In geometry , a singularpoint on a curve is one where the curve is not given by a smooth function smooth embedding of a parameter. The precise definition of a singularpoint depends on the type of curve ... curve, g t t sup 2 sup , t sup 3 sup . Both definitions give a singularpoint at the origin ... 1 partial f over partial y , math so the curve is non singular or regular at the origin if at least one of the partial derivative s of f is non zero. The singular points are those points on the curve ... sub 1 sub c sub 2 sub m sup 2 sup is not 0 then the curve has a point of double contact with y mx ... of x sup 3 sup is not then the origin is a Inflection pointpoint of inflection of the curve ... of undulation of the curve. This analysis can be applied to any point on the curve by translating ... curve has an acnode at the origin, which is an isolated point in the plane. The central curve ... point of the curve. Again putting y mx , f can be written math f c 0 2mc 1 c 2m 2 x 2 d 0 3md 1 3m ... sup 0, then the origin is called a acnode . In the real plane the origin is an isolated point on the curve ... . The curve in this case changes direction at the origin creating a sharp point. The curve has a single ... then the corresponding branch of the curve has a point of inflection at the origin. In this case the origin ... 3 Petal rose.svg thumb 200px right A curve with a triple point at the origin. In general, if all ... is said to have a multiple point of order k or a k ple point . The curve will have, in general, k tangents ... point of a curve. The above definitions can be extended to cover Implicit function implicit curves ... of singular points of curves can be studied as a classification of singularpoint of an algebraic variety . Types of singular points Some of the possible singularities are An isolated point x sup 2 ... If the origin 0, 0 is on the curve then a sub 0 sub 0. If b sub 1 sub 0 then the implicit function theorem guarantees there is a smooth function h so that the curve has the form y h x near the origin ... more details
of the mapping truncated at degree k and deleting the constant term . See also Singularpoint of a curve Singularity theory References reflist refimprove date September 2008 cite book title Singular Points ...In mathematics , a singularpoint 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 to be regular . An algebraic variety which has no singularpoint is said to be 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 singularpoint at the origin. An example of singularpoint is when a graph crosses over itself Image Singularptfn.JPG The reason ... on a point P to be a singularpoint of V is that the linear parts of those polynomials are linearly ... that the geometric criterion for a point of a variety to be singular mentioned earlier , that it is a point ..., and therefore a real analytic manifold but this equation also defines a variety having a singularpoint ... that the curve has equation F x , y 0, then the partial derivative s of F with respect to both x and y ... axes. In general for a hypersurface F x , y , z , ... 0 the singular points are those at which ... of coordinates . 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 ... fields of finite 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 ... where all derivatives exist . Analysis of these singular points can be reduced to the algebraic variety ... varieties Category Singularity theory pt Ponto singular de uma variedade alg brica ... more details
by p sub n sub x . This may introduce singular points to consider. The equation should be studied on the Riemann sphere to include the point at infinity as a possible singularpoint. A M bius transformation ... disc around a . This presents no difficulty for a an ordinary point Lazarus Fuchs 1866 . When a is a regular singularpoint , which by definition means that p sub n &minus i sub z math p n i z , math ... whose only singular points, including the point at infinity, are regular singular points is called ... x p 0 x f x 0. , math One distinguishes the following cases Point a is an ordinary point when functions p sub 1 sub x and p sub 0 sub x are analytic at x a . Point a is a regular singularpoint if p sub ... point a is an irregular singularpoint . Listed below are several examples from ordinary differential equations from mathematical physics that have singular points and known solutions. Bessel differential ... and provide n independent solutions near a . Otherwise the point a is an irregular singularity ... 2 f 0. math This differential equation has regular singular points at 1, 1, and . Hermite differential ... z 1 z f 0. math This differential equation has regular singular points at 0, 1 and . A solution is the hypergeometric ... more details
Elliptic curvepoint multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography as a means of producing a trap door function . Basics Given a curve E defined along some equation in a finite field such as math E y 2 x 3 ax b math we define point multiplication as the repeated addition of a point along that curve. Denote as math nP P P P cdots P math for some scalar integer n and a point math P lbrace x, y rbrace math that lies on the curve E . The security of modern ECC depends on the intractability of determining n from math Q nP math given known values of Q and P . It is known as the elliptic curve discrete logarithm problem. Point addition Point addition is defined as taking two points along a curve E and computing where a line through them intersects the curve. We use the negative of the intersection point as the result of the addition. The operation is denoted by br P Q R or, br x sub P sub , y ... P sub y sub Q sub x sub Q sub x sub P sub Point doubling Like point addition except we take the tangent of a single point and find the intersection with the tangent line. br x sub R sub L sup 2 sup 2x ... P sub Point multiplication The straight forward way of computing a point multiplication is through repeated addition with the exception of the first addition since adding a point to itself is usually undefined since the slope of the line through the point is 0 . However, this is a fully exponential ... to 0 do Q 2 Q using point doubling if d sub i sub 1 then Q Q P using point addition Return Q An alternative ... 2 n math iterations of point doubling and addition to compute the full point multiplication. There are many ... Q 0 for i from 0 to m do Q 2 sup w sup Q using repeated point doubling if d sub i sub > 0 then Q Q d sub i sub P using a single point addition with the pre computed value of d sub i sub P Return ... fewer point additions which in practice are slower than doubling . Typically, the value of w is chosen ... 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
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
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 Strunk and White have been proven wrong on this point by logical analysis of quantification in natural ... exclusively singular nor exclusively plural, they are typically indeterminate in number. ref name Pinker ... more details
mathematical fields. The term curve has several meanings in non mathematical language as well. For example, it can be almost synonymous with mathematical function as in learning curve , or graph of a function as in Phillips curve . An Arc geometry arc or segment of a curve is a part of a curve that is bounded by two distinct end points and contains every point on the curve between its end points ... point of the curve. A curve math , gamma math is said to be closed or a loop if math , I a, b math ...other uses File Parabola.svg right thumb A parabola , a simple example of a curve In mathematics , a curve ... line is a special case of curve, namely a curve with null curvature . ref In current language, a line ... instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In every day language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola ... of the more modern term curve . Hence the phrases straight line and right line were used to distinguish ... was the advent of analytic geometry in the seventeenth century. This enabled a curve to be described ... be defined using algebraic equation s, algebraic curve s, and those that cannot, transcendental curve s. Previously, curves had been described as geometrical or mechanical according to how they were ... curves, in general. Newton had studied the cubic curve s, in the general description of the real ... accessible to the geometry of the time, to do with singular points and complex solutions. From the nineteenth century there is not a separate curve theory, but rather the appearance of curves ... , when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis . The era of the space filling curve s finally provoked the modern definitions of curve. Topology File Mandelbrot Components.svg 250px right thumb Boundaries of hyperbolic components ... more details
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 ... curve math y c x math at the point math c,0 math . The failure of uniqueness can be used to construct ...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 ... mean that there is a point x where y sub s sub x y sub c sub x and y sub s sub x y sub c sub x where 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 ... point, math x c math , and for the second solution, uniqueness fails at every value of math x math . 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 ... of the differential equation at every point, including math x c 1 math and math x ... are singular, in the sense that the second derivative fails to exist, at math x c 1 math ... 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
The Curve may refer to The Curve film , a 1998 thriller neo noir film The Curve Theatre, Leicester, UK. Curve theatre The Curve, an art gallery within Barbican Centre , London, UK The Curve shopping mall , a shopping mall in Malaysia See also Curve disambiguation disambiguation ... more details
S Curve can refer to the following S Curve art , an art term for a sinuous body position, noted in ancient marble sculpture Sigmoid function , a mathematical function that produces a sigmoid curve or a curve having an S shape S Curve Records , a record label Reverse curve , a type of horizontal curve disambig fr Courbe en S ... 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 ... math a curve going 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 ... the boundary operator. Consider first the set of all possible singular n simplices math sigma n Delta ... X math . Elements of math C n X math are called singular n chains they are formal sums of singular ... boundary math partial math is readily extended to act on singular n chains. The extension, called ... the singular complex . It is often denoted as math C bullet X , partial bullet math or more simply ... the group 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 ..., except math H 0 X mathbb Z math . A proof for the homotopy invariance of singular homology groups ... 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 Category Edgar Allan Poe in popular culture Hist novel stub ... 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 .... 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 .... end matrix math Its solution when math varepsilon 0.1 math is the solid curve shown below. Note that the solution ... 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
Unreferenced date December 2009 Orphan date December 2009 In English language English grammar , a false singular 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 false singular is a form of back formation . Some false singulars become standard English. For example, pea was originally a false singular 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 False Singular Category Grammar ... 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
The collective singular is a grammatical term for referring to a group as one entity rather than as a collection of individuals. This rule is standard in the United States , but not found in Great Britain . Examples Creedence Clearwater Revival was founded in El Cerrito, California . Nintendo is a video game company headquartered in Japan . This does not, however, affect the tense later in the sentence. Cream is a psychedelic rock band who were primarily popular in the 1960s. Exceptions to the rule include singular group names preceded by an article. The Who are a rock band from Great Britain. External links http www.chompchomp.com terms collectivenoun.htm Collective Nouns Category grammar ... 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
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
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 ... 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 ... Articles created via the Article Wizard Category Thai pop music groups pt Singular banda ... 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
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