Unreferenced date December 2009 Orphan date December 2009 In English language English grammar , a falsesingular occurs when a Grammatical number singular noun ending in a s or z sound is understood as a plural from which a new singular is constructed. The falsesingular is a form of back formation . Some false singulars become standard English. For example, pea was originally a falsesingular from pease pl. peasen . The old word remains in the phrase pease porridge . The non standard historical forms Chinee and Portuguee are also false singulars, from Chinese and Portuguese . DEFAULTSORT FalseSingular Category Grammar ... more details
20usage&pg PA185 v onepage&q singular 20they&f false ref generic use of the pronoun he has been preferred ...italic title prefixed 8 singular they Singular they is the use of wiktionary they they or its inflection ... plural. Though singular they is widespread in everyday English and has a long history of usage, debate ... to either a singular or plural entity. This usage is also known as generic they . For example ... in general notwithstanding the fact that anyone is strictly grammatically singular . In some ... singular or ambiguous, singular they remains morphology linguistics morphologically and syntax syntactically ... Sharp as an example. In neither case is singular they unambiguously a semantic or morpho syntactic singular. What it actually Agreement linguistics agrees with is the plurality implicit in the indeterminacy ... . ref In this kind of analysis, singular they in English is typically an example of a semantically ... Since these make the quantification explicit. ref where the preference many languages show for singular pronouns probably gives rise to the singular in singular they . ref For, specifically, donkey ... as a whole, they are most often conceived of as singular, and a singular pronoun is used. England ... forms are sometimes used. ref Either the plural or the singular may be acceptable for a true bound ... that singular forms are, nonetheless, more natural in distributive constructions is inadvertently ... singular interpretations of they in what are actually translations of plurals. ref http www.crossmyt.com ... LanguageLog http itre.cis.upenn.edu myl languagelog archives 003572.html Singular they God said ... languages because it forms distributives with pronouns and marks for singular and plural. Such languages demonstrate a preference for singular pronouns but attest plurals in a substantial minority ... one person, requires the pronoun to be in the singular. Similar to this, but with even less justification ... . ref name LanguageLog Prescriptions of taste are not true or false, so they cannot be proven right ... more details
Other uses Singular disambiguation notability date September 2011 SINGULAR typeset span style font variant small caps Singular span is a computer algebra system for polynomial computations with special emphasis on the needs of commutative algebra , algebraic geometry , and singularity theory . S small INGULAR small is free software released under the GNU General Public License . Problems in non commutative algebra can be tackled with the S small INGULAR small offspring PLURAL. S small INGULAR small was designed by Gert Martin Greuel, Gerhard Pfister and Hans Sch nemann. See also Portal Free software Comparison of computer algebra systems External links http www.singular.uni kl.de SINGULAR website http www.singular.uni kl.de plural PLURAL website http www math.science.unitn.it costanti singular Interface from GAP to Singular http www.mathematik.uni kl.de greuel en Gert Martin Greuel s website http www.mathematik.uni kl.de pfister en Gerhard Pfister s website http www.mathematik.uni kl.de hannes de index.html Hans Sch nemann s website Computer algebra systems DEFAULTSORT Singular Category Free computer algebra systems Category Linux computer algebra system software free software stub de Singular Computeralgebrasystem es SINGULAR ja SINGULAR vi SINGULAR ... more details
A grammatical number denoting a unit quantity as opposed to the plural and other forms wiktionarypar singular singularity Singular may also refer to Gravitational singularity , a location where the quantities that are used to measure the gravitational field become infinite Technological singularity , a hypothesis that technological progress will reach such an infinite or extremely high value at a point in the near future A group of boar s In mathematics Mathematical singularity SINGULAR , an open source Computer Algebra System CAS Singular matrix , a matrix that is not invertible Singular measure , a measure or probability distribution whose support has zero Lebesgue measure. More generally, one may speak of an object singular with respect to a measure , meaning that replaces the Lebesgue measure above An infinite cardinal number is called singular if it is not a regular cardinal Possible misspelling Singulair , Merck trademark for Montelukast, a common prescription drug used in maintenance treatment of asthma and to relieve symptoms of seasonal allergies. Cingular Wireless , a major mobile network operator in North America disambig es Singular desambiguaci n fr Singulier la Singularis nl Singulier th ... more details
wiktionary false falsehood False or falsehood may refer to False logic Lie or falsehood, a type of deception in the form of an untruthful statement Falsity or falsehood, in law, deceitfulness by one party that results in damage to another Falsies padding for use in a brassiere to create the appearance of larger breasts FALSE , a programming language false Unix , a Unix command False album False album , an album by Gorefest Matthew Dear or False, American DJ and producer Falsehood film Falsehood film , a 2001 American short film starring Marie Noelle Marquis See also columns list 2 False accusations False advertising False alarm False arrest False confession False consciousness False conviction False dilemma False document False ending False etymology False flag False friend False gharial False hero False imprisonment False memory False neurotransmitter False pregnancy False prophet False self False start True disambig de False it Falso scn False ... more details
Infobox programming language name FALSE released Start date 1993 developer Wouter van Oortmerssen influenced by Forth programming language Forth influenced Brainfuck website http strlen.com false strlen.com About the programming language other uses False disambiguation FALSE is an esoteric programming ... in 68k 68000 Assembly language assembly . According to Van Oortmerssen, FALSE provided the inspiration for various well known esoteric languages, including brainfuck and Befunge . FALSE is notably more ... contrast to the behemoths Intercal and Malbolge . The difficulty of programming in FALSE comes mostly ... flow statements, and input output operations. FALSE operations are done using a stack data structure ... values 0 representing false 1 representing true , and lambda calculus expressions. These can be used on the stack or stored in Variables variables . Basic operators FALSE supports binary operation ... a code would push 3 onto the stack if a has been assigned 3 . The heavy use of the stack in FALSE ... this to 3, leaving the stack as 4. Control flow FALSE has two control flow statements, if and while ... science String s are not a real data type in FALSE they only exist as string literal s and cannot ... to 1. Input Output Apart from strings, which print themselves, FALSE has a number of operators ... code . Comments cannot be nested. Code examples Sample programs taken from the FALSE Programming Language ... > outfile code 1 , Factorial calculator for numbers 1 through 8 1 1 f ? f fac in FALSE calculate ... the structure of FALSE was derived. Esoteric programming language Stack oriented programming language External links http strlen.com false false.txt The FALSE Programming Language Manual http strlen.com false The FALSE Programming Language Web Page these two links are also mirrored at http wouter.fov120.com false false.txt The FALSE Programming Language Manual http wouter.fov120.com false The FALSE Programming Language Web Page removed from de wiki in March, and again in April 2005 de False Programmiersprache ... more details
In probability , a singular distribution is a probability distribution concentrated on a Null set set of Lebesgue measure zero , where the probability of each point in that set is zero. These distributions are sometimes called singular continuous distributions . Such distributions are not absolutely continuous with respect to Lebesgue measure . A singular distribution is not a discrete probability distribution because each discrete point has a zero probability. On the other hand, neither does it have a probability density function , since the Lebesgue integral of any such function would be zero. An example is the Cantor distribution . See also Singular measure Lebesgue s decomposition theorem External links http eom.springer.de S s085530.htm Springer Encyclopaedia of Mathematics ProbDistributions DEFAULTSORT Singular Distribution Category Probability distributions Category Types of probability distributions Statistics stub probability stub it Distribuzione singolare ... more details
In mathematics , in particular functional analysis , the singular values , or s numbers of a compact operator nowrap T &thinsp X Y acting between Hilbert space s X and Y , are the square roots of the eigenvalue s of the nonnegative self adjoint operator nowrap T T &thinsp X X where T denotes the adjoint operator adjoint of T . The singular values are nonnegative real number s, usually listed in decreasing order s sub 1 sub T , s sub 2 sup T , . If T is self adjoint operator self adjoint , then the largest singular value s sub 1 sub T is equal to the operator norm of T see Courant minimax principle . File Singular value decomposition.gif thumb right 280px Visualisation of a singular value decomposition SVD of a 2 dimensional, real en Shear mapping shearing matrix M . First, we see the unit disc in blue together with the two standard basis canonical unit vectors . We then see the action of M ... axes and a second rotation U . &Sigma is a diagonal matrix containing in its diagonal the singular ... geometric interpretation for the singular values Consider the image by T of the N sphere unit sphere this is an ellipsoid , and its semi axes are the singular values of T the figure ... U math and so the singular values are simply the absolute values of the eigenvalues . Most normed ... Fan k norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the Schatten norm is the p th root of the sum of the p th powers of the singular values. Note ... matrix with the singular values lying on the diagonal. This is the singular value decomposition . History This concept was introduced by Erhard Schmidt in 1907. Schmidt called singular values eigenvalues at that time. The name singular value was first quoted by Smithies in 1937. In 1957, Allakhverdiev ... to operators in Banach space . See also Singular value decomposition Category Operator theory Category Singular value decomposition ar ... more details
In algebraic topology , a branch of mathematics , singular homology refers to the study of a certain ... . Intuitively spoken, singular homology counts, for each dimension n , the n dimensional holes of a space. Singular homology is a particular example of a homology theory , which has now grown to be a rather ... to understand, being built on fairly concrete constructions. In brief, singular homology is constructed ... sum s, called singular chains . The boundary topology boundary operation on a simplex induces a singular chain complex . The singular homology is then the homology mathematics homology of the chain ... can be applied to all topological spaces, and so singular homology can be expressed in terms of category ... to the category of graded abelian group s. These ideas are developed in greater detail below. Singular simplices A simplex singular n simplex is a continuous mapping math sigma n math from the standard ... n to X math . This mapping need not be injective , and there can be non equivalent singular simplices ... n sigma n Delta n math , is defined to be the formal sum of the singular n &minus 1 simplices represented ... from math p 0 math to math p 1 math is the formal sum or formal difference math p 1 p 0 math . Singular chain complex The usual construction of singular homology proceeds by defining formal sums of simplices .... Consider first the set of all possible singular n simplices math sigma n Delta n math on a topological ... of math C n X math are called singular n chains they are formal sums of singular simplices with integer ... partial math is readily extended to act on singular n chains. The extension, called the boundary operator ..., together with the math C n math , form a chain complex of abelian groups, called the singular ... of singular n cycles . The image of the boundary operator is math B n X operatorname im partial n 1 math , and is called the group of singular n boundaries . It can also be shown that math partial ... H 0 X mathbb Z math . A proof for the homotopy invariance of singular homology groups can be sketched ... more details
In optimal control , problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin s minimum principle fails to yield a complete solution. Only a few such problems have been solved, such as Merton s portfolio problem in financial economics or trajectory optimization in aeronautics. A more technical explanation follows. The most common difficulty in applying Pontryagin s principle arises when the Hamiltonian depends linearly on the control math u math , i.e., is of the form math H u phi x, lambda,t u cdots math and the control is restricted to being between an upper and a lower bound math a le u t le b math . To minimize math H u math , we need to make math u math as big or as small as possible, depending on the sign of math phi x, lambda,t math , specifically math u t begin cases b, & phi x, lambda,t 0 ?, & phi x, lambda,t 0 a, & phi x, lambda,t 0. end cases math If math phi math is positive at some times, negative at others and is only zero instantaneously, then the solution is straightforward and is a bang bang control that switches from math b math to math a math at times when math phi math switches from negative to positive. The case when math phi math remains at zero for a finite length of time math t 1 le t le t 2 math is called the singular control case. Between math t 1 math and math t 2 math the maximization of the Hamiltonian with respect to u gives us no useful information and the solution in that time interval is going to have to be found from other considerations. One approach would be to repeatedly differentiate math partial H partial u math with respect to time until the control u again explicitly appears ... called singular arc will be optimal if it satisfies the Kelley condition math 1 k frac partial partial ... bang singular control refers to a control that has a bang bang portion as well as a singular portion. References reflist DEFAULTSORT Singular Control Category Control theory ... more details
A singular solution y sub s sub x of an ordinary differential equation ordinary differential equation is a solution that is Mathematical singularity singular or one for which the Initial value problem initial value problem also called the Cauchy problem by some authors fails to have a unique solution at some point on the solution. The set on which a solution is singular may be as small as a single point or as large as the full real line. Solutions which are singular in the sense that the initial value problem fails to have a unique solution need not be Mathematical singularity singular functions . In some cases, the term singular solution is used to mean a solution at which there is a failure of uniqueness to the initial value problem at every point on the curve. A singular solution in this stronger sense is often given as tangent to every solution from a family of solutions. By tangent we ... y sub c sub is a solution in a family of solutions parameterized by c . This means that the singular solution is the envelope mathematics envelope of the family of solutions. Usually, singular solutions ... check what happens if the term is equal to zero, and whether it leads to a singular solution. The Picard ... to rule out the existence of singular solutions. Other theorems, such as the Peano existence theorem ... being unique, which can allow for the existence of singular solutions. A divergent solution Consider ... the Picard Lindel f theorem Picard Lindel f theorem . Thus, the solutions above are all singular solutions ... . Thus, the solution math y s math is a singular solution in the stronger sense that uniqueness fails at every value of x . However, it is not a Mathematical singularity singular function since it and all ... are singular, in the sense that the second derivative fails to exist, at math x c 1 math ... x 2 1 4 cdot x 2. , math Now we shall check when these solutions are singular solutions. If two solutions ... Singular solutions in http eom.springer.de default.htm Encyclopaedia of Mathematics . Springer ... more details
mathcal Z R R neq mathcal Z R R math . This article will develop several notions in terms of the singular submodule and singular ideals, including the definition of singular module , nonsingular module ... a singular module if math mathcal Z M M , math . M is called a nonsingular module if math mathcal Z M 0 , math . R is called right nonsingular if math mathcal Z R R 0 , math . Using the left singular ... R , math , and so right singular ring is not usually defined the same way as singular modules are. Some authors have used singular ring to mean has a nonzero singular ideal , however this usage is not consistent with the usage of the adjectives for modules. Properties Some general properties of the singular ... N N cap mathcal Z M , math . The properties singular and nonsingular are Morita equivalence Morita invariant properties . The singular ideals of a ring contain central nilpotent elements of the ring. Consequently the singular ideal of a commutative ring contains the nilradical of a ring nilradical of the ring ... not necessarily hold for the singular submodule. However if R is a right nonsingular ring, then math ... N is singular. If M is a free module , or if R is right nonsingular, then the converse is true. A semisimple ... more details
Infobox musical artist name Singular image caption Singular origin Bangkok , Thailand genre Pop music Pop , Acoustic music acoustic , jazz years active 2010 present label Sony Music Entertainment operating Thailand associated acts Depapepe , Scrubb , Armchair , Stamp band Stamp current members Sin, Tossaporn Achawanuntakul br Nut, Chotiwut Boonyasit website URL http www.singularband.com background group or band Singular is a band from Thailand . The group includes Sin born on 1 October , a singer songwriter who has performed with the Bangkok Opera , and Nut born on 12 August , the band s guitarist who won a gold medal at the national guitar awards . Their musical character is likened to the Metro Acoustic style. History In May 2010, Singular released its first ever single 24.7 Twenty Four Seven , which reached number one on top radio charts all over Thailand. The music video for 24.7 also reached 590,000 views after three months on Youtube. Singular s second single Bao Bao Tender catapulted the band to greater heights with over four million views on Youtube. Within two weeks of its release, Bao Bao also reached number one on top radio charts all over the Thailand and the phrase lyric for Bao Bao Singular became the sixth most searched phrase on Google Zeitgeist 20 26 September 2010 . The song won a number of national music and media awards, including Song of the Year and Best New Acts for Thailand. Singular also worked on an international single with the Japanese guitar duo, Depapepe . Their joint single release is called Some Other Day , which was written by Sin, while incorporating an existing instrumental piece by Depapepe, Kitto Mata Itsuka . Discography Albums 2011 The White Room Decoration Peak Chart Position 1 ONE Try Tender GAME Days More 24.7 Twenty four ... links http www.singularband.com Official website http www.facebook.com thesingularband Singular ... Singular Press conference http play.you2play.com music 8619 you2play.com http seedspace.dice.in.th event ... more details
In mathematics , more precisely in perturbation theory , a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. This is in contrast to Perturbation theory regular perturbation problems, for which an approximation can be obtained by simply setting the small parameter to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion math varphi x approx sum n 0 N delta n varepsilon psi n x , math as math varepsilon to 0 math . Here math varepsilon math is the small parameter of the problem and math delta n varepsilon math are a sequence of functions of math varepsilon math of increasing order, such as math delta n varepsilon varepsilon n math . This is in contrast to perturbation .... Several classes of singular perturbations are outlined below. Methods of analysis A perturbed ... problem cannot be approximated in this way As seen in the examples below, a singular perturbation generally ... is decreased. Singular perturbation theory is a rich and ongoing area of exploration for mathematicians ... averaging . For books on singular perturbation in ODE and PDE s, see for example Holmes, Introduction ... . Springer, 1999. ISBN 978 0387989310 ref Examples of singular perturbative problems Each ... is regular instead of singular, will fail. Some show how the problem may be solved by more sophisticated singular methods. Vanishing coefficients in ordinary differential equations Differential equations ... one of them separately. Through a singular perturbation technique, we can make these two subsystems .... Methods and Applications of Singular Perturbations Boundary Layers and Multiple Timescale Dynamics ... math 1 x 2 math with roots at math x pm 1 math . Singular perturbation analysis suggests that the cubic ... math decreases, while the third becomes arbitrarily large. References references DEFAULTSORT Singular Perturbation Category Differential equations Category Nonlinear control id Usikan singular ... more details
Orphan date December 2010 Unreferenced date December 2006 A Singular Conspiracy 1974 by Barry Perowne is a fictional treatment of the unaccounted period in Edgar Allan Poe s life from January to May 1844. Poe visits Paris under an assumed name, having used travel papers belonging to a stranger he has seen wounded in a bar room brawl in New York. He has the intention of parlaying his West Point training into a position in the Lafayette Circle , a group of volunteer soldiers about to aid Poland against its Russia n occupiers. This inveigles Poe with a young Charles Baudelaire in a plot to expose Baudelaires stepfather who rejects Poe s application to blackmail, to free up Baudelaires patrimony. See also portal Novels Edgar Allan Poe in popular culture DEFAULTSORT Singular Conspiracy Category 1974 novels Category Historical novels Category Novels by Barry Perowne Category 1844 in fiction Category Novels about writers Hist novel stub ... more details
In mathematics , singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator ... R sup n sup is Mathematical singularity singular along the diagonal x y . Specifically ... n sup . The Hilbert transform main Hilbert transform The archetypal singular integral operator is the Hilbert ... Harmonic Analysis work pages publisher Princeton University Press year 1993 url accessdate ref Singular integrals of convolution type A singular integral of convolution type is an operator T defined by convolution ... publisher Pearson Education, Inc. place New Jersey year 2004 url accessdate ref Singular integrals ... whenever y y leq frac 1 2 max x y , x y math Singular integrals of non convolution type T is said to be a singular integral operator of non convolution type associated to the Calder n&ndash Zygmund ... Zygmund operators A singular integral of non convolution type T associated to a Calder n&ndash ... with 1 p . The T b theorem The T b theorem provides sufficient conditions for a singular integral operator to be a Calder n&ndash Zygmund operator, that is for a singular integral ... b . The T b theorem states that a singular integral operator T associated to a Calder n&ndash Zygmund ... of certain singular integrals issue 1 mr 0052553 zbl 0047.10201 year 1952 journal Acta Mathematica ... title On singular integrals mr 0084633 zbl 0072.11501 year 1956 journal American Journal of Mathematics ... 0 521 42001 6 Citation last Mikhlin first Solomon G. author link Solomon Mikhlin title Singular integral ... link Solomon Mikhlin title Multidimensional singular integrals and integral equations place Oxford ... Pr ssdorf first2 Siegfried title Singular Integral Operators place Berlin &ndash Heidelberg &ndash ... first Elias last Stein authorlink Elias Stein title Singular integrals and differentiability properties ... Singular integrals and differentiability properties of functions year 1970 pages XIV 287 ... more details
There is no really adequate definition of singular term . Here are some definitions proposed by different writers A term that tells us which individual is being talked about. John Stuart Mill , Arthur Prior , P. F. Strawson ref Strawson 1950, Prior 1976, Mill 1908 ref A term that is grammatically singular, i.e. a proper name proprium nomen , a demonstrative pronoun pronomen demonstrativum or a demonstrative pronoun with a common name cum termino communi . William of Ockham ref Ockham, loc. cit. ref A term that is inherently about the object to which it applies or Reference refers . Gottlob Frege ref Frege 1892 ref A term that is true in the same sense of only one object. Peter of Spain ref Hispanus 1947 ref References reflist Works cited Frege, G. 1892 On Sense and Reference , originally published as ber Sinn und Bedeutung in Zeitschrift f r Philosophie und philosophische Kritik , vol. 100, pp. 25 50. Transl. Geach & Black 56 78. Mill, J.S., A System of Logic , London 1908 8th edition . Petrus Hispanus, Summulae Logicales , ed. I. M. Bochenski Turin, 1947 also quoted in Prior 1976 Prior, A.N. The Doctrine of Propositions & Terms London 1976 Strawson, P.F. On Referring , Mind 1950 pp. 320 44. William of Ockham, Sum of Logic Summa logicae Paris 1448, Bologna 1498, Venice 1508, Oxford 1675 Category Grammar Category Names Category Concepts in logic Category Philosophy of language ur ... more details
Hatnote The term false cognate is sometimes used incorrectly for False friend . Refimprove date April 2010 False cognates are pairs of words in the same or different language s that are similar in form and meaning but have different root philology roots . That is, they appear to be, or are sometimes considered, cognate s, when in fact they are not. Even if false cognates lack a common root, there may still be an indirect connection between them. Phenomenon As an example of false cognates, the word for dog in the Australian Aboriginal languages Australian Aboriginal language Mbabaram language Mbabaram happens to be dog , although there is no common ancestor or other connection between that language ... . Similarly, in the Japanese language the word to occur happens to be okoru . The term false cognate is sometimes misused to describe false friend s. One difference between false cognates and false friends is that while false cognates mean roughly the same thing in two languages, false friends bear two distinct sometimes even opposite meanings. In fact, a pair of false friends may be true cognates see false friend Causes false friends causes . A related phenomenon is the expressive loan ... ard earth and Dutch language Dutch aarde earth Arabic Amharic anta you, masculine singular and Japanese ... mina Finnish min I , and Zulu language Zulu mina I Estonian sina Finnish sin singular you and Turkish language Turkish sen singular you see also Ural Altaic languages Estonian ta short form of tema ... Lallnamen comprise a special case of false cognates. dubious date July 2011 The striking cross linguistical ... 2 False friend col 2 Translation Equivalence Translation col end References Jakobson, R. 1962 Why mama .... The Hague Mouton. Geoff Parkes and Alan Cornell 1992 , NTC s Dictionary of German False Cognates , National Textbook Company, NTC Publishing Group. Reflist 2 External links Wiktionary false cognate http web.archive.org web 20070227031854 http members.aol.com yahyam coincidence.html A list of false ... more details
False Sandalwood may refer to any of the following plant species Adenanthera pavonina False Red Sandalwood Eremophila mitchellii Myoporum platycarpum disambig ... more details
False Hopes may refer to False Hopes Dessa album False Hopes Dessa album False Hopes Doomtree album False Hopes Doomtree album , 2007 disambiguation Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
False breeching can refer to False breeching on the shafts of an animal drawn vehicle see Breeching tack False breeching on a firearm or other weapon see Firearm See also Breech disambiguation Breeching disambiguation deliberate link to redirect, per MOSDAB disambig ... more details
In mathematics , a singular point of an algebraic variety V is a point P that is special so, singular , in the geometric sense that V is not Local flatness locally flat there. A point of an algebraic variety which is not singular is said regular . An algebraic variety which has no singular point is said non singular or smooth . In the case of an algebraic curve , a plane curve that has a double point , such as the cubic curve y sup 2 sup x sup 2 sup x 1 exhibits at 0, 0 , cannot simply be parametrized near the origin. A plot of this curve is below with the singular point at the origin. An example of singular point is when a graph crosses over itself Image Singularptfn.JPG The reason for that algebraically is that both sides of the equation show powers higher than 1 of the variables x and y .... In general for a hypersurface F x , y , z , ... 0 the singular points are those at which all the partial ... P to be a singular point of V is that the linear parts of those polynomials are linearly dependent ... . Points of V that are not singular are called non singular or regular . It is always true that most points are non singular in the sense that the non singular points form a set that is both open ... criterion for a point of a variety to be singular mentioned earlier , that it is a point where ... a real analytic manifold but this equation also defines a variety having a singular point at the origin ... characteristic, or ultrametric fields, is even more vexed. Singular points of smooth mappings As the notion of singular points is a purely local property the above definition can be extended to cover ... exist . Analysis of these singular points can be reduced to the algebraic variety case by considering ... truncated at degree k and deleting the constant term . See also Singular point of a curve Singularity theory References reflist refimprove date September 2008 cite book title Singular Points of Complex ... Category Singularity theory pt Ponto singular de uma variedade alg brica ... more details
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