Other uses Null disambiguation In linear algebra , the null vector or zero vector is the vector geometric vector 0, 0, , 0 in Euclidean space , all of whose components are zero. It is usually written with an arrow head above or below it math vec 0 math or 0 or simply 0. A zero vector has arbitrary direction, but is orthogonal ie perpendicular, normal to all other vectors with the same number of components. In vector spaces with an inner product for which the requirement of positive definiteness has been dropped, a vector that has zero length is referred to as a null vector. The term zero vector is then still reserved for the additive identity of the vector spaces. Linear algebra For a general vector space , the zero vector is the uniquely determined vector that is the identity element for vector addition . The zero vector is unique if a and b are zero vectors, then a a b b . The zero vector is a special case of the zero tensor . It is the result of scalar multiplication by the scalar 0 here meaning the additive identity of the underlying Field mathematics field , not necessarily the real number 0 . The preimage of the zero vector under a linear transformation f is called kernel algebra kernel or null space . A zero space is a linear space whose only element is a zero vector. The zero vector is, by itself, linear independence linearly dependent , and so any set of vectors which includes it is also linearly dependent. In a Norm mathematics normed vector space there is only one vector of norm equal to 0. This is just the zero vector. In vector algebra its coordinates are 0,0 and its unit vector is n Seminormed vector spaces In a Norm mathematics seminormed vector space there might be more than one vector of norm equal to 0. These vectors are often called null vectors. Examples The Minkowski space Causal structure light like vectors of Minkowski space are null vectors. In general, the coordinate representation of a null vector in Minkowski space contains non zero values ... more details
For the counting result sometimes called Burnside s theorem Burnside s lemma In mathematics , Burnside s theorem in group theory states that if G is a finite group of Order group theory order math p a q b math where p and q are prime number s, and a and b are negative and positive numbers non negative integer s, then G is Solvable group solvable . Hence each non Abelian finite simple group has order divisible by three distinct primes. Furthermore, as a consequence of the Feit Thompson theorem , one of those can be chosen to be 2. History The theorem was proved by William Burnside in the early years of the 20th century. Burnside s theorem has long been one of the best known applications of Representation theory of finite groups representation theory to the theory of finite groups, though a proof avoiding the use of group characters was published by D. Goldschmidt around 1970. Outline of Burnside s proof By induction, it suffices to prove that a finite simple group G whose order has the form math p a q b math for primes p and q is cyclic. Suppose then that the order of G has this form, but G is not cyclic. Suppose for definiteness that b 0 . Using the modified class equation, G has a non identity conjugacy class of size prime to q . Hence G either has a non trivial Group center center , or has a conjugacy class of size math p r math for some positive integer r . The first possibility is excluded since G is assumed simple, but not cyclic. Hence there is a non central element x of G such that the conjugacy class of x has size math p r math . Application of Character theory column orthogonality relations and other properties of group characters and algebraic integers lead to the existence of a non trivial Character theory irreducible character math chi math of G such that math chi x chi 1 math . The simplicity of G then implies that any non trivial complex irreducible representation is faithful, and it follows that x is in the center of G , a contradiction. References Ja ... more details
In physics , front velocity is the speed at which the first rise of a pulse above zero moves forward. In mathematics , it is also used to describe the velocity of a possibly propagating front in the solution of hyperbolic partial differential equation . Various velocities Associated with propagation of a disturbance are several different velocities. ref name Milonni cite book title Fast light, slow light and left handed light author Peter W Milonni url http books.google.com books?id kE8OUCvt7ecC&pg PA26 pages 26 ff isbn 0750309261 year 2004 publisher CRC Press ref For definiteness, consider an amplitude modulation amplitude modulated electromagnetic carrier wave. The phase velocity is the wave speed of the carrier. The group velocity is the wave speed of the modulation or envelope detector envelope . Initially it was thought that the group velocity coincided with the speed at which information traveled. However, it turns out that this speed can exceed the speed of light in some circumstances, causing a conflict with the theory of relativity . That observation led to consideration of what constitutes a signal . A signal involves new information or an element of surprise that cannot be predicted from the wave motion at an earlier time. ref name Milonni Thus, a possible form for a signal is math f t u t sin omega t , math where u t is the Heaviside step function . Using such a form for a signal, it can be shown, subject to the expected condition that the refractive index of any medium tends to one as the frequency tends to infinity, that the wave discontinuity, called the front , propagates at a speed less than or equal to the speed of light c in any medium. ref name Milonni In fact, the earliest appearance of the front the precursor physics precursor travels at the front velocity c , no matter what the medium . ref name Milonni ref name Stratton cite book title Electromagnetic theory author Julius Adams Stratton url http books.google.com books?id zFeWdS2luE4C&pg PA337 ... more details
Infobox language name Maay nativename Maay Maay, af Maay states Somalia , Ethiopia , Kenya significant communities in North America , and Yemen . speakers 1,5 2 million native and at least 200,000 second language speakers. familycolor Afro Asiatic fam2 Cushitic languages Cushitic fam3 East Cushitic languages East fam4 Somali languages Somali nation Somalia iso3 ymm Culture of Somalia Maay Maay also known as Af Maay, Afmaay, Af May arti, Af May, Af Maymay, Rahanween, Rahanweyn is a member of the East Cushitic languages East Cushitic branch of the Afro Asiatic languages Afro Asiatic family and is written using the Latin script . It is spoken mostly in Somalia and adjacent parts of Ethiopia and Kenya . Its speakers are known as Rahanweyn Sab Somalis. The center of the language is around Baidoa . Grammar Sounds Maay Maay exhibits significant amounts of epenthesis, inserting central or high central vowels to break up consonant clusters. Vowel length is contrastive minimal pairs such as bur flour and buur mountain are attested. Words Maay Maay is fairly agglutinative. It has complex verb forms, inflecting at least for tense aspect and person number of both subject and object. There is also a prefix indicating negation. In addition, verbs exhibit derivational morphology, including a causative and an applicative. Nominal morphology includes a definiteness suffix, whose form depends on the gender of the head noun, and possessive suffixes. Sentences Maay Maay exhbits SVO and SOV word orders, apparently in fairly free variation. When the object is postverbal, the prefix maay appears on the verb. Within the noun phrase, the head noun is generally initial. Possessors, adjectives and some strong quantifiers follow the head noun. Numerals and the indefinite quantifier precede the head noun. References http www.ethnologue.com show language.asp?code ymm Ethnologue entry for Maay External links http www.cal.org co bantu sblang.html Cultural Orientation Resource Center Category East C ... more details
The Davidon Fletcher Powell formula or DFP named after William C. Davidon, Roger Fletcher mathematician Roger Fletcher , and Michael J. D. Powell finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition see below . It was the first quasi Newton method which generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix . Given a function math f x math , its gradient math nabla f math , and positive definite matrix positive definite Hessian matrix math B math , the Taylor series is math f x k s k f x k nabla f x k T s k frac 1 2 s T k B s k, math and the Taylor series of the gradient itself secant equation math nabla f x k s k nabla f x k B s k, math is used to update math B math . The DFP formula finds a solution that is symmetric, positive definite and closest to the current approximate value of math B k math math B k 1 I gamma k y k s k T B k I gamma k s k y k T gamma k y k y k T, math where math y k nabla f x k s k nabla f x k , math math gamma k frac 1 y k T s k . math and math B k math is a symmetric and positive definite matrix . The corresponding update to the inverse Hessian approximation math H k B k 1 math is given by math H k 1 H k frac H k y k y k T H k y k T H k y k frac s k s k T y k T s k . math math B math is assumed to be positive definite, and the vectors math s k T math and math y math must satisfy the curvature condition math s k T y k s k T B s k 0. , math The DFP formula is quite effective, but it was soon superseded by the BFGS method BFGS formula , which is its dual interchanging the roles of y and s . See also Newton s method Newton s method in optimization Quasi Newton method BFGS method Broyden Fletcher Goldfarb Shanno BFGS method L BFGS L BFGS method SR1 formula Nelder Mead method References Citation doi 10.1137 0801001 first1 W. C. last1 Davidon title Variable metric method for minimization journa ... more details
Orphan date February 2009 File Munsk nksn lar.jpg thumb Pins for members of Munsk nkarna. Far left a plain member pin with the logo of Munsk nkarna, to the right pins for members which have passed the tests for some of the different course levels 1 betyg grade 1 green, druvbetyg grape grade yellow, 2 betyg grade 3 blue. Munsk nkarna is a Sweden Swedish and Finland Finnish wine tasting organization with over 20,000 members. The Swedish word Munsk nk corresponding to Mundschenk in German language German is a term which is synonumous to cup bearer . It is used to refer to a single member, with the organisation s name Munsk nkarna being the plural Definiteness definite form . The organisation was established in Stockholm in 1958 and has continuously expanded with chapters in other locations, some outside of Sweden. In 2000, the chapters in Finland had become numerous enough to split off to form their own Finnish language organisation, Suomen Munsk nkarna . In 2002, a Swedish language organisation in Finland called Svenska Munsk nkarna i Finland was also formed. All three organisations are established as non profit organisations . As of 2006, the Swedish branch of Munsk nkarna had over 19,000 members in 137 chapters, of which 129 in Sweden and 8 in other countries. In Finland there were 13 chapters in the Finnish speaking organisation and 9 chapters in the Swedish speaking organisation. Munsk nkarna claims to be the world s largest wine tasting organisation. Activities of Munsk nkarna primarily include wine tastings and wine related courses. The courses are organised much in the same way as those of the Wine & Spirit Education Trust there are several different levels of progressing difficulty, and both a theoretical and a practical i.e., blind tasting of wine test at each level, plus a thesis at the highest level. Munsk nkarna in Sweden publishes a magazine Munsk nken where, among other things, most new wines appearing in the Swedish monopoly wine stores Systembolaget ar ... more details
Image Macedonian Slavic dialects.png thumb 300px right The location of the Upper Polog dialect among the others Macedonian dialects The Upper Polog dialect Macedonian language Macedonian , gornopolo ki dijalekt is a member of the western and north western subgroup of the western group of dialects of the Macedonian language . The dialect is mainly spoken in the area around the city of Gostivar to the villages Brvenica and Bogovinje on north, Reka region on west, Por ie on east and Gali nik on south. The dialect is closely related with the neighbouring dialects, particularly with the Ki evo Pore e dialect , Reka dialect and Gali nik dialect . Also in some extent, the dialect shares some similarities with the Lower Polog dialect . The dialect is very well known for using masculine forms of direct and indirect objects, for male and female. ref p. 246, Makedonski jazik za srednoto obrazovanie S. Bojkovska, D.Pandev, L. Minova urkova, . Cvetkovski Prosvetno delo AD Skopje 2001 ref Phonological characteristics the yat has reflexed into cena , price the Proto Slavic has denazalized to a the older x has been replaced with v in most words prah prav , dust the consonant group is substituted with cvet cut , flower ref p.247 ,Makedonski jazik za srednoto obrazovanie S.Bojkovska, D.Pandev, L.Minova urkova, .Cvetkovski Prosvetno delo AD Skopje 2001 ref absence of the intervocalic IPA v in the plural forms of monosyllabic nouns e.g. , , etc. Morphological chacteristics use of masculine direct and indirect object for males and females Daj mu ja topkava na Toni Daj mu ja topkava na Ivona Give this ball to Toni Ivona three definite article s pertaining to the position of the object see Macedonian grammar Definiteness Macedonian grammar use of suffix t for third person singular toj pi uva he writes ref p.247 248, Makedonski jazik za sre ... more details
orphan date August 2009 In linguistics , determiner spreading DS is the appearance of more than one determiner associated with a noun phrase , usually marking an adjective as well as the noun itself. ref name Marinis cite book last Marinis first Theodoros title The acquisition of the DP in modern Greek url http books.google.com books?id eiBBt1tXgYC&pg PA165&dq 22determiner spreading 22 PPA165,M1 accessdate 2009 05 05 year 2003 publisher John Benjamins Publishing Company isbn 9027225001 pages 165 190 chapter The acquisition of Determiner Spreading 6 ref The extra determiner has been called an adjectival determiner . ref name Rivero cite book last Rivero first Mar a Luisa coauthors Angela Ralli title Comparative syntax of Balkan languages url http books.google.com books?id 4scXTHHkMckC&pg PA189&dq 22determiner spreading 22 PPA165,M1 accessdate 2009 05 05 year 2001 publisher Oxford University Press isbn 0195129520 pages 165 166, 191 192 ref Typical examples involve multiple occurrences of the definite article or definiteness marking, such as is found in Modern Greek 1 class wikitable border 1 Agorasa to kokkino to forema. I.bought the red the dress Determiner spreading in Greek is not obligatory, and it contrasts with a non spreading example 2 class wikitable border 1 Agorasa to kokkino forema. I.bought the red dress Researchers have tried to elucidate the nature of the difference both syntax syntactically and semantics semantically between these two kinds of structures. One widely accepted conclusion is that the determiner spreading structure requires a kind of focus, usually contrastive, on the adjective so that 1 is appropriate as where I bought the RED dress , not the BLUE one would be and that the adjective in question must be intersective so no determiner spreading is possible in the equivalent of the former minister , Greek o proigoumenos o ipurgos , and that loose compounds cannot participate in this ref Angeliki Ralli, Morphology , Ekdoseis Pataki A ... more details
infobox Book name Topic Continuity in Discourse title orig translator image image caption author Talmy Giv n illustrator cover artist country language English series Typological Studies in Language subject pragmatics genre nonfiction publisher John Benjamins pub date 1983 english pub date media type pages 492 isbn 9027228671 congress P302 .T66x 1983 oclc 10313658 preceded by followed by Topic Continuity in Discourse subtitled A Quantitative Cross Language Study is a book edited by Talmy Giv n , with contributions by himself and other experts in various languages. It is part of the series Typological Studies in Language a supplement series to the academic journal Studies in Language and was published by John Benjamins in 1983. The book presents a cross linguistic hierarchy of natural language Syntax syntactic coding of topic comment topic accessibility including, for example, discourse participant prominence . ref name Giv n 1983 17 Giv n 1983 17. ref Giv n describes the aim of the research, documented in the book, as the rather ambitious goal ... to define, in a preliminary but cross linguistically stable fashion, the basic principles of iconicity underlying the syntactic coding of the topic identification domain. ref Giv n 1983 18, emphasis original. ref Giv n s starting point was his previously published 1978, 1979, 1981 and 1982 one dimensional scale. As listed by him, from most continuous accessible topic to most discontinuous inaccessible topic this was as follows ref name Giv n 1983 17 zero Anaphora linguistics anaphora unstressed Bound variable pronoun bound pronoun s and grammatical agreement stressed independent pronouns right dislocated Definiteness definite noun phrase s NP neutral ordered NPs left dislocated NPs Y moved NPs or contrastive topicalization Cleft sentence cleft and focus constructions Reference referential indefinite NPs The language specific studies provided in the book are on Japanese language Japanese , Amharic , Ute language Ute , Biblic ... more details
definiteness grammatical state s of nouns in Arabic, the other two being the indefinite state and the definite ... marks definiteness. Since they are definite, they do not receive the indefinite suffix n nunation . Some ..., titles and names. See also Compound linguistics Definiteness References Reflist Refimprove date January ... more details
Outwitting the Devil is a book that was written by Napoleon Hill and annotated by Sharon Lechter . It was originally written in 1938 by Hill, but was said to be too controversial to be published during that time period. It was released by Sterling Publishing in June, 2011. The book is an interview between Hill Mr. Earthbound and The Devil Your Majesty . Hill uncovers the secrets to freedom and success by evaluating the greatest obstacles that humans face in order to attain their personal goals in life. Summary During the book, Mr. Earthbound interrogates The Devil, Your Majesty, to find out how people limit their success and how The Devil achieves his manipulation. br Some of the topics that are discussed are The difference between drifters and non drifters Maintaining a definiteness of purpose Finding one s other self Hill s seven principles The dangers of hypnotic rhythm History Just after the release of Think and Grow Rich in 1937, Hill began writing Outwitting the Devil as an explanation of why some were still seeing failure after following all of the steps in Think and Grow Rich . His wife, Annie Lou, did not want the book published because of the role the Devil played in it. When Hill died in 1970, the manuscript went in the possession of Annie Lou, who died in 1984. After her death, the manuscript went into the hands of Dr. Charles Johnson, who was Annie Lou s nephew and president of the Napoleon Hill Foundation . While Dr. Johnson believed the book s message to be powerful, his wife, Frankie Johnson, shared Annie Lou s feelings and told Dr. Johnson that she did not want the manuscript published while she was alive. After Frankie s death, Dr. Johnson passed the manuscript to Don Green, CEO of the Napoleon Hill Foundation. Sharon Lechter was then asked to edit the manuscript, and after several years of annotations and reviews, it was released in June, 2011. Bibliography Outwitting the Devil the Secret to Freedom and Success , by Napoleon Hill and Sharon L. Lec ... more details
definiteness, a form of ontological realism implicit in classical physics. Some interpretations ... definiteness . This has given rise to a contentious debate of the interpretation of quantum mechanics . Although locality and realism in the sense of counterfactual definiteness, are jointly ... definiteness in favor of locality, since non locality is held to be contrary to relativity. The implications ... definiteness realism of physics is a much more specific notion than general philosophical realism ... more details
A referring expression RE , in linguistics, is any noun phrase, or surrogate for a noun phrase, whose function in a text spoken, signed or written on a particular occasion is pick out someone an individual person, place, object, or a set of persons, places, objects, etc. The technical terminology for pick out differs a great deal from one school of linguistics to another. The most widespread term is probably refer , and a thing picked out is a referent , as for example in the work of John Lyons linguist John Lyons . In linguistics, the study of reference belongs to pragmatics , the study of language use, though it is also a matter of great interest to philosophers, especially those wishing to understand the nature of knowledge , perception and cognition more generally. The kinds of expressions which can refer as so defined are a noun phrase of any structure, such as the taxi in The taxi s waiting outside the apple on the table in Bring me the apple on the table and those five boys in Those five boys were off school last week . In those languages which, like English, encode definiteness , REs are typically marked for definiteness. In the examples given, this is done by the definite article the or the demonstrative adjective , here those . a noun phrase surrogate, i.e. a pronoun , such as it in It s waiting outside and Bring me it and they in They were off school last week. The referent of such a pronoun may vary according to context e.g. the referent of me depends on who the speaker is and this property is technically an instance of deixis . a proper name , like Sarah , London , The Eiffel Tower , or The Beatles . The intimate link between proper names and type 1 REs is shown by the definite article that appears in many of them. In many languages this happens far more consistently than in English. Proper names are often taken to refer, in principle, to the same referent independently of the context in which the name is used and in all possible worlds, i.e. they are i ... more details
PSD may refer to Sciences PID controller Proportional Sum Derivative , a version of the common discrete controller Proportional Integral Derivative Particle size distribution Phase sensitive detector Phase space density, number of particles atoms populating the same state. Important in Bose Einstein Condensation Position sensitive device or position sensitive detector, a device that measures the one or two dimensional position of a light spot Positive definite matrix Positive semi definiteness as it relates to matrices Postsynaptic density , a specialization of the cytoskeleton at the synaptic junction Power spectral density , the power of a signal per some unit of measurement such as temporal or spatial frequency used in signal analysis Computers Adobe Photoshop File format .psd Photoshop document , the default file extension of the proprietary file format of Adobe System s Photoshop program. A portable or personal storage device , small hard disks designed to copy digital photographs from a camera Programmable system device , an integrated circuit manufactured by ST Microelectronics and including Flash ROM, RAM, and logic functions on a single chip Program structure diagram, also known as a Nassi Shneiderman diagram Pose Space Deformation , a computer character animation technique http www.scrum.org professionalscrumdeveloper Professional Scrum Developer , a course leading to certification for Scrum development Medicine Post traumatic stress disorder more commonly abbreviated PTSD Politics Civil Movement People s Self Defense , a political movement in Ukraine and part of the Our Ukraine People s Self Defense Bloc electoral alliance Party of Socialists and Democrats , a political party of San Marino Social Democratic Party Angola , a political party of Angola Social Democratic Party Benin , a political party of Benin Social Democratic Party Brazil , a defunct political party of Brazil Social Democratic Party El Salvador , a political party of El Salvador Social Dem ... more details
In mathematics , the term positive definite function may refer to a couple of different concepts. In dynamical systems A real number real valued, continuously differentiable function mathematics function f is positive definite on a neighborhood of the origin, D , if math f 0 0 math and math f x 0 math for every non zero math x in D math . ref cite book last Verhulst first Ferdinand title Nonlinear Differential Equations and Dynamical Systems edition 2nd ed. publisher Springer year 1996 isbn 3 540 60934 2 ref ref cite book last Hahn first Wolfgang title Stability of Motion publisher Springer year 1967 ref A function is negative definite if the inequality is reversed. A function is semidefinite if the strong inequality is replaced with a weak math geq , math or math leq , math one. In analysis A positive definite function of a real variable x is a complex number complex valued function f R &rarr C such that for any real numbers x sub 1 sub , ..., x sub n sub the n × n matrix mathematics matrix math A a i,j i,j 1 n , quad a ij f x i x j math is positive definite matrix positive semi definite in particular, A should be Hermitian , therefore f x is the complex conjugate of f x . In particular, it is necessary but not sufficient that math f 0 geq 0 , quad f x leq f 0 math these inequalities follow from the condition for n 1,2. Bochner s theorem main Bochner s theorem Positive definiteness arises naturally in the theory of the Fourier transform it is easy to see directly that to be positive definite it is sufficient for f to be the Fourier transform of a function g on the real line with g y &ge 0. The converse result is Bochner s theorem , stating that any continuous positive definite function on the real line is the Fourier transform of a positive Measure mathematics measure . ref cite book last Bochner first Salomon authorlink Salomon Bochner title Lectures on Fourier integrals publisher Princeton University Press year 1959 ref Applications In statistics , and espec ... more details
conson. monosyllabic monosyl. fem. neut. Definiteness is expressed by a definite ... adjective agrees in Grammatical gender gender , Grammatical number number and Definite article definiteness ... gender gender , Grammatical number number , definiteness and Grammatical case case . The distinguishable ... more details
In probability theory and statistics, covariance is a measure of how much two variables change together and the covariance function describes the variance of a random variable process or field. For a random field or stochastic process Z x on a domain D , a covariance function C x , y gives the covariance of the values of the random field at the two locations x and y math C x,y operatorname cov Z x ,Z y . , math The same C x , y is called autocovariance in two instances in time series to denote exactly the same concept, where x is time , and in multivariate random fields to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different variables at different locations, Cov Z x sub 1 sub , Y x sub 2 sub . ref cite book title Multivariate Geostatistics first Hans last Wackernagel year 2003 publisher Springer ref Admissibility For locations x sub 1 sub , x sub 2 sub , &hellip , x sub N sub &isin D the variance of every linear combination math X sum i 1 N w i Z x i math can be computed as math operatorname var X sum i 1 N sum j 1 N w i C x i,x j w j. math A function is a valid covariance function if and only if ref name Cressie cite book title Statistics for Spatial Data first Noel A.C. last Cressie year 1993 publisher Wiley Interscience ref this variance is non negative for all possible choices of N and weights w sub 1 sub , &hellip , w sub N sub . A function with this property is called Positive definite kernel positive definite . Simplifications with stationarity In case of a weakly Stationary process stationary random field , where math C x i,x j C x i h,x j h , math for any lag h , the covariance function can be represented by a one parameter function math C s h C 0,h C x,x h , math which is called a covariogram and also a covariance function . Implicitly the C x sub i sub , x sub j sub can be computed from C sub s sub h by math C x,y C s y x . , math The Positive definite function positive d ... more details
The Symmetric Rank 1 SR1 method is a quasi Newton method to update the second derivative Hessian based on the derivatives gradients calculated at two points. It is a generalization to the secant method for a multidimensional problem. This update maintains the symmetry of the matrix but does not guarantee that the update be positive definite matrix positive definite . The sequence of Hessian approximations generated by the SR1 method converges to the true Hessian under mild conditions, in theory in practice, the approximate Hessians generated by the SR1 method show faster progress towards the true Hessian than do popular alternatives BFGS or Davidon Fletcher Powell formula DFP , in preliminary numerical experiments. ref name CGT The SR1 method has computational advantages for sparsity sparse or partial separability partially separable problems. Alternative quasi Newton methods like BFGS impose positive definiteness, which is an inappropriate constraint on indefinite problems. ref name CGT harvtxt Conn Gould Toint 1991 ref A twice continuously differentiable function math x mapsto f x math has a gradient math nabla f math and Hessian matrix math B math The function math f math has an expansion as a Taylor series at math x 0 math , which can be truncated math f x 0 Delta x f x 0 nabla f x 0 T Delta x frac 1 2 Delta x T B Delta x math its gradient has a Taylor series approximation also math nabla f x 0 Delta x nabla f x 0 B Delta x math , which is used to update math B math . The above secant equation need not have a unique solution math B math . The SR1 formula computes via an update of Rank linear algebra rank 1 the symmetric solution that is closest to the current approximate value math B k math math B k 1 B k frac y k B k Delta x k y k B k Delta x k T y k B k Delta x k T Delta x k math , where math y k nabla f x k Delta x k nabla f x k math . The corresponding update to the approximate inverse Hessian math H k B k 1 math is math H k 1 H k frac Delta x k H k y k Delt ... more details
Wallace Chafe IPAc en icon t e f born 1927 is an American linguist . He is currently listed as a Professor Emeritus and research professor at The University of California Santa Barbara. ref http www.linguistics.ucsb.edu people index.html UCSC EDU PEOPLE Faculty Listing Accessed January 14, 2012 ref Chafe was born in Cambridge, Massachusetts . He graduated from Yale University , where he obtained his doctorate in 1958. From 1975 to 1986 he was the director of the Survey of California and Other Indian Languages at the University of California, Berkeley . ref name survey Cite web url http linguistics.berkeley.edu survey about us history.php title Survey of California and Other Indian Languages, University of California, Berkeley work linguistics.berkeley.edu accessdate May 4, 2010 ref He later moved to the University of California, Santa Barbara , and became professor emeritus at UCSB in 1991. Chafe is a cognitive linguistics cognitivist he considers semantics to be a basic component of language. He is a critic of Noam Chomsky s generative linguistics . Citation needed date January 2012 He is an influential scholar in indigenous languages of the Americas , notably Iroquoian languages Iroquoian and Caddoan languages , in discourse analysis and psycholinguistics , and also Prosody linguistics prosody of speech. Together with Johanna Nichols , he edited a seminal volume on evidentiality in language in 1986. Works 1962. Phonetics, semantics, and language. Language 38.335 344. 1967. Seneca Morphology and Dictionary . Smithsonian Contributions to Anthropology, vol. 4. Washington Smithsonian Institution. 1968. Idiomaticity as an Anomaly in the Chomskyan Paradigm. Foundations of Language 4.109 127. 1970. Meaning and the Structure of Language . Chicago The University of Chicago Press. 1970. A Semantically Based Sketch of Onondaga. International Journal of American Linguistics , Memoir 25 Supplement to vol. 36, no. 2 . 1976. Givenness, contrastiveness, definiteness, subjects ... more details
In fluid dynamics , a similarity solution is a form of solution in which at least one co ordinate lacks a distinguished origin more physically, it describes a flow which looks the same either at all times, or at all length scales. These include, for example, the Blasius boundary layer or the blast wave Sedov Taylor shell . ref Pringle and King, 2007, http books.google.co.uk books?id 0KV e8 kyZwC&lpg PP1&dq Astrophysical 20Flows&pg PA54 v onepage&q&f false Astrophysical Flows , p54 ref Concept A powerful tool in physics is the concept of dimensional analysis and scaling laws by looking at the physical effects present in a system we may estimate their size and hence which, for example, might be neglected. If we have catalogued these effects we will occasionally find that the system has not fixed a natural lengthscale timescale , but that the solution depends on space time . It is then necessary to construct a lengthscale timescale using time space and the other dimensional quantities present such as the viscosity math nu math . These constructs are not guessed but are derived immediately from the scaling of the governing equations. Example The impulsively started plate Consider a semi infinite domain bounded by a rigid wall and filled with viscous fluid. ref Batchelor 2006 edition , http books.google.co.uk books?id Rla7OihRvUgC&dq An Introduction to Fluid Dynamics&source gbs navlinks s An Introduction to Fluid Dynamics , p189 ref At time math t 0 math the wall is made to move with constant speed math U math in a fixed direction for definiteness, say the math x math direction and consider only the math x y math plane . We can see that there is no distinguished length scale given in the problem, and we have the boundary conditions of no slip math u U math on math y 0 math and that the plate have no effect on the fluid at infinity math u rightarrow 0 math as math y rightarrow infty math . Now, if we examine the Navier Stokes equations math rho left dfrac partial vec u pa ... more details
indicate definiteness , like the the definite article the . Archaic forms are thy and mine for my ... adjectives indicate definiteness, in other languages the definiteness needs to be added separately ... more details
between the definiteness and indefiniteness of the word. As a particle, al does not inflect at all ..., there are many ways in which Arabic words can be made definiteness definite . These include ..., prefixing a noun with al is the weakest form of definiteness. ref Ibid ref That is, saying the man ... alif swapped positions. It is noteworthy that the negation denoted by l and the definiteness denoted ... is the hamza part of al , nor does it contribute to the definiteness of the following word. Khal l ... and they assert that it contributes to the definiteness of the following word. Others assert that the hamza contributes to the definiteness of the following word, but it is still volatile. ref Ibn ... fat a vowel. The l m in al main Sun and moon letters In very early Semitic languages, definiteness was achieved ... Definiteness The primary and most profuse function of al is to render the following word definite ... Because nouns require the functions provided by al namely definiteness , al is prefixed to them ... always be prefixed to. Prohibited prefixation Nouns that do not inflect for definiteness The definite article al is not typically prefixed to nouns that do not inflect for definiteness. Examples include ... more details
Article grammar articles , compensated by the rise of postnominal means of expressing definiteness ... agreement varies with postnominal la as expressions of definiteness on the noun. 6 a j l ou l ab la ... adverb there , survives as the only means of expressing definiteness. The agglutination of the etymological ... more details
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