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Bifurcation
Bifurcation or bifurcated may refer to: Science and technology * Bifurcation theory, the study of sudden changes in dynamical systems ** Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow * River bifurcation, the forking of a river into its tributaries * Bifurcation lake, a lake that flows into two different drainage basins * Bifurcated bonding, a single hydrogen atom participates in two hydrogen bonds Other uses * Bifurcation (law), the division of issues in a trial See also * Aortic bifurcation, the point at which the abdominal aorta bifurcates into the left and right common iliac arteries * Tracheal bifurcation, or the carina of trachea (Latin: ''bifurcatio tracheae'') * Bifurcation diagram * Bifurcate merging, a kinship system * False dilemma or bifurcation * Tongue bifurcation (other) * Fork (other) A fork is a utensil for eating and cooking. Fork may also refer to: Implements * Fork (road), a type of intersection where a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them . Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bifurcations, which can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
River Bifurcation
River bifurcation (from la, furca, fork) occurs when a river flowing in a single stream separates into two or more separate streams (called distributaries) which then continue downstream. Some rivers form complex networks of distributaries, typically in their deltas. If the streams eventually merge again or empty into the same body of water, then the bifurcation forms a river island. River bifurcation may be temporary or semi-permanent, depending on the strength of the material that is dividing the two distributaries. For example, a mid-stream island of soil or silt in a delta is most likely temporary, due to low material strength. A location where a river divides around a rock fin, e.g. a volcanically formed dike, or a mountain, may be more lasting as a result of higher material strength and resistance to weathering and erosion. A bifurcation may also be man-made, for example when two streams are separated by a long bridge pier. Scientific study of bifurcation River bifurcati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation (law)
Bifurcation is a judge's ability in law to divide a trial into two parts so as to render a judgment on a set of legal issues without looking at all aspects. Frequently, civil cases are bifurcated into separate liability and damages proceedings. Criminal trials are also often bifurcated into guilt and sentencing phases, especially in capital cases. In divorce cases, some states allow bifurcation, that permits a divorce case to be finalized with certain aspects, such as property, to be dealt with after dissolution. Some states permit bifurcation, some do not allow it, and some state statutes do not address the issue. In arbitration, bifurcation can be used to get past certain issues, that might otherwise stall negotiations, concluding certain points that are agreed upon, while working on a solution to whatever problem initiated the need for bifurcation. Bifurcation under the Federal Rules of Civil Procedure In Federal Court, judges have wide discretion to structure trials. Fact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable values with a solid line and unstable values with a dotted line, although often the unstable points are omitted. Bifurcation diagrams enable the visualization of bifurcation theory. Logistic map An example is the bifurcation diagram of the logistic map: : x_=rx_n(1-x_n). \, The bifurcation parameter ''r'' is shown on the horizontal axis of the plot and the vertical axis shows the set of values of the logistic function visited asymptotically from almost all initial conditions. The bifurcation diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation. The ratio of the lengths of successive intervals between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Lake
A bifurcation lake is a lake that has outflows into two different drainage basins and thus the drainage divide cannot be defined exactly because it is situated in the middle of the lake. Examples Vesijako (the name ''Vesijako'' actually means "drainage divide") and Lummene in the Finnish Lakeland are two nearby lakes in Finland. Both drain in two directions: into the Kymijoki basin that drains into the Gulf of Finland and into the Kokemäenjoki basin that drains into the Gulf of Bothnia. Similarly the lakes Isojärvi and Inhottu in the Karvianjoki basin in the Satakunta region of western Finland both have two outlets: from Inhottu the waters flow into the Gulf of Bothnia through the Eteläjoki River in Pori and into lake Isojärvi through the Pomarkunjoki River. From lake Isojärvi the waters flow to the Gulf of Bothnia through the Pohjajoki river in Pori and through the Merikarvianjoki river in Merikarvia. In the Karvianjoki basin there have formerly been two other bifurcatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squeeze Mapping
In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is ''not'' a rotation or shear mapping. For a fixed positive real number , the mapping :(x, y) \mapsto (ax, y/a) is the ''squeeze mapping'' with parameter . Since :\ is a hyperbola, if and , then and the points of the image of the squeeze mapping are on the same hyperbola as is. For this reason it is natural to think of the squeeze mapping as a hyperbolic rotation, as did Émile Borel in 1914, by analogy with ''circular rotations'', which preserve circles. Logarithm and hyperbolic angle The squeeze mapping sets the stage for development of the concept of logarithms. The problem of finding the area bounded by a hyperbola (such as is one of quadrature. The solution, found by Grégoire de Saint-Vincent and Alphonse Antonio de Sarasa in 1647, required the natural logarithm function, a new concept. Some insight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aortic Bifurcation
The aortic bifurcation is the point at which the abdominal aorta bifurcates (forks) into the left and right common iliac arteries. The aortic bifurcation is usually seen at the level of L4, just above the junction of the left and right common iliac veins. The right common iliac artery passes in front of the left common iliac vein. In some individual, mainly women with lumbar lordosis this vein can be compressed between the vertebra and the artery. This is the so-called Cockett syndrome or May–Thurner syndrome can cause a slower venous flow and the possibility of deep venous thrombosis in the left leg mainly in pregnancy. In surface anatomy, the bifurcation approximately corresponds to the umbilicus. Additional images Image:Gray531.png, The abdominal aorta and its branches. Image:Gray847.png, Abdominal portion of the sympathetic trunk, with the celiac and hypogastric plexuses. Image:Gray1121.png, Posterior abdominal wall, after removal of the peritoneum, showing kidney ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcated Bonding
In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Such an interacting system is generally denoted , where the solid line denotes a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond. The most frequent donor and acceptor atoms are the second-row elements nitrogen (N), oxygen (O), and fluorine (F). Hydrogen bonds can be intermolecular (occurring between separate molecules) or intramolecular (occurring among parts of the same molecule). The energy of a hydrogen bond depends on the geometry, the environment, and the nature of the specific donor and acceptor atoms and can vary between 1 and 40 kcal/mol. This makes them somewhat stronger than a van der Waals interaction, and weaker than fully covalent or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tracheal Bifurcation
In anatomy, the carina or tracheal bifurcation is a ridge of cartilage in the trachea that occurs between the division of the two main bronchi. Structure The carina occurs at the lower end of the trachea (usually at the level of the 4th to 5th thoracic vertebra). This is in line with the sternal angle, but the carina may raise or descend up to two vertebrae higher or lower with breathing. The carina lies to the left of the midline, and runs antero-posteriorly (front to back). The bronchial arteries supply the carina and the rest of the lower trachea. The carina is around the area posterior to where the aortic arch crosses to the left of the trachea. The azygos vein crosses right to the trachea above the carina. Clinical significance Foreign bodies that fall down the trachea are more likely to enter the right bronchus. The mucous membrane of the carina is the most sensitive area of the trachea and larynx for triggering a cough reflex. Widening and distortion of the carina i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcate Merging
Iroquois kinship (also known as bifurcate merging) is a kinship system named after the Haudenosaunee people, also known as the ''Iroquois'', whose kinship system was the first one described to use this particular type of system. Identified by Lewis Henry Morgan in his 1871 work ''Systems of Consanguinity and Affinity of the Human Family'', the Iroquois system is one of the six major kinship systems (Eskimo, Hawaiian, Iroquois, Crow, Omaha, and Sudanese). Kinship system The system has both classificatory and descriptive terms. In addition to gender and generation, Iroquois kinship also distinguishes 'same-sex' and 'cross-sex' parental siblings: the brothers of Ego's (the subject from whose perspective the kinship is based) father, and the sisters of Ego's mother, are referred to by the same parental kinship terms used for Ego's Father and Mother. The sisters of Ego's father, and the brothers of Ego's mother, on the other hand, are referred to by non-parental kinship terms, comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Dilemma
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when in fact, there could be many. For example, a false dilemma is committed when it is claimed that "Stacey spoke out against capitalism; therefore, she must be a communist". One of the options excluded is that Stacey may be neither communist nor capitalist. False dilemmas often have the form of treating two contraries, which may both be false, as contradictories, of which one is necessarily true. Various inferential schemes are associated with false dilemmas, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tongue Bifurcation (other)
Tongue bifurcation may refer to: *Tongue splitting, a type of body modification *Forked tongue A forked tongue is a tongue split into two distinct tines at the tip; this is a feature common to many species of reptiles. Reptiles smell using the tip of their tongue, and a forked tongue allows them to sense from which direction a smell is co ..., a physical characteristic of certain animals See also {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
