graph, connected graph. The pulmonary system used by humans to breat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal Canopy
In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely.Bello, Ignacio; Kaul, Anton; and Britton, Jack R. (2013). ''Topics in Contemporary Mathematics'', p.511. Cengage Learning. . Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: #The angle between any two neighboring line segments is the same throughout the fractal. #The ratio of lengths of any two consecutive line segments is constant. #Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a Graph (discrete mathematics)#Connected graph, connected graph. The pulmonary system used by humans to breat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
