Wiktionary Characteristic from the Greek word for a property or attribute wikt trait trait of an entity may refer to In physics and engineering , any characteristic curve that shows the relationship between certain input and output parameters, for example I V or current voltage characteristic , the current in a circuit as a function of the applied voltage Receiver operating characteristic In navigation Light characteristic , pattern of a lighted beacon In mathematics Characteristic algebra of a ring R , a number that describes what happens to integers when interpreted in R Characteristic function disambiguation , usually the indicator function of a subset, though the term has other meanings in specific domains Characteristic polynomial , a polynomial associated to a square matrix in linear algebra Euler characteristic , a topological invariant Characteristic subgroup , a subgroup that is invariant under all automorphisms in group theory Method of characteristics , a technique for solving partial differential equations Characteristic, integer part of a common logarithm In fiction Another name for Dungeons & Dragons gameplay Ability scores ability score in Dungeons & Dragons disambig de Charakteristik Begriffskl rung es Caracter stica fr Caract ristique io Karakterizo nl Karakteristieke functie pt Caracter stica sk Charakteristika zh ... more details
In mathematics , the term characteristic exponent may refer to Characteristic exponent of a field , a number equal to 1 if the field has characteristic 0, and equal to p if the field has characteristic p 0 Lyapunov characteristic exponent , a quantity that characterizes the rate of separation of infinitesimally close trajectories in a dynamical system Characteristic exponent of Stable distribution mathdab ... more details
Unreferenced stub auto yes date December 2009 Orphan date December 2009 The characteristic time is an estimate of the order of magnitude of the reaction time scale. It can loosely be defined as the inverse of the reaction rate. In chemistry, the characteristic time is used to determine whether the problem needs to be solved as an equilibrium problem or a kinetic problem. For RC circuit s, the characteristic time is the time the capacitor takes to discharge by 1 e approximately 63 of the way to the final voltage. In various fields of physics and astrophysics , the characteristic or relaxation time refers to the time needed for a system to relax under external stimuli. See also Half life DEFAULTSORT Characteristic Time Category Fundamental physics concepts Physics stub ... more details
orphan date July 2010 A characteristic property is a Chemical property chemical or physical property that helps identify and classify substances. The characteristic properties of a substance are always the same whether the sample you are observing is large or small. Examples of characteristic properties include freezing melting point, boiling condensing point, density , magnetism , and solubility . ref name def1 cite web url http www.cuesd.tehama.k12.ca.us maywood staff farmer characteristic properties.htm title Characteristic Properties publisher www.cuesd.tehama.k12.ca.us accessdate 9 December 2009 ref References reflist Category Chemical properties physics stub ... more details
In mathematics , and particularly ordinary differential equations , a characteristic multiplier is an eigenvalue of a monodromy matrix . External links http www.exampleproblems.com wiki index.php Ordinary Differential Equations Linear Systems Examples of finding characteristic multipliers of systems of ODEs from www.exampleproblems.com. See also multiplier other meanings Category Ordinary differential equations ... more details
Context date September 2010 A characteristic length is an important dimension that defines the scale of a physical system. Often such a length is used as an input to a formula in order to predict some characteristics of the system. Examples Reynolds number Biot number External links http www.answers.com topic characteristic length Definition physics stub DEFAULTSORT Characteristic Length Category Physical constants de Charakteristische L nge nl Hydraulische diameter pt Comprimento caracter stico ... more details
In mathematics, characteristic function can refer to any of several distinct concepts The most common and universal usage is as a synonym for indicator function , that is the function math mathbf 1 A X to 0, 1 math which for every subset A of X , has value 1 at points of A and 0 at points of X &minus A . In probability theory, the characteristic function probability theory of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question math varphi X t operatorname E left e itX right , math where E means expected value. This concept extends to multivariate distributions. The characteristic function convex analysis in convex analysis math chi A x begin cases 0, & x in A infty, & x not in A. end cases math The characteristic state function in statistical mechanics. The characteristic polynomial in linear algebra. The Euler characteristic , a topological invariant. The cooperative game in game theory. disambig DEFAULTSORT Characteristic Function Category Mathematical disambiguation ca Funci caracter stica de Charakteristische Funktion eo Karakteriza funkcio it Funzione caratteristica pl Funkcja charakterystyczna ... more details
wikibooks Discrete Mathematics Finite fields In mathematics , the characteristic of a ring mathematics ... to have characteristic zero if this repeated sum never reaches the additive identity. That is, char ... n exists, and 0 otherwise. The characteristic may also be taken to be the exponent group ... definitions include taking the characteristic to be the natural number n such that n Z is the kernel ... a ring homomorphism R S , then the characteristic of S divides the characteristic of R . This can sometimes be used to exclude the possibility of certain ring homomorphisms. The only ring with characteristic ... not have any zero divisor s, then its characteristic is either 0 or prime number prime . In particular ... ring s. Any ring of characteristic 0 is infinite. The ring Z n Z of integers modular arithmetic modulo n has characteristic n . If R is a subring of S , then R and S have the same characteristic. For instance ... ring Z p Z X q X is a field of characteristic p . Since the complex number s contain the rationals, their characteristic is 0. If a commutative ring R has prime characteristic p , then we have ... from Elliptic curve cryptography As mentioned above, the characteristic of any field is either 0 or a prime ... Q , or a finite field of prime order, F sub p sub the structure of the prime field and the characteristic each determine the other. Fields of characteristic zero have the most familiar properties ... , that is . The p adic field s are characteristic zero fields, much applied in number theory, that are constructed from rings of characteristic p sup k sup , as k . For any ordered field for example, the rational number rationals or the real number reals the characteristic is 0. The finite field GF p sup n sup has characteristic p . There exist infinite fields of prime characteristic. For example ... p Z is another example. The size of any finite ring of prime characteristic p is a power of p . Since ... sup sup m sup p sup nm sup . See also Characteristic exponent of a field References Neal H. McCoy 1964 ... more details
In mathematics , particularly in the area of abstract algebra known as group theory , a characteristic ... inner automorphism conjugation is an automorphism, every characteristic subgroup is normal subgroup normal , though not every normal subgroup is characteristic. Examples of characteristic subgroups include the commutator subgroup and the center of a group . Definitions A characteristic subgroup of a group ... of H under &phi . The statement &ldquo H is a characteristic subgroup of G &rdquo is written math H mathrm char G. math Characteristic vs. normal If G is a group, and g is a fixed element of G , then the conjugation ... . Since a characteristic subgroup is invariant under all automorphisms, every characteristic subgroup is normal. Not every normal subgroup is characteristic. Here are several examples Let H be a group ... 1 × H and H × 1 are both normal, but neither is characteristic ... of these are characteristic. However, the subgroup 1, &minus 1 is characteristic, since it is the only subgroup of order 2. Note If H is the unique subgroup of a group G , then H is characteristic ... index two, all of which are normal. One of these is the cyclic subgroup, which is characteristic ... of the parent group, and are therefore not characteristic. Normality is not transitive but Characteristic ... stronger constraint, a fully characteristic subgroup also called a fully invariant subgroup H of a group ... . Containments Every subgroup that is fully characteristic is certainly distinguished and therefore characteristic but a characteristic or even distinguished subgroup need not be fully characteristic ... characteristic. The finite group of order 12, Sym 3 Z 2 Z has a homomorphism taking , y to 1,2 ... normal subgroup characteristic subgroup distinguished subgroup fully characteristic subgroup verbal ... in the center, so here the center is not a fully characteristic subgroup of G . Cyclic groups Every subgroup of a finite cyclic group is characteristic. Subgroup functors The derived subgroup ... more details
In mathematics , a characteristic class is a way of associating to each principal bundle on a topological ... is twisted &mdash particularly, whether it possesses fiber bundle section s or not. In other words, characteristic ... pullback operation f sup sup . A characteristic class c of principal G bundles is then a natural ... . In other words, a characteristic class associates to any principal G bundle P X an element c ... map in cohomology. Characteristic numbers Characteristic classes are elements of cohomology groups ref Informally, characteristic classes live in cohomology. ref one can obtain integers from characteristic classes, called characteristic numbers . Respectively Stiefel Whitney class Stiefel Whitney ... numbers Pontryagin numbers , and the Euler class Relations to other invariants Euler characteristic ... bundle with characteristic classes math c 1, dots,c k math , one can pair a product of characteristic classes of total degree n with the fundamental class. The number of distinct characteristic numbers is the number of monomial s of degree n in the characteristic classes, or equivalently the partitions ... sum mbox deg ,c i j n math , the corresponding characteristic number is math c i 1 cup c i 2 cup dots cup c i m M math These are notated various as either the product of characteristic classes, such as math ... characteristic. From the point of view of de Rham cohomology , one can take differential form s representing the characteristic classes, ref By Chern Weil theory , these are polynomials in the curvature ... have a math mathbf Z 2 math orientation, in which case one obtains math mathbf Z 2 math valued characteristic numbers, such as the Stiefel Whitney numbers. Characteristic numbers solve the oriented ... or unoriented cobordant if and only if their characteristic numbers are equal. Motivation Characteristic ... theories based on mapping into a space and characteristic class theory in its infancy in the 1930s as part of obstruction theory was one major reason why a dual theory to homology was sought. The characteristic ... more details
Otheruses4 the characteristic polynomial of a matrix the characteristic polynomial of a matroid Matroid ... matrix its characteristic polynomial . This polynomial encodes several important properties of the matrix ... trace . The characteristic polynomial of a graph mathematics graph is the characteristic polynomial ... have the same characteristic polynomial. Motivation Given a square matrix A , we want to find a polynomial whose roots are precisely the eigenvalues of A . For a diagonal matrix A , the characteristic ... 3 sub , etc. then the characteristic polynomial will be math t a 1 t a 2 t a 3 cdots. , math ... number real or complex number complex numbers and an n × n matrix A over K . The characteristic ... t , the Polynomial ring ring of polynomials in t over K . Some authors define the characteristic ... always has constant term det A . Example Suppose we want to compute the characteristic polynomial ... 1 t 2 2t 1. , math This is the characteristic polynomial of A . Properties The polynomial p sub A sub t is monic its leading coefficient is 1 and its degree is n . The most important fact about the characteristic ... linear algebra minimal polynomial of A , but its degree may be less than n . The coefficients of the characteristic ...× 2 matrix A , the characteristic polynomial is therefore given by t sup 2 sup tr A t det A . The Cayley Hamilton theorem states that replacing t by A in the characteristic ... characteristic equation. This statement is equivalent to saying that the Minimal polynomial linear algebra minimal polynomial of A divides the characteristic polynomial of A . Two similar matrices have the same characteristic polynomial. The converse however is not true in general two matrices with the same characteristic polynomial need not be similar. The matrix A and its transpose have the same characteristic polynomial. A is similar to a triangular matrix if and only if its characteristic ... instead of the characteristic polynomial . In this case A is similar to a matrix in Jordan ... more details
Characteristic curve may refer to In electronics , a representation of certain electrical characteristics of a device or component Semiconductor curve tracer , a device for displaying the above curve In photography, a plot of film density see sensitometry In mathematics, used in the method of characteristics for solving partial differential equations disambig ... more details
A characteristic earthquake is a repeating, large earthquake that occurs more frequently than local Seismology seismic monitoring would suggest. http www.earth.northwestern.edu people seth research eqrec.html Characteristic earthquakes are usually defined from paleoseismology observations. This has important implications for seismic hazard calculations and earthquake insurance rates . Basically, it implies that there is a section of a Fault geology fault that has very little observed seismicity, but is a high hazard because the paleoseismic studies show a regular pattern of large earthquakes. References Reflist Unreferenced date January 2010 Category Seismology geophysics stub ja ... more details
In mathematics , the characteristic sequence of a given sequence s is a sequence of 1 s and 0 s which tells which elements of s are in some Set mathematics set . Given two sets math A subseteq B math and a sequence s math langle s n n in mathbb N rangle math of elements of math B math , the characteristic sequence of math s math is the sequence math langle c n n in mathbb N rangle math defined so that math c n 1 math if and only if math s n in A math math c n begin cases 0 & s n not in A, 1 & s n in A. end cases math mathlogic stub Category Mathematical logic Category Binary sequences ... more details
Characteristic admittance is the mathematical inverse of the characteristic impedance . The general expression for the characteristic admittance of a transmission line is math Y 0 sqrt frac G j omega C R j omega L math where math R math is the Electrical resistance resistance per unit length, math L math is the inductance per unit length, math G math is the Electrical conductance conductance of the dielectric per unit length, math C math is the capacitance per unit length, math j math is the imaginary unit , and math omega math is the angular frequency . The current and voltage Phasor electronics phasor s on the line are related by the characteristic admittance as math frac I V Y 0 frac I V math where the superscripts math math and math math represent forward and backward traveling waves, respectively. See also Characteristic impedance References cite book last Guile first A. E. title Electrical Power Systems year 1977 isbn 0 0802 1729 X cite book last Pozar first D. M. title Microwave Engineering edition 3rd edition year 2004 month February isbn 0 471 44878 8 cite book last Ulaby first F. T. title Fundamentals Of Applied Electromagnetics edition media edition year 2004 publisher Prentice Hall isbn 0 13 185089 X DEFAULTSORT Characteristic Admittance Category Electricity Category Physical quantities Category Distributed element circuits ... more details
characteristic or Euler&ndash Poincar characteristic is a topological invariant , a number that describes ... by math chi math Greek alphabet Greek letter chi letter chi . The Euler characteristic was originally ... for much of this early work. In modern mathematics, the Euler characteristic arises from homology mathematics homology and connects to many other invariants. Polyhedra The Euler characteristic math ... has Euler characteristic math chi V E F 2. , math This result is known as Euler s formula . This corresponds to the Euler characteristic of the sphere which is 2 , and applies identically to spherical ... Image Vertices BR V Edges BR E Faces BR F Euler characteristic BR V &minus E F align center Tetrahedron ... Name Image Vertices BR V Edges BR E Faces BR F Euler characteristic BR V &minus E F align center Tetrahemihexahedron ... s math d v V E d f F 2D math Further, projective polyhedra all have Euler characteristic 1, corresponding to the real projective plane , while toroidal polyhedra all have Euler characteristic 0, corresponding to the torus . Planar graphs The Euler characteristic can be defined for connected planar ... in the graph, including the exterior face. The Euler characteristic of any planar graph is 2 ... maps to a polygonal decomposition of the sphere, which has Euler characteristic 2. This viewpoint is implicit ... complex es. In general, for any finite CW complex, the Euler characteristic can be defined as the alternating ... group. The Euler characteristic can then be defined as the alternating sum math chi b 0 b 1 b 2 b 3 ... value for math chi math . Properties As a corollary of Poincar duality , the Euler characteristic ... dimensional. Furthermore, the Euler characteristic behaves well with respect to many basic operations ... isomorphism isomorphic homology groups , so is the Euler characteristic. For example, any convex ... 2. This explains why convex polyhedra have Euler characteristic 2. Inclusion exclusion principle If M and N are any two topological spaces, then the Euler characteristic of their disjoint union is the sum ... more details
About impedance in electronics impedance of electromagnetic waves Wave impedance characteristic acoustic impedance Acoustic impedance File Transmission line schematic.svg thumb Schematic representation of a electrical circuit circuit where a source is coupled to a electrical load load with a transmission line having characteristic impedance math Z 0 math . The characteristic impedance or surge impedance of a uniform transmission line , usually written math Z 0 math , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of Reflections of signals on conducting lines reflections . The SI unit of characteristic Electrical impedance impedance is the Ohm unit ohm . The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component math Z 0 Z 0 j0 math . Characteristic impedance appears like a resistance in this case, such that power generated by a source on one end of an infinitely long lossless transmission line is transmitted through the line but is not dissipated in the line itself. A transmission line of finite length lossless or lossy that is terminated at one end with a resistor equal to the characteristic impedance math Z mathrm L Z 0 math appears to the source like ... the characteristic impedance. File Transmission line element.svg thumb Schematic representation ... s equations , the general expression for the characteristic impedance of a transmission ... . The voltage and current Phasor electronics phasor s on the line are related by the characteristic ... zero, so the equation for characteristic impedance reduces to math Z 0 sqrt frac L C math The imaginary ... , the characteristic impedance of a transmission line is expressed in terms of the surge impedance ... lightly loaded or open ended transmission line. Underground cable s normally have a very low characteristic ..., Characteristic Category Electricity Category Physical quantities Category Distributed element circuits ... more details
Characteristic velocity or math c math is a measure of the combustion performance of a rocket engine independent of Rocket engine nozzle nozzle performance, and is used to compare different Rocket propellant propellants and Spacecraft propulsion propulsion systems . Formula math c frac p 1 times A t dot m math math c math is the characteristic velocity meters second math p 1 math is the chamber pressure pascals math A t math is the area of the throat square meters math dot m math is the mass flow rate of the engine kilograms per second References Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz Category Rocketry Category Rocket propulsion Category Aerospace engineering ... more details
In telecommunication , the term halftone characteristic has the following meanings In Fax facsimile systems, the relationship between the density of the recorded Facsimile copy and the density of the object, i.e. , the original. In facsimile systems, the relationship between the amplitude of the facsimile Signalling telecommunication signal to either the density of the object or the density of the recorded copy when only a portion of the system is under consideration. In an FM facsimile system, an appropriate parameter other than the amplitude is used. See also halftone References FS1037C MS188 Category Telecommunications terms ... more details
Loading characteristic In multichannel telephone systems, a plot, for the busy hour , of the equivalent mean power and the peak power as a function of the number of voice channels. The equivalent power of a multichannel Signalling telecommunication signal referred to the zero transmission level point is a function of the number of channels and has for its basis a specified voice channel communications channel mean power. References FS1037C MS188 Category Telephony telecomm stub ... more details
In astrodynamics a characteristic energy math C 3 , math , a form of specific energy , is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity over an escape velocity required for additional orbital maneuver s. The unit of the characteristic energy is kilometre km sup 2 sup second s sup 2 sup . Characteristic energy can be computed as math C 3 v infty 2 , math where math v infty , math is the orbital velocity when the orbital distance tends to infinity. Note that, since the kinetic energy is one half m math v 2, math C sub 3 sub is in fact equal to twice the magnitude of the specific orbital energy math epsilon math of the escaping object. Parabolic trajectory For a spacecraft that is leaving the central body e.g. earth on a parabolic trajectory math C 3 0 , math Hyperbolic trajectory For a spacecraft that is leaving the central body on a hyperbolic trajectory math C 3 mu over a , math where math mu , math is standard gravitational parameter , math a , math is length of semi major axis of orbit s hyperbola . See also Specific orbital energy Orbit Parabolic trajectory Hyperbolic trajectory References cite book last Wie first Bong title Space Vehicle Dynamics and Control publisher American Institute of Aeronautics and Astronautics location Reston, Virginia date 1998 series AIAA Education Series chapter Orbital Dynamics isbn 1563472619 accessdate 2009 07 05 Category Astrodynamics Category Celestial mechanics Category Energy in physics ... more details
In mathematics , a theta characteristic of a non singular algebraic curve C is a divisor class such that 2 is the canonical class , In terms of holomorphic line bundle s L on a connected compact Riemann surface , it is therefore L such that L sup 2 sup is the canonical bundle , here also equivalently the holomorphic cotangent bundle . In terms of algebraic geometry , the equivalent definition is as an invertible sheaf , which squares to the sheaf of differentials of the first kind . History and genus 1 The importance of this concept was realised first in the analytic theory of theta function s, and geometrically in the theory of bitangent s. In the analytic theory, there are four fundamental theta functions in the theory of Jacobian elliptic function s. Their labels are in effect the theta characteristics of an elliptic curve . For that case, the canonical class is trivial zero in the divisor class group and so the theta characteristics of an elliptic curve E over the complex numbers are seen to be in 1 1 correspondence with the four points P on E with 2 P 0 this is counting of the solutions is clear from the group structure, a product of two circle group s, when E is treated as a complex torus . Higher genus For C of genus 0 there one such divisor class, namely the class of P , where P is any point on the curve. In case of higher genus g , assuming the field over which C is defined does not have characteristic 2 , the theta characteristics can be counted as 2 sup 2 g sup in number if the base field is algebraically closed. This comes about because the solutions of the equation on the divisor class level will form a single coset of the solutions of 2 D 0. In other words, with K the canonical class and any given solution of 2&Theta K , any other solution will be of form &Theta D . This reduces counting the theta characteristics to finding the 2 rank of the Jacobian ... of the p rank of an abelian variety . The answer is the same, provided the characteristic of the field ... more details
otheruses Characteristic equation disambiguation In mathematics , the characteristic equation or auxiliary equation ref name edwards is an Algebraic function algebraic equation of Degree of a polynomial degree math n , math on which depends the solutions of a given math n , math sup th sup Derivative Higher derivatives order differential equation . ref name smith cite web url http etc.usf.edu lit2go contents 2800 2892 2892 txt.html title History of Modern Mathematics Differential Equations last Smith first David Eugene publisher University of South Florida accessdate 2 March 2011 ref The characteristic equation can only be formed when the differential equation is Linear differential equation linear , Linear homogeneous differential equation homogeneous , and has constant coefficient s. ref ... a characteristic equation of the form math a n r n a 1 r n 1 cdots a 1 r a 0 0 math where math ... that the solutions depended on an algebraic characteristic equation. ref name smith The qualities of the Euler s characteristic equation were later considered in greater detail by French mathematicians ... equate to zero, it can be divided out, giving the characteristic equation math a n r n a n 1 r n 1 cdots a 1 r a 0 0 math By solving for the roots, math r , math , in this characteristic equation, one ... math y 5 y 4 4y 3 16y 20y 12y 0 , math has the characteristic equation math r 5 r 4 4r 3 16r 2 20r 12 0 , math By Factorization factoring the characteristic equation into math r 3 r 2 2r 2 2 ... x xe x c 4 cos x c 5 sin x , math Solving the characteristic equation for its roots, math r 1 , ldots ... be real number real and or complex number complex , as well as distinct and or repeated. If a characteristic ... first Paul work Paul s Online Math Notes accessdate 2 March 2011 ref Therefore, if the characteristic ... If the characteristic equation has a root math r 1 math that is repeated math k , math times, then it is clear ... roots If the characteristic equation has Complex number complex roots of the form math r 1 a bi math ... more details
Orphan date June 2009 An acquired characteristic is a hereditary non hereditary change in function or structure in living biotic material caused by disease, mutilation, repeated use or disuse, or other environmental influence. For example, a person constantly exercising may develop stronger muscles or a cat that goes into a fight with another feline, thus getting injured, may lose an eye or an ear. None of these acquired traits will be passed on to offspring through reproduction alone. The inheritance of acquired characters was historically proposed by renowned theorists such as Hippocrates , Aristotle , and French naturalist Jean Baptiste Lamarck . On the other hand, it was also disputed by other famous theorists such as Charles Darwin . Today, although Lamarckism is generally discredited, there is still debate on whether some acquired characteristics in organisms are actually inheritable. ref http www.pubmedcentral.nih.gov articlerender.fcgi?artid 1320859 ref ref http www.pubmedcentral.nih.gov articlerender.fcgi?artid 348875 ref Types Acquired characteristics can stem from various environmental influences such as diseases, mutilation, and use or atrophy of body parts. Disease Disorders such as hypothyroidism and gout are known to cause permanent or near permanent changes to the human body. Hypothyroidism is known to cause goiters, depression, and sluggishness. ref http www.nlm.nih.gov medlineplus ency article 000353.htm ref Gout, on the other hand, can cause tophi . When these diseases are caused by environmental influences such as iodine deficiency or lead poisoning, their resultant symptoms are said to be acquired characteristics. However, it is debatable on whether the changes in bodily function due to disorders caused either in part or fully genetically are actually acquired. Mutilation Also known as maiming, mutilation is any form of physical injury aimed at degrading the body of a living organism. Examples, include amputation , foot binding , and genital cutting ... more details
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