Wiktionarypar fundamentalFundamental may refer to Foundation of reality . Fundamental frequency , as in music or phonetics, often referred to as simply a fundamental . Fundamentalism , the belief in, and usually the strict adherence to, the simplistic or fundamental ideas based on faith of a system of thought. The Fundamentals , a set of books important to Christian fundamentalism Any of a number of fundamental theorem s identified in mathematics, such as The fundamental theorem of algebra , a theorem regarding the factorization of polynomials. The fundamental theorem of arithmetic , a theorem regarding prime factorization. Fundamental analysis , a method that uses financial and economic analysis to predict the movement of security prices such as bond prices, but more commonly stock prices. In music Fundamental Bonnie Raitt album Fundamental Pet Shop Boys album Fundamental Puya album Fun Da Mental , a rap group. disambig cs Fundament ln es Fundamental gl Fundamental id Fundamental it Fundamental nl Fundamental ... more details
The fundamental plane may refer to The fundamental plane spherical coordinates fundamental plane which divides a spherical coordinate system. The fundamental plane elliptical galaxies fundamental plane which shows an empirical relationship between mean surface brightness, velocity dispersion and effective radius of an elliptical galaxy. disambig ... more details
The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming ... ref For example, the fundamental theorem of calculus gives the relationship between differential .... The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory . The mathematical literature sometimes refers to the fundamental ... in and of itself. The fundamental lemma of a field is often, but not always, the same as the fundamental theorem of that field. Fundamental lemmas Fundamental lemma of calculus of variations Fundamental lemma of Langlands and Shelstad Fundamental lemma of sieve theory Feinstein s fundamental lemma information theory Fundamental lemma of interpolation theory numerical analysis Fundamental theorems of mathematical topics Fundamental theorem of algebra Fundamental theorem of arithmetic Fundamental theorem of calculus Fundamental theorem of curves Fundamental theorem of cyclic groups Fundamental theorem of surfaces Fundamental theorem of finitely generated abelian groups Fundamental theorem of Galois theory Fundamental theorem on homomorphisms Fundamental theorem of linear algebra Fundamental theorem of projective geometry Fundamental theorem of Riemannian geometry Fundamental theorem of vector analysis Fundamental theorem of linear programming Non mathematical fundamental theorems There are also a number of fundamental theorems more aptly a series of rule of thumb not directly related to mathematics Fundamental theorem of arbitrage free pricing Fisher s fundamental theorem of natural selection Fundamental theorems of welfare economics Thermodynamic potentials The fundamental equations Fundamental equations of thermodynamics Fundamental theorem of poker See also List of theorems Notes reflist Fundamental theorems Category Mathematical theorems Category Fundamental theorems es Teorema fundamental fr Th or me fondamental hi ka nl Hoofdstelling ... more details
The mathematical term fundamental sequence can refer to In analysis, Cauchy sequence . In discrete mathematics and computer science, Unary coding . In set theory, a fundamental sequence ordinals fundamental sequence for an ordinal is a sequence of ordinals approaching the limit ordinal from below. disambig ... more details
Fundamental law s may refer to Organic law , in particular, Constitution , in particular, The Russian Constitution of 1906 . The German Grundgesetz more commonly translated as Basic Law . The four individual laws that together make up the Constitution of Sweden . The Fundamental Laws of England . The Fundamental Law of Vatican City State The Basic Law s of a country which does not use the term constitution , or has an uncodified constitution. The fundamental physical law s of the universe Religion The Ten Commandments disambig es Leyes fundamentales fr Loi fondamentale ... more details
Fundamental science or basic science, pure science is science that describes the most basic object s, force s, relations between them and laws governing them, such that all other phenomena may be in principle derived from them following the logic of scientific reductionism . Physics is a typical fundamental science, chemistry is often included. There is a difference between fundamental science and applied science or practical science . ref American Association for the Advancement of Science, Science. 1917. Page 645 ref Fundamental science, in contrast to applied science, is defined as a fundamental knowledge it develops. The progress of fundamental science is based on well controlled experiments and careful observation. Fundamental science is dependent upon deductions from demonstrated truths, or is studied without regard to practical applications. Fundamental science has traditionally been associated with the natural sciences , however, research in the social science social and behavioral sciences can be deemed fundamental e.g., cognitive neuroscience, personality . See also Exact science Fundamental research Philosophy of science Scientific method Hard and soft science Hard science vs. Soft science References Reflist Further reading Henry James Clarke, http books.google.com books?id YBUHAAAAQAAJ The fundamental science . 1885. DEFAULTSORT Fundamental Science Category Philosophy of science science stub philosophy stub cy Gwyddoniaeth bur de Grundlagenwissenschaft et Alusteadused fr Science fondamentale it Scienza fondamentale nl Fundamentele wetenschap ja ru uk ... more details
A fundamental matrix may refer to fundamental matrix computer vision fundamental matrix linear differential equation disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
In representation theory of Lie group s and Lie algebra s, a fundamental representation is an irreducible finite dimensional representation of a semisimple Lie algebra semisimple Lie group or Lie algebra whose highest weight is a fundamental weight . For example, the defining module of a classical Lie group is a fundamental representation. Any finite dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to lie Cartan . Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite dimensional representations. Examples In the case of the general linear group , all fundamental representations are exterior power s of the defining module. In the case of the special unitary group SU n SU n , the n &minus 1 fundamental representations are the wedge products math operatorname Alt k mathbb C n math consisting of the alternating tensor s, for k 1, 2, ..., n &minus 1. The spin representation of the twofold cover of an odd orthogonal group , the odd spin group , and the two half spin representations of the twofold cover of an even orthogonal group, the even spinor group, are fundamental representations that cannot be realized in the space of tensors. The adjoint representation of the simple Lie group of type E8 mathematics E sub 8 sub is a fundamental representation. Explanation The Representation ... integral weights. It can be proved that there exists a set of fundamental weights , indexed by the vertices ... combinations of the fundamental weights. The corresponding irreducible representations are the fundamental representations of the Lie group. From the expansion of a dominant weight in terms of the fundamental weights one can take a corresponding tensor product of the fundamental representations ... uses Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer ... more details
about the type of unit of measure the concept in number theory Fundamental unit number theory A set of fundamental units is a set of Units of measurement units for physical quantity physical quantities from which every other unit can be generated. In the language of measurement , quantities are quantifiable aspects of the world, such as time , distance , velocity , mass , momentum , energy , and weight , and units are used to describe their measure. Many of these quantities are related to each other by various physical laws, and as a result the units of some of the quantities can be expressed as products ... that cannot be so expressed can be regarded as fundamental in this sense. There are other relationships between physical quantities which can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions ... of fundamental constants by one. For instance, time and distance are related to each other by the speed of light , c, which is a fundamental constant. It is possible to use this relationship to eliminate either the fundamental unit of time or that of distance. Similar considerations apply to Planck ... but not in others. In the SI system there are 7 fundamental units kilogram , meter , candela , second , ampere , kelvin , and mole unit mole . In theory a system of fundamental quantities or sometimes fundamental dimensions would be such that every other physical quantity or dimension of physical ... charge to such a number. One could similarly eliminate the mole as a fundamental unit by reference ... in terms of other physical quantities. That just leaves one fundamental dimension and one fundamental unit, but we still have plenty of fundamental constants left to eliminate that too for instance ... physicists who have cast doubt on the very existence of incompatible fundamental quantities. ref M. J. Duff, L. B. Okun and G. Veneziano, Trialogue on the number of fundamental constants , JHEP ... more details
Infobox Single Name Fundamental Love Cover ELT FundamentalLove.jpg Artist Every Little Thing band Every Little Thing from Album commonplace album commonplace Released July 30, 2003 Format CD single Recorded Genre J pop Length 10 16 Fundamental Love and nostalgia only Label AVEX Records avex trax Writer Kaori Mochida Producer Last single Grip br 2003 This single Fundamental Love br 2003 Next single Mata Ashita br 2003 nihongo Fundamental Love was the th single by the Japan ese j pop group Every Little Thing band Every Little Thing , released on July 30, 2003. Track listing nihongo Fundamental Love nostalgia 2003614 version nihongo Fundamental Love Instrumental Chart positions class wikitable align left Chart 2003 align center Peak br position align center Time in br chart align left Japan Oricon align center 9 align 7 weeks External links http avexnet.jp item every disc product AVCD 30501.html nihongo Fundamental Love information at AVEX Records Avex Network . http www.oricon.co.jp music release d 514178 1 nihongo Fundamental Love information at Oricon . Category 2003 singles Category Every Little Thing songs Category Songs written by Kaori Mochida Category Singles certified gold by the Recording Industry Association of Japan 2000s Japan single stub gl Fundamental Love ja ... more details
Unreferenced date December 2009 Dablink For the fundamental class in class field theory see class formation . In mathematics , the fundamental class is a homology mathematics homology class M associated to an oriented manifold M , which corresponds to the whole manifold , and pairing with which corresponds to integrating over the manifold . Intuitively, the fundamental class can be thought of as the sum of the top dimensional simplices of a suitable triangulation of the manifold. Definition Closed, orientable When M is a connected space connected orientable closed manifold of dimension n , the top homology group is infinite cyclic math H n M, mathbf Z cong mathbf Z math , and an orientation is a choice of generator, a choice of isomorphism math mathbf Z to H n M, mathbf Z math . The generator is called the fundamental class . If M is disconnected but still orientable , a fundamental class is a fundamental class for each connected component corresponding to an orientation for each component . It represents, in a sense, integration over M , and in relation with de Rham cohomology it is exactly that namely for M a smooth manifold, an differential form n form can be paired with the fundamental class as math langle omega, M rangle int M omega math to get a real number, which is the integral ..., one cannot define a fundamental class, or more precisely, one cannot define a fundamental class ... there is no ambiguity in choice of orientation , and has a math mathbf Z 2 math fundamental class. This math mathbf Z 2 math fundamental class is used in defining Stiefel Whitney numbers . With boundary ... of isomorphism is a fundamental class. Poincar duality Main Poincar duality Expand section date December 2008 Under Poincar duality , the fundamental class is dual to the bottom class of a connected ... decomposition of the flag variety of a Lie group , the fundamental class corresponds to the top dimension ... of a Coxeter group Poincar duality DEFAULTSORT Fundamental Class Category Algebraic topology ... more details
In geometry , the fundamental domain of a symmetry group of an object is a part or pattern, as small .... A fundamental domain is a subset of the space which contains exactly one point from each of these orbits .... There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected .... The images of a chosen fundamental domain under the group action then tessellation tile the space. One general construction of fundamental domains uses Voronoi cell s. Hints at general definition ... s, a fundamental domain also called fundamental region for this action is a set D of representatives ... quasi invariant measure mathematics measure on X . A fundamental domain always contains a free regular ..., but the repeated part has measure zero. This is a typical situation in ergodic theory . If a fundamental ... lattice Z sup n sup acting on it by translations, the quotient X G is the n dimensional torus . A fundamental ... fold rotation an orbit is either a set of n points around the axis, or a single point on the axis the fundamental ... on each side of the plane, or a single point in the plane the fundamental domain is a half space bounded ..., except for one orbit, consisting of the center only the fundamental domain is a half space bounded ... opposite to each other with respect to the axis, or a single point on the axis the fundamental ... the fundamental domain is an infinite slab for discrete translational symmetry in two directions the orbits are translates of a 2D lattice in the plane through the translation vectors the fundamental ... in three directions the orbits are translates of the lattice the fundamental domain is a primitive ... diagram. In the case of translational symmetry combined with other symmetries, the fundamental domain is part of the primitive cell. For example, for wallpaper group s the fundamental domain is a factor 1, 2, 3, 4, 6, 8, or 12 smaller than the primitive cell. Fundamental domain for the modular group ... set of H &Gamma the grey one with the third point of the triangle at infinity is the canonical fundamental ... more details
In mathematics , a fundamental solution for a linear partial differential operator L is a formulation in the language of Distribution mathematics distribution theory of the older idea of a Green s function . In terms of the Dirac delta function x , a fundamental solution F is the solution of the inhomogeneous equation LF &delta x . Here F is a priori only assumed to be a Schwartz distribution . This concept ... dimensions for the Laplacian by Marcel Riesz . The existence of a fundamental solution for any operator ... frac partial 2 partial x 2 math . The fundamental solutions can be obtained by solving LF x , explicitly ... as zero, we get math F x x H x frac 1 2 x frac 1 2 x math Motivation Once the fundamental solution ... is achieved by convolution. Fundamental solutions also play an important role in the numerical solution ... hand side math sin x math with the fundamental solution math F x frac 1 2 x math math f x int infty ... F g LF g , provided L has constant coefficients. If F is the fundamental solution, the right side ... g x math Therefore, if F is the fundamental solution, the convolution F g is the solution of Lf g x . Fundamental solutions for some partial differential equations Laplace equation math nabla 2 Phi mathbf x , mathbf x delta mathbf x mathbf x math The fundamental solutions in two and three dimensions ... x frac 1 4 pi mathbf x mathbf x math Helmholtz equation where the parameter k is real and the fundamental ... x mathbf x math The two and three dimensional Helmholtz equations have the fundamental solutions math ... x , mathbf x delta mathbf x mathbf x math The biharmonic equation has the fundamental solutions math ... processing , the analog of the fundamental solution of a differential equation is called the impulse ... f f042250 title Fundamental solution DEFAULTSORT Fundamental Solution Category Partial differential equations Category Generalized functions de Fundamentall sung es Soluci n fundamental fa pt Solu o fundamental sv Fundamentall sning ... more details
Image Schenkerian Ursatz 321IVI.png thumb audio Ursatz.mid Play . In Schenkerian analysis , the fundamental structure lang de Ursatz is a specific musical pattern that occurs at the most remote or Background Schenker background structural level level of structure . A basic elaboration of the tonic music tonic triad music triad , it consists of the fundamental line accompanied by the bass arpeggiation . Hence the fundamental structure, like the fundamental line itself, takes one of three forms, according to which tonic triad pitch is the primary tone . The following is an example in C major , with the fundamental line descending from degree music scale degree sub music scale 3 sub Fundamental line The fundamental line lang de Urlinie is the melodic aspect of the Fundamental structure de Ursatz Ursatz , a step wise descent from one of the Triad music triad notes to the Tonic music tonic sub music scale 3 sub sub music scale 2 sub sub music scale 1 sub , sub music scale 5 sub sub music scale 4 sub sub music scale 3 sub sub music scale 2 sub sub music scale 1 sub , or sub music scale 8 sub sub music scale 7 sub sub music scale 6 sub sub music scale 5 sub sub music scale 4 sub sub music scale 3 sub sub music scale 2 sub sub music scale 1 sub with the bass arpeggio arpeggiation being the harmony harmonic aspect. Middleton 1990, p.193 Image Urlinie.PNG thumb center 550px Urlinie See also Linear progression Source Middleton, Richard 1990 2002 . Studying Popular Music . Philadelphia Open University Press. ISBN 0 335 15275 9. Further reading Cadwallader, Allen and Gagn , David. Analysis of Tonal Music A Schenkerian Approach . New York Oxford University Press, 1998. Schenker, Heinrich. Free Composition . Ernst Oster, tr. and ed. New York Longman. Category Post tonal music theory Category Schenkerian analysis de Ursatz DEFAULTSORT Fundamental Structure ... more details
A fundamental point in German Fundamentalpunkt is the geometric origin of a geodetic network and defines the datum geodesy geodetic datum of a national survey . Some fundamental stations are an astronomical or satellite geodetic observatory . In any case, the geographic latitude and longitude of the station is precisely determined by methods of astrogeodesy and is chosen as ellipsoid al latitude and longitude at the Earth ellipsoid which is used to calculate the coordinates of the whole network. Also, precise azimuth s to one or two nework points are observed, and are taken over as orientated Direction geometry directions of these network lines. By these procedure, the polar axis of the reference ellipsoid becomes parallel to the Earth rotation axis, and therefore the vertical deflection of the fundamental point is zero . The term Fundamental station is used for special observatories which combine several space positioning techniques like VLBI , Satellite laser ranging Satellite Laser Ranging , GPS , Glonass etc. They are the basis of Plate tectonic analyses which allow the monitoring of continental drift rates with accuracies of mm year. Important fundamental stations in Europe are Grasse , central France Graz Lustb hel Austria Malvern , England ? Onsala large Radio telescope , Sweden Wettzell 20m Radio telescope in the Bayerischer Wald, Germany Zimmerwald near Berne, Switzerland . Worldwide about 30 fundamental stations are existing about 5 in the USA and in GUS countries, 2 3 in South America, Africa, Eastern Asia, Australia and Antarctica. The basic coordinate system is the International Terrestrial Reference System ITRF reference frame, which is related to the ICRS celestial ... universe, and on some 3000 fundamental star s of our galaxy . The actual coordinates of the latter FK6 ... wettzell.html Two Fundamental stations at the southern hemisphere german website http www.ari.uni heidelberg.de publikationen vhd vhd035 fulltext gifframe.htm Fundamental system FK6, Astronomisches Rechen ... more details
Financial markets Fundamental analysis of a business involves analyzing its financial statements and health ..., or currency using fundamental analysis there are two basic approaches one can use bottom up analysis and top down analysis. ref cite web title An Introduction to Fundamental Analysis and the US ... fundamental analysis us economy.html post13168 accessdate 2009 07 27 ref The term is used to distinguish ... analysis . Fundamental analysis is performed on historical and present data, but with the goal ... price, there are two basic methodologies Fundamental analysis maintains that markets may misprice ... complementary methods for stock picking. For example many fundamental investors use technicals ... Valuation, Market based valuation , and Behavioral finance . Fundamental analysis includes Economic ... styles Investors may use fundamental analysis within different portfolio finance portfolio Investment ... onto good businesses allows the investor s asset to grow with the business. Fundamental analysis lets ... fundamental analysis to correctly value good and bad companies. Eventually bad companies stock goes ... date December 10, 2004 isbn 978 0071448208 ref Fundamental analysis allows you to make your own decision ... valued companies, believing that it s hard to fall out of a ditch . The value comes from fundamental analysis. Managers may use fundamental analysis to determine future growth rates for buying high priced growth stock s. Managers may also include fundamental factors along with technical factors ... widely by Thomson Reuters and others can be considered either fundamental they are facts or technical ... interpretation of fundamental data along with technical data in the industry. Since about year 2000 ... pip.asp ref Criticisms Economists such as Burton Malkiel suggest that neither fundamental analysis nor ... Page Fundamental Analysis and Stock Valuation E Book from IACAM http ocw.mit.edu courses sloan school ... market DEFAULTSORT Fundamental Analysis Category Fundamental analysis Category Commodities market ... more details
lambda 4 math lambda can be found using the following equation math lambda frac v F 0 math The fundamental ... F 0 math fundamental Frequency br math L math length of the tube br math v math velocity of the sound ... equipments, the frequency of 1st mode is called fundamental frequency. See also Missing fundamental ... DEFAULTSORT Fundamental Frequency Category Musical tuning Category Acoustics Category Fourier ... es Frecuencia fundamental eo Fundamenta frekvenco fa fr Fr quence fondamentale nl Grondtoon natuurkunde ja pl Ton podstawowy pt Frequ ncia fundamental sv Grundfrekvens zh ... more details
Infobox Album See Wikipedia WikiProject Albums Name Fundamental Destiny Type Live album Artist Art Ensemble of Chicago & Don Pullen Cover Fundamental Destiny.jpg Released 2007 Recorded June 1, 1991 Genre Jazz Length Label AECO Records AECO Producer Reviews Allmusic class album id r1206360 Rating 4 5 Chronology Art Ensemble of Chicago Last album Live at the 6th Tokyo Music Joy br 1991 This album Fundamental Destiny br 2007 Next album Salutes the Chicago Blues Tradition br 1993 Fundamental Destiny is a live album by the Art Ensemble of Chicago and Don Pullen recorded in June 1991 in Frankfurt , Germany and released in 2007 on the group s AECO Records AECO label. It features performances by Lester Bowie , Joseph Jarman , Roscoe Mitchell , Malachi Favors Maghostut , and Don Moye with Don Pullen joining on piano. The Allmusic review by Scott Yanow states that This live recording, while not flawless, has enough bright moments to make it easily recommended to Art Ensemble collectors . ref Yanow, S. Allmusic class album id r1206360 pure url yes Allmusic review accessed 16 February 2009. ref Track listing People in Sorrow Bowie, Favors, Jarman, Mitchell 19 47 Song For Atala Mitchell 16 48 Fundamental Destiny Jarman 11 56 Odwalla The Theme Mitchell 3 35 Recorded live at Frankfurt Jazz Festival, Germany on June 1, 1991 Personnel Lester Bowie trumpet, percussion Malachi Favors Maghostut bass, percussion Roscoe Mitchell soprano saxophone, alto saxophone, tenor saxophone, baritone saxophone, clarinet, flute, percussion Joseph Jarman soprano saxophone, alto saxophone, tenor saxophone, synthesizer, clarinet, flute, percussion Famoudou Don Moye drums, percussion Don Pullen piano References Reflist Category Don Pullen albums Category Art Ensemble of Chicago live albums Category 2007 live albums Category AECO Records live albums pl Fundamental Destiny ... more details
Fundamental justice is a legal term that signifies a dynamic concept of Equity law fairness underlying the administration of justice and its operation, whereas principles of fundamental justice are specific legal principles that command significant societal consensus as fundamental to the way in which ... process or procedure that affects fundamental rights and freedoms, and certain substantive ... of fundamental justice. ref Charkaoui v. Canada Citizenship and Immigration , 2007 SCC 9 at para. 25. ref A legislative or administrative framework that respects the principles of fundamental ... in the Canadian Bill of Rights and the Canadian Charter of Rights and Freedoms . Fundamental ... fundamental justice can be traced back at least to 1960, when the Canadian Bill of Rights was brought ... of fundamental justice for the determination of his rights and obligations. According to the legal ... the Bill. Some wanted the words natural justice in the place of fundamental justice, as natural justice was indeed a more common phrase with judges and authors. Fundamental justice was a more obscure alternative with these figures other such alternatives include universal justice . Still, fundamental justice was chosen, and in the case Duke v. The Queen 1972 , it was ruled that fundamental ... through fundamental justice is not precisely duplicated in the Charter. While the term fundamental ... s had been denied hearings, and thus their section 2 e and fundamental justice rights were infringed ... 1982 when the term fundamental justice was first constitutionalized. The phrase was included ... in accordance with the principles of fundamental justice. To limit the rights to life, liberty and security of the person, the authors of the Charter specifically chose the term fundamental justice over due process because they believed the term fundamental justice would still be interpreted to mean ... found in the Canadian Bill of Rights, which meant the definition of fundamental justice was now ... more details
Dablink For the fundamental group of a factor see von Neumann algebra . In mathematics , more specifically algebraic topology , the fundamental group discovered by Henri Poincar who gave the definition ... information about the basic shape, or holes , of the topological space. The fundamental group is the first and simplest of the homotopy group s. Fundamental groups can be studied using the theory of covering space s, since a fundamental group coincides with the group of deck transformation ... fundamental group can be described explicitly in terms of finitely presented group generators and relations . Historically, the concept of fundamental group first emerged in the theory of Riemann surface ... of combining and this equivalence between them is the fundamental group. For the precise definition ..., the set of all homotopy classes of loops with base point x sub 0 sub forms the fundamental group of X ... g defined by g t f 1 &minus t . That is, g follows f backwards. Although the fundamental ... ambiguity whenever we care about the isomorphism class only. Examples Trivial fundamental group. In Euclidean ... class of loops, and the fundamental group is therefore the trivial group with one element. A path connected space with a trivial fundamental group is said to be Simply connected space simply connected . Infinite cyclic fundamental group. The circle . Each homotopy class consists of all loops ... around n times is a loop which winds around m n times. So the fundamental group of the circle ... the fundamental group is a homotopy invariant, the theory of the winding number for the complex plane ... group s and higher homotopy groups associated to a topological space, the fundamental group need not be abelian group abelian . For example, the fundamental group of the Rose topology figure eight is the free group on two letters. More generally, the fundamental group of any graph mathematics graph ... with a non abelian fundamental group is the complement of a trefoil knot in R sup 3 sup . Functoriality ... more details
A fundamental breach of a contract , sometimes known as a repudiatory breach , is a Breach of contract breach so fundamental that it permits the distressed party to terminate performance of the contract, in addition to entitling that party to sue for damages. History Contract law The law of fundamental breach was historically treated as an extension of the doctrine of Deviation law deviation . The development of this doctrine can be traced down to the first half of the 19th century, when Tindal C.J. stated in Davis v. Garrett that deviation made by the carrier from the agreed voyage route brings the latter outside of contract and therefore outside of exceptions or limitation clauses provided by such a contract. This harsh attitude to deviation cases originated from the earlier marine insurance practice when cargo insurance policy was lost in case of deviation. Thereby strict obligations imposed ... contract law The doctrine of fundamental breach further developed in numerous cases and by the second ..., 189 at p. 193 ref labelled the fundamental term as the hard core of the contract . Lord Reid in Suisse ... s Rep. 529 ref defined fundamental breach as a blockquote well known type of breach which entitles ... of law, under the doctrine of fundamental breach of contract, exclusion clauses were deemed not to be available to a party in fundamental breach of the contract. In particular, the common law approach ... of fundamental breach was doubted in favour of such cases as falling within authority of the ordinary ... of fundamental breach and liability limitations. Former by giving the force of law to the Hague ..., fundamental breach was first examined by the House of Lords in the Suisse Atlantique case ref 1966 2 All E.R. 61 ref , wherein they decided that a contract can be voided if a breach of a fundamental ... maintained a strict Rule of Construction approach whereby a fundamental breach is found only through ... of fundamental breach has been laid to rest ref 2010 SCC 4, para. 81 ref by the Supreme Court of Canada ... more details
In mathematics , a fundamental discriminant D is an integer invariant mathematics invariant in the theory of integer integral binary function binary quadratic form s. If nowrap 1 Q x , y ax sup 2 sup bxy cy sup 2 sup is a quadratic form with integer coefficients, then nowrap 1 D b sup 2 sup &minus 4 ac is the discriminant of Q x , y . Conversely, every integer D with nowrap D 0, 1 mod 4 is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory. Every discriminant may be written as D D sub 0 sub f sup 2 sup with D sub 0 sub a discriminant and f a positive integer. A discriminant D is called a fundamental discriminant if f 1 in every such decomposition. Conversely, every discriminant D 0 can be written uniquely as D sub 0 sub f sup 2 sup where D sub 0 sub is a fundamental discriminant. Thus, fundamental discriminants play a similar role for discriminants as prime number s do for all integers. There are explicit Modular arithmetic congruence conditions that give the set of fundamental discriminants. Specifically, D is a fundamental discriminant if, and only if, one ... m 2 or 3 mod 4 and m is square free. The first ten positive fundamental discriminants are 1 number ... 24 , 28 number 28 , 29 number 29 , 33 number 33 OEIS id A003658 . The first ten negative fundamental ... quadratic number fields . A basic property of this connection is that D sub 0 sub is a fundamental ... for every fundamental discriminant D sub 0 sub 1, up to isomorphism . Caution This is the reason why some authors consider 1 not to be a fundamental discriminant. One may interpret D sub 0 sub 1 as the degenerated quadratic field Q the rational number s . Factorization Fundamental discriminants may also be characterized by their fundamental theorem of arithmetic factorization ... D sub 0 sub 1 is a fundamental discriminant if, and only if, it is the product of Greatest ... more details
A sound is said to have a missing fundamental , suppressed fundamental , or phantom fundamental when its overtone s suggest a fundamental frequency but the sound lacks a component at the fundamental frequency itself. However, the brain perceives the pitch of a tone not only by its fundamental frequency ... timbre even if the fundamental frequency is missing from a tone. For example, when a note ... may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard. Explanation A low pitch psychophysics pitch also known as the pitch of the missing fundamental or virtual ... books.google.com books?id dX5P5mxtYYIC&pg PA233&dq phantom fundamental pitch perception&lr &as brr 0 ... that this effect was because the missing fundamental was replaced by distortions introduced by the physics ... fundamental, as reported by J. C. R. Licklider in 1954. ref cite book title Music and Connectionism ... http books.google.com books?id NxycaQH6PeoC&pg PA86&dq missing fundamental pitch perception distortion ... widely accepted that the brain processes the information present in the overtones to calculate the fundamental ... nerve. This very concept of missing fundamental being reproduced based on the overtones in the tone ... the sense of the missing fundamental by synthesizing higher harmonics. ref US patent 5930373 ref Waves ... fundamental concept to give the illusion of low bass. ref name Maximum PC 2004 cite journal ...&dq 22missing fundamental 22 v onepage&q 22missing 20fundamental 22&f false accessdate May 11, 2010 ... versions of missing fundamental based bass augmentation products. The poor bass reproduction of earbuds ... Timpani kettle drums are tuned by listening for the missing fundamental. Hit in the usual way half to three quarters the distance from the center to the rim , the fundamental note of a timpano is very ... and body resonances generally fall between 250 Hz and 300 Hz. The fundamental frequency of the open ... inflation most historical tunings , so the lowest notes of a violin have an attenuated fundamental ... more details
The Fundamental Epistle , or Epistle of Foundation , Latin Epistola Fundamenti , was one of the sacred writings of the Manichaean religion, written by the founder Mani prophet Mani c. 210 276 CE , originally in Syriac . Since none of the original Syriac writings of Manichaeism remain, we only have translations of small sections of this book, made by either Manichaeans or anti Manichaeans. One of the most well known references to this book is found in the writings of Saint Augustine 354 430 CE , who before converting to Christianity, was a Manichaean hearer for a number of years. In two of his anti Manichaean books, he quotes a few paragraphs of the Fundamental Epistle. Wikisourcelang la Epistola Fundamenti External links http www.sant agostino.it latino index.htm Augustine s writings in Latin http www.biblestudytools.com history early church fathers nicene vol 4 saint augustin anti manichaean writings Augustine s anti Manichaean writings in English E. Feldmann, Die Epistula Fundamenti der nordafrikanischen Manich er. Versuch einer Rekonstruktion, Altenberge, 1987. English The Fundamental Epistle of the North African Manichaeans an attempt at its reconstruction Category Manichaean texts ... more details
sided oriented polygon , called a fundamental polygon , by pairwise identification of its edges. Image Fundamental parallelogram.png thumb right Fundamental parallelogram defined by a pair of vectors ... edge has the orientation opposing the one of the fundamental polygon. Examples class ..., the two generators math A,B math can be taken to generate a parallelogram tiling, of fundamental ... half plane . Such lattices are known as Fuchsian group s. Standard fundamental polygons An orientable closed surface of genus mathematics genus n has the following standard fundamental polygon math A 1 B 1 A 1 1 B 1 1 A 2 B 2 A 2 1 B 2 1 cdots A n B n A n 1 B n 1 1 math This fundamental ... has the following standard fundamental polygon math A 1 A 1 A 2 A 2 cdots A n A n math Alternately ... . Fundamental polygon of a compact Riemann surface The fundamental polygon of a hyperbolic compact ... space have the standard fundamental polygon as a representative element. In the following, note that all Riemann surfaces are orientable. Metric fundamental polygon Given a point math z 0 math in the upper ... on the upper half plane, then one can define the metric fundamental polygon as the set of points ... metric on the upper half plane. The metric fundamental polygon is more usually called the Dirichlet region or the Voronoi polygon . This fundamental polygon is a fundamental domain . This fundamental ... F math where math overline F math is the closure of F . Standard fundamental polygon Given any metric fundamental polygon F , one can construct, with a finite number of steps, another fundamental polygon, the standard fundamental polygon , which has an additional set of noteworthy properties The vertices ... H . As such, each side can thus an element of the fundamental group math pi 1 mathbb H Gamma math . In particular, the fundamental group math pi 1 mathbb H Gamma math has 2 n generators math A 1, B ... The metric fundamental polygon and the standard fundamental polygon will usually have a different ... more details
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