Infobox Film name Splitting Heirs image Splitting Heirs.jpg caption Theatrical release poster. director Robert Young director Robert Young producer Simon Bosanquet br Redmond Morris writer Eric Idle narrator starring Eric Idle br Rick Moranis br Barbara Hershey br Catherine Zeta Jones br John Cleese music Michael Kamen cinematography Tony Pierce Roberts editing John Jympson distributor Universal Pictures released 30 April 1993 runtime 87 minutes country FilmUK language English budget preceded by followed by Splitting Heirs is a 1993 in film 1993 cinema of the United Kingdom British film starring Eric Idle , Rick Moranis , Barbara Hershey , Catherine Zeta Jones , John Cleese and Sadie Frost . The film was directed by Robert Young director Robert Young , and features music by Michael Kamen . It was entered in the 1993 Cannes Film Festival . ref name festival cannes.com cite web url http www.festival cannes.com en archives ficheFilm id 2584 year 1993.html title Festival de Cannes Splitting Heirs accessdate 2009 08 22 work festival cannes.com ref . It was released in Britain as a PAL VHS, which is still in circulation ref http www.amazon.co.uk dp B000L3U682 ref ref http www.amazon.co.uk dp B000OOICQQ ref it has not been Film release released on DVD in Britain, but is released in Region 1 in United States America ref http www.amazon.co.uk dp B00049QJO8 ref . It is also available in an all region, NTSC version in Australia by Umbrella Entertainment ref http www.umbrellaent.com.au Product ProductView DAVID1325 ref . Plot The movie centres on the aristocracy aristocratic family of the Dukes of Bournemouth England , upon which misfortune has befallen throughout history, leading it to believe itself cursed. The most recent heir, Thomas Henry Butterfly Rainbow Peace, was left in a restaurant ... m splitting heirs ref References reflist External links imdb title id 0108207 title Splitting Heirs Amg movie 46158 Splitting Heirs Category 1993 films Category British films Category 1990s comedy ... more details
In abstract algebra , a splitting field of a polynomial with coefficients in a field mathematics field is a smallest field extension of that field over which the polynomial splits or decomposes into linear factors . Definition A splitting field of a polynomial p X over a field K is a field extension L of K over which p factors into linear factors math p X prod i 1 deg p X a i in L X math and such that the coefficients a sub i sub generate L over K . The extension L is then an extension of minimal Degree of a field extension degree over K in which p splits. It can be shown that such splitting fields ... is a splitting field for multiple polynomials p X over K is called a Field extension Normal.2C separable ... , there is a unique splitting field L of p between K and A , generated by the root of a function root ..., the existence of algebraic closures in general is usually proved by passing to the limit from the splitting ... . Given a separable extension K &prime of K , a Galois closure L of K &prime is a type of splitting .... Such a Galois closure should contain a splitting field for all the polynomials p over K that are minimal polynomials over K of elements a of K &prime . Constructing splitting fields Motivation Finding ... , the real numbers. By constructing the splitting field for such a polynomial one can find the roots ... ring F X of degree n . The general process for constructing K , the splitting field of p ... may lead to different subfield sequences the resulting splitting fields will be isomorphic. Since ... math omega 2 math or math omega 3 1 omega 2 math . It follows that a splitting field L of p will contain ... examples A splitting field of math x 2 1 math over math mathbb F 7 math is math mathbb F 49 math ... of 0, 1, 4, and 2, which does not include the class of 1 6. ref The splitting field of math ... 4 sup r sup 2 sup r . Hence x sup 2 sup ax b factors into linear factors in F r x and E F r is a splitting ... 471 36857 1. MathWorld title Splitting field urlname SplittingField DEFAULTSORT Splitting Field Category ... more details
Water splitting is the general term for a chemical reaction in which water is separated into oxygen and hydrogen. Efficient and economical water splitting would be a key technology component of a hydrogen economy . Various techniques for water splitting have been issued in water splitting patents in the United ... 2FPTO 2Fsearch adv.htm&r 0&p 1&f S&l 50&Query ttl 2F 22water splitting 22 0D 0A&d PTXT Patent Database Search Results ttl water splitting in US Patent Collection Bot generated title ref In photosynthesis , water splitting donates electrons to power the electron transport chain in photosystem II . Electrolysis ... scale. Photoelectrochemical water splitting Main photoelectrochemical cell artificial photosynthesis ... M.E. title Influence of Zn concentration in the activity of Cd1 xZnxS solid solutions for water splitting ... pmid pmc doi 10.1016 j.cattod.2008.09.024 bibcode ref ref Photocatalytic water splitting Main Photocatalytic water splitting The conversion of solar energy to hydrogen by means of water splitting process .... title Water Splitting on Semiconductor Catalysts under Visible Light Irradiation journal Chemsuschem ... J.L.G. title Photocatalytic water splitting under visible Light concept and materials requirements ... S0065 2377 09 00404 9 bibcode ref CONACYT Mexico ref Photobiological water splitting Image Algae ... temperatures. Thermal water splitting has been investigated for hydrogen production since the 1960s ... used in any thermal water splitting device. For industrial or commercial application, the material ... water splitting and with few exceptions most recent developments are in the area of the catalysis ... form of the aluminum, and solution composition. Research Main Photocatalytic water splitting ... driven Photocatalysts for Water Splitting Akihiko Kudo, Hideki Kato1 and Issei Tsuji Chemistry Letters ... and oxygen. Recently, this has been successful in splitting water into hydrogen and oxygen using ... source of heat. More than 352 thermochemistry thermochemical cycles have been described for water splitting ... more details
Loop splitting is a compiler optimization technique. It attempts to simplify a Control flow Loops loop or eliminate dependencies by breaking it into multiple loops which have the same bodies but iterate over different contiguous portions of the index range. Loop peeling Loop peeling is a special case of loop splitting which splits any problematic first or last few iterations from the loop and performs them outside of the loop body. Suppose a loop was written like this int p 10 for int i 0 i 10 i y i x i x p p i Notice that code p 10 code only for the first iteration, and for all other iterations, code p i 1 code . A compiler can take advantage of this by loop unwinding unwinding or peeling the first iteration from the loop. After peeling the first iteration, the code would look like this y 0 x 0 x 10 for int i 1 i 10 i y i x i x i 1 This equivalent form eliminates the need for the variable code p code inside the loop body. Loop peeling was introduced in GNU Compiler Collection gcc in version 3.4. Brief history of the term Apparently the term was for the first time used by Cannings, Thompson and Skolnick ref name Cannings1976 Cite journal author Cannings, C. author2 Thompson, EA author3 Skolnick, HH title The recursive derivation of likelihoods on complex pedigrees journal Advances in Applied Probability volume 8 pages 622 625 year 1976 issue 4 doi 10.2307 1425918 ref in their 1976 paper on computational models for human inheritance. There the term was used to denote a method for collapsing phenotypic information onto parents. From there the term was used again in their papers, including their seminal paper on probability functions on complex pedigrees. ref name Cannings1978 Cite journal author Cannings, C. author2 Thompson, EA author3 Skolnick, HH title Probability functions on complex pedigrees journal Advances in Applied Probability volume 10 pages 26 61 year 1978 issue ... Loop Splitting Category Compiler optimizations ... more details
Orphan date September 2011 In applied mathematics and computer science , variable splitting is a decomposition method that relaxation technique mathematics relaxes a set of constraint s. Details When the variable x appears in two sets of constraints, it is possible to substitute the new variables x 1 in the first constraints and x 2 in the second, and then join the two variables with a new linking constraint, ref name Vanderbei harvtxt Vanderbei 1991 ref which requires that x 1 x 2. This new linking constraint can be Lagrangian relaxation relaxed with a Lagrange multiplier in many applications, a Lagrange multiplier can be interpreted as the price of equality between x 1 and x 2 in the new constraint. For many problems, when the equality of the split variables is relaxed, then the system is decomposed, and each subsystem can be solved independently, at substantial reduction of computing time and memory storage. A solution to the relaxed problem with variable splitting provides an approximate solution to the original problem further, the approximate solution to the relaxed problem provides a warm start , a good initialization of an iterative method for solving the original problem having only the x variable . ref name Vanderbei ref harvtxt Alvarado 1990 ref ref harvtxt Adlers Bj rck 2000 Reprinted as Appendix A, in Mikael Adlers, 2000, Topics in Sparse Least Squares Problems , Linkoping Studies in Science and Technology , Linkoping University, Sweden. ref Notes references Bibliography cite journal last1 Adlers first1 Mikael last2 Bj rck first2 ke authorlink2 ke Bj rck title Matrix stretching for sparse least squares problems year 2000 pages 51 65 journal Numerical Linear Algebra with Applications volume 7 issue 2 publisher John Wiley & Sons, Ltd. ISSN 1099 1506 doi 10.1002 SICI 1099 1506 200003 7 2 ref harv cite journal last Alvarado first Fernando title Matrix enlarging ... year 1990 cite journal first Robert J. last Vanderbei authorlink Robert J. Vanderbei title Splitting ... more details
Pole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier . When a capacitor is introduced between the input and output sides of the amplifier with the intention of moving the Pole complex analysis pole lowest in frequency usually an input pole to lower frequencies, pole splitting causes the pole next in frequency usually an output pole to move to a higher frequency. This pole movement increases the stability of the amplifier and improves its step response at the cost of decreased speed. ref That is, the rise time is selected to be the fastest possible consistent with low overshoot signal overshoot and ringing signal ringing . ref ref name Toumazou cite book author C. Toumazu, Moschytz GS & Gilbert B Editors title Trade offs in analog circuit design the designer s companion year 2007 pages 272 275 publisher Springer location New York Berlin Dordrecht isbn 1402070373 url http books.google.com books?id VoBIOvirkiMC&pg PA272&lpg PA272&dq 22pole splitting 22&source web&ots MC083mOWhv&sig duZQKaGECaAH80qDj YNMdRd8nA ref ref name Thompson cite book author Marc T. Thompson title Intuitive analog circuit design a problem solving approach using design case studies year 2006 pages 200 publisher Elsevier Newnes location Amsterdam isbn 0750677864 url http books.google.com books?id 1Tyzjmf0DI8C&pg PA200&dq pole splitting analog amplifier&lr &as brr 0&sig gmvG9dtlK48hcqpvf3NwwqcF2Hk ref ref name Sansen cite book author Wally M. C. Sansen ... York Berlin isbn 0 387 25746 2 url http worldcat.org isbn 0 387 25746 2 ref Example of pole splitting Image Pole Splitting Example.png thumbnail 250px Figure 1 Operational amplifier with compensation ... sub and output impedance R sub o sub . Image Pole Splitting Example with Miller Transform.png thumbnail ... tau 2 math . See Pole splitting Selection of CC Selection of C sub C sub below. At low frequencies ... sub C sub moved the low pole lower and the high pole higher, so the term pole splitting seems a good ... more details
EDITING GUIDELINES for DISAMBIGUATION DAB PAGES DAB pages are not normal articles and have a special style DAB pages help users find specific articles Please Point to link only one article on each line Please Start each line with the target article Remember These are guidelines not absolute rules More information WP MOSDAB The Word may mean in Music Surfin Bird The Bird is the Word The Word band , a blues jam rock group The Word song The Word song , a song by The Beatles The Word 1953 film The Word 1953 film , a 1953 documentary film The Word 1955 film The Word 1955 film or Ordet , a 1955 Danish film in bookstores The Word Bookstore , a philosophy and poetry bookstore in Montreal Word bookstore , a Christian bookstore chain in Australia in the Christian faith The Bible Christ the Logos The Word Bible Software , Bible study software in Media The Word novel The Word novel , a novel by Irving Wallace The Word radio The Word radio , a weekly BBC World Service book programme The Word TV series The Word TV series , a British late night variety series Recurring segments on The Colbert Report The W.C3.B8rd The W rd , a recurring segment on Stephen Colbert s The Colbert Report The Word magazine The Word magazine , a UK music magazine The Word free love The Word free love , a 19th century anarchist free love magazine edited by Ezra and Angela Heywood See also Word & Void , a series of fantasy novels by Terry Brooks disambig ... more details
Other uses pp move indef In language , a word is the smallest element that may be uttered in isolation ... stand on its own. A word may consist of a single morpheme for example oh , rock, red, quick, run, expect ... to stand on its own as a word in the words just mentioned, these are s, ness, ly, ing, un , ed . A complex word will typically include a root linguistics root and one or more affix es rock s, red ness, quick ly, run ning, un expect ed , or more than one root in a compound word compound black board, rat ... . The term word may refer to a spoken word or to a written word, or sometimes to the abstract concept ... morphology The ease or difficulty of deciphering a word depends on the language. Dictionaries categorize ... of what constitutes a word in the opinion of the writers of that language. Semantic definition ..., the word bears has semantic features it denotes real world objects, bear s , Lexical category ... a certain way , etc. Word boundaries The task of defining what constitutes a word involves determining where one word ends and another word begins&mdash in other words, identifying word boundaries. There are several ways to determine where the word boundaries of spoken language should be placed ... will tend to insert pauses at the word boundaries. However, this method is not foolproof the speaker ... words will tend to be added in the word boundaries of the original sentence. However, some languages have infix es, which are put inside a word. Similarly, some have separable affix es in the German ... boundaries Some languages have particular rules of pronunciation that make it easy to spot where a word ... of a word, a word boundary is likely to fall after each stressed syllable. Another example can ... within a given word share the same quality , so a word boundary is likely to occur whenever the vowel ... of what is considered a single word. Word separator s typically space punctuation spaces are common ... , get up , and these must thus be considered as more than one word. Ice , cream , air etc. indisputably ... more details
Multiple issues orphan March 2012 The A Word is a radio show on CFCR 90.5 FM in Saskatoon , also heard on cfcr.ca , that is focused on visual arts and culture in the Saskatoon and sometimes wider Saskatchewan area, hosted by Bart Gazzola, a local artist, writer, curator and critic. He also hosts a blog where past radio shows are available for download in MP3 format, at no cost. In April 2012, the show will begin its fifth year on the air. update after 2012 05 Description The description of the show found at the blog is as follows blockquote This blog started partly in response to how despite my writing something for nearly ever issue of Planet S Magazine, and producing The A Word on CFCR 90.5 FM that there are often exhibitions and events that fall through the cracks, worthy of notice both for positive and negative reasons, and although blogs are often best described as being like an opinion everyone has one, but some should never leave their kitchens , I thought I would see what shape this would take. And its all for the art bitches of Saskatoon to bastardize the wonderful words of Frida Kahlo, when confronted with the art bitches of Paris . I also toyed with naming this blog Denkverbot , as a nod to Slavoj i ek, but also for the literal translation of the word, being a prohibition to think this may be an acknowledgement of the sad state of art criticism these days, propagated by many sites and writers , which is alternately cheerleading or publishing the press release. That is something I ve never been accused of, and probably never will. ref http www.bartgazzola.com aword aword s blog ref blockquote Guests Past guests have included Jayce Salloum, Jeff Thomas, David Clark, Adrian Stimson and other artists and cultural producers who may call the city of Saskatoon home, or others who may have exhibitions at any of a number of local galleries, such as curators Shauna McCabe ... A Word ... more details
Infobox Single See Wikipedia WikiProject Songs Name Splitting Up Type single Artist Adequate Seven Cover Released 29th August 2005 Recorded 2005 Genre Punk Hardcore Punk Ska Funk Length Label Audio Rehab Producer Reviews Last album Songs Of Innocence And Of Experience This album Splitting Up Next album Here on Earth album Here on Earth Splitting Up is the first single from Adequate Seven s final record, Here on Earth album Here on Earth . Track listing Splitting Up Forward Motion Splitting Up Afghan Headspin Remix Splitting Up End User Remix Category 2005 singles 2000s single stub ... more details
Unreferenced date December 2009 Orphan date December 2009 Energy level splitting occurs in physics when the degenerate energy level s of two or more states are split because of external fields or other effects. The term is most commonly used in quantum mechanics quantum theory in reference to the electron configuration in atoms or molecules . Examples The Zeeman effect the splitting of electronic levels in an atom because of an external magnetic field . The Stark effect splitting because of an external electric field . The Jahn Teller effect splitting of electronic levels in a molecule because breaking the symmetry lowers the energy when the degenerate orbitals are partially filled. See also Energy level Physics stub DEFAULTSORT Energy Level Splitting Category Quantum mechanics ... more details
In computational complexity theory , the Set Splitting problem is the following decision problem given a family F of subsets of a finite set S , decide whether there exists a partition of S into two subsets S sub 1 sub , S sub 2 sub such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S sub 1 sub or S sub 2 sub . It is an NP complete problem. ref cite book last Garey first M.R. authorlink Michael Garey coauthors David S. Johnson Johnson, D.S. title Computers and Intractability A Guide to the Theory of NP Completeness year 1979 publisher W.H. Freeman location New York isbn 0 7167 1045 5 ref The optimization version of this problem is called Max Set Splitting and requires finding the partition which maximizes the number of split elements of F . It is an APX complete ref Erez Petrank E. Petrank , The hardness of approximation Gap location , Computational Complexity journal Computational Complexity , 4 1994 , 133 157. ref and NP hard problem. The problem remains NP hard even if all subsets in F contain the same fixed number of elements m greater than 1 ref name dehne The decision variant of Max Set Splitting, also called Set Splitting is stated as follows given an integer k , whether there exists a partition of S which splits at least k subsets of F ? If k taken to be a fixed parameter, then Set Splitting is fixed parameter tractable , i.e., a polynomial algorithm exists for any fixed k . ref name dehne http books.google.com books?id PuHeuUucopEC&pg PA180&lpg PA180&dq 22set splitting 22 NP&source bl&ots Y9AsQexW7H&sig jdT0O c68zCrqnriux9DdYwti80&hl en&sa X&oi book result&resnum 4&ct result An FPT Algorithm for Set Splitting ref The Weighted Set Splitting is a variant in which the subsets in F have weights and the objective is to maximize the total weight of the split subsets. References reflist Category NP complete problems Category Computational problems es Problema de la divisi n de un conjunto ... more details
HTTP HTTP response splitting is a form of web application vulnerability computing vulnerability , resulting from the failure of the application or its environment to properly sanitize input values. It can be used to perform cross site scripting attacks, cross user defacement, web cache poisoning, and similar exploit computer security exploits . The attack consists of making the server print a carriage return CR, ASCII 0x0D line feed LF, ASCII 0x0A sequence followed by content supplied by the attacker in the List of HTTP headers header section of its response, typically by including them in input fields sent to the application. Per the Hypertext Transfer Protocol HTTP standard RFC 2616 , headers are separated by one CRLF and the response s headers are separated from its body by two. Therefore, the failure to remove CRs and LFs allows the attacker to set arbitrary headers, take control of the body, or break the response into two or more separate responses hence the name. Prevention The generic solution is to Percent encoding URL encode strings before inclusion into List of HTTP headers HTTP header s such as Location or Set Cookie . Typical examples of sanitization include Type conversion casting to integer s or aggressive regular expression replacement. Although response splitting is not specific to PHP , the PHP interpreter contains protection against the attack since version 4.4.2 and 5.1.2. ref http php.net releases 5 1 2.php PHP PHP 5.1.2. Release Announcement ref References references External links http www.webappsec.org projects threat classes http response splitting.shtml HTTP Response Splitting, The Web Application Security Consortium http wapiti.sf.net Wapiti Open Source XSS, Header, SQL and LDAP injection scanner http lwn.net Articles 303445 LWN article http cwe.mitre.org ... Response Splitting https www.owasp.org index.php CRLF Injection CRLF Injection OWASP Category Web security exploits cs HTTP response splitting de HTTP Response Splitting fr S paration de r ponse HTTP ... more details
Zero field splitting describes various interactions of the energy levels of an electron spin S 1 2 even in the absence of an applied magnetic field. It is important in the electron spin resonance of biological molecule s. The value of the ZFS parameter is usually defined as D. Values of D have been obtained for a wide number of organic biradicals by Electron paramagnetic resonance EPR ESR measurements. This value may be measured by other magnetometry techniques such as SQUID , however EPR measurements provide more accurate data in most cases. For an S 1 spin system, in the presence of a magnetic field, the singlet and triplet are separated and the Zeeman splitting dictates their separation. To first order the 3 levels of the triplet are isoenergetic. However, when we incorporate the effect one electron has on the other, the energy of the sublevels of the triplet are separated out. The separation of these sub levels manifest in peaks of the frozen solution EPR spectrum. External links http www.ncsu.edu chemistry das zero field splitting.pdf Description of the origins of Zero Field Splitting Category Spectroscopy Category Article Feedback 5 biochem stub es Desdoblamiento a campo nulo ... more details
Photocatalytic water splitting is the term for the production of hydrogen H sub 2 sub and oxygen O sub ... such as photocatalytic water splitting are being investigated to produce hydrogen fuel, which burns cleanly and can be used in a hydrogen fuel cell . Water splitting holds particular interest since it utilizes water, an inexpensive renewable resource. Photocatalytic water splitting has the simplicity ... text 2 text H 2 text O 2 math The process of water splitting is a highly endothermic process H 0 . Water splitting occurs naturally in photosynthesis when photon energy is absorbed and converted ... strict requirements for a photocatalyst to be useful for water splitting. The minimum potential ... band gap for successful water splitting at pH 0 is 1.23 eV, corresponding to light of 1008 nm, the electrochemical ... splitting can transfer charges, but not be able to corrosion for long term stability. Defects within ... used in photocatalytic water splitting fulfill the band requirements outlined previously and typically ... materials for water splitting Chem. Soc. Rev., 38, 253 278 2009 . http dx.doi.org 10.1039 ... to one of hydrogen evolution as opposed to water splitting. Recombination of the electron hole .... ref name AKUDO The conversion of solar energy to hydrogen by means of water splitting .... G. title Water Splitting on Semiconductor Catalysts under Visible Light Irradiation journal Chemsuschem ... J.L.G. title Photocatalytic water splitting under visible Light concept and materials requirements ... must conform to several key principles in order to be considered effective at water splitting. A key ... of which do not indicate a reliable photocatalyst for water splitting. The prime measure of photocatalyst ... sub 3 sub La yields the highest water splitting rate of photocatalysts demonstrated as of October 2008 ... effective with water splitting rates of 9.7 mmol h and a quantum yield of 56 . The nanostep structure of the material promotes water splitting as edges functioned as H sub 2 sub production ... more details
Earthquakes Shear wave splitting , also called seismic birefringence , is the phenomenon that occurs ... polarized shear waves Fig. 2 . Shear wave splitting are typically used as a tool for testing the anisotropy ... area as a black box and the shear wave splitting measurements as a way of looking at what ... Figure 2. Animation of shear wave splitting upon entering an anisotropic medium. Courtesy of Ed Garnero ... 10.1016 j.tecto.2008.01.021 author Vecsey, L., J coauthors Babuska, V. year 2008 title Shear wave splitting ... mantle . This study focused on shear wave splitting recorded near the Chubu Volcano Volcanic Area ..., slow approximately 0.7 seconds apart. It was concluded that the splitting was not caused by the earthquake ... prediction using shear wave splitting measurements. This theory is based on the fact that microcracks ... shear wave splitting signatures are dependent on both the orientation of the microcracks perpendicular ... the phenomenon of azimuthally aligned shear wave splitting in the crust geology crust . He reviewed the current theory, updated equations to better understand shear wave splitting, and presented ... a media with small or even closed cracks. Shear wave splitting will continue to occur until the shear ... of seismic shear wave splitting in the Earth s crust and common fallacies in interpretation ... have split. Measurement of shear wave splitting parameters Modeling ref name Silver cite journal author P. Silver coauthor W. Chan title Shear Wave Splitting and Subcontinental Mantle Deformation ... propagation propagation . br The process of shear wave splitting can be represented as the application of the splitting operator to the shear wave function. NumBlk math Gamma exp left i omega ... splitting and the seismic signature generated by the arrivals of two polarized shear waves at the surface ... Image Erin Sws 2010.gif center thumb 800px Figure 6. Schematic animation of shear wave splitting ... shot of Matlab demo of shear wave splitting Applications Justification Usefulness Shear wave splitting ... more details
In mathematics , and in particular combinatorics , the necklace splitting problem arises in a variety of contexts including exact division its picturesque name is due to mathematicians Noga Alon ref name Alon 1987 cite journal doi 10.1016 0001 8708 87 90055 7 last Alon first Noga title Splitting Necklaces journal Advances in Mathematics year 1987 volume 63 issue 3 pages 247&ndash 253 postscript . ref and Douglas B. West . ref name Alon 1986 cite journal last Alon first Noga coauthors West, D. B. title The Borsuk Ulam theorem and bisection of necklaces journal Proceedings of the American Mathematical Society month December year 1986 volume 98 issue 4 pages 623&ndash 628 postscript . ref Suppose a necklace , open at the clasp, has k n beads. There are k a sub i sub beads of colour i , where 1 i t . Then the necklace splitting problem is to find a partition of the necklace into k parts not necessarily contiguous , each of which has exactly a sub i sub beads of colour i such a split is called a k split. The size of the split is the number of cuts that are needed to separate the parts the opening at the clasp is not included . Inevitably, one interesting question is to find a split of minimal size. div class thumb tright div style width 231px Image necklace cropped.png alt a stylized picture of a necklace, with 8 red and 6 green pearls. The pearls ... break . The breaks correspond to those in the text 200px Necklace splitting problem div class thumbcaption Example of necklace splitting with k 2 i.e. two thieves , and t 2 i.e. two types of beads .... If the beads of each colour are contiguous on the open necklace, then any k splitting must contain ... ref name Alon 1987 use the Borsuk Ulam theorem to prove that a k splitting can always be achieved ... shows that there is a t split with equal numbers of each real colour. Splitting multidimensional necklaces ... title Splitting multidimensional necklaces journal Advances in Mathematics year 2008 volume 218 issue ... more details
Infobox single See Wikipedia WikiProject Albums Name Splitting Up Christmas from Album Make the Clocks Move Cover Splittingupchristmas digital.jpg Type Single Artist Kevin Devine Released November 2009 flagicon UK Genre Indie rock , Alternative rock Label Big Scary Monsters Last single Another Bag of Bones br 2008 This single Splitting Up Christmas br 2009 Splitting Up Christmas , originally from 2003 s Make The Clocks Move , is a UK Christmas single by Kevin Devine released in support of the 2009 Big Scary Monsters Christmas Tour ref http www.bsmrocks.com news.php?newsid 352 Christmas Tour 09 ref ref http www.bsmrocks.com news.php?newsid 354 K Dev xmas single ref . At each date on the tour, an exclusive CD single was sold, limited to 25 copies, hand numbered and signed by Kevin. Each date s CD had its own exclusive b side. On December 12, 2009, the title track was offered as a free mp3 on the record label s website. On December 17, 2009, the single was made available as a limited digital download featuring all nine b sides, only being available up until December 31, 2009. ref http bsmrocks.com news.php?newsid 364 Kdev free MP3 ref ref http bsmrocks.com news.php?newsid 365 Splitting Up MP3s ref Both the CDs and MP3 downloads are now unavailable. Tracklist writing credits yes title1 Splitting Up Christmas length1 3 26 writer1 Kevin Devine title2 Joey Concrete Blonde song Joey length2 5 04 writer2 Johnette Napolitano title3 Harvest Moon album Harvest Moon length3 6 13 writer3 Neil Young title4 The Longer I Lay Here length4 3 08 writer4 David Bazan title5 You ll Only End Up Joining Them Acoustic length5 3 55 writer5 Kevin Devine title6 Holland, 1945 length6 3 27 writer6 Jeff Mangum title7 Lord, I Know We Don t Talk live at Old Blue Last length7 4 23 writer7 Kevin Devine title8 Write Your Story Now live at Old Blue Last length8 1 34 writer8 Kevin Devine title9 Whatever Some Folk Song in C length9 2 26 writer9 Elliott Smith title10 Wolf s Mouth Alternative version length10 ... more details
In particle physics , the doublet triplet splitting problem is a problem of some Grand unification theory Grand Unified Theories , such as Georgi Glashow model SU 5 , SO 10 physics SO 10 , math E 6 math . Grand unified theories predict Higgs boson s doublets of math SU 2 math arise from Group representation representations of the unified group that contain other states, in particular, states that are triplets of color. The primary problem with these color triplet Higgs, is that they can mediate proton decay in Supersymmetry supersymmetric theories that are only suppressed by two powers of GUT scale i.e. they are dimension 5 supersymmetric operators . In addition to mediating proton decay, they alter gauge coupling unification . The doublet triplet problem is the question what keeps the doublets light while the triplets are heavy? Doublet triplet splitting and the math mu math problem In minimal SU 5 , the way one accomplishes doublet triplet splitting is through a combination of interactions math int d 2 theta lambda H bar 5 Sigma H 5 mu H bar 5 H 5 math where math Sigma math is an adjoint of SU 5 and is traceless . When math Sigma math acquires a vacuum expectation value math langle Sigma rangle rm diag 2, 2, 2, 3, 3 f math that breaks SU 5 to the Standard Model gauge symmetry the Higgs doublets and triplets acquire a mass math int d 2 theta 2 lambda f mu H bar 3 H 3 3 lambda f mu H bar 2 H 2 math Since math f math is at the GUT scale math 10 16 math GeV and the Higgs doublets need to have a weak scale mass 100 GeV , this requires math mu sim 3 lambda f pm 100 mbox GeV math . So to solve thus doublet triplet splitting problem requries a tuning of the two terms to within 1 ... MSSM i.e. why are the Higgs doublets so light and doublet triplet splitting are so closely intertwined ... triplet splitting problem known as the Dimopoulos Wilczek mechanism. In SO 10 , the adjoint field ... doublet remains massless. This is very similar to the way that doublet triplet splitting ... more details
See also splitting lemma in homological algebra . In mathematics , especially in singularity theory the splitting lemma is a useful result due to Ren Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point mathematics critical point . Formal statement Let math scriptstyle f mathbb R n,0 to mathbb R ,0 math be a smooth function germ, with a critical point at 0 so math scriptstyle partial f partial x i 0 0, i 1, dots, n math . Let V be a subspace of math scriptstyle mathbb R n math such that the restriction f V is critical point mathematics non degenerate , and write B for the Hessian matrix of this restriction. Let W be any complementary subspace to V . Then there is a change of coordinates math Phi x,y math of the form math Phi x,y phi x,y ,y math with math scriptstyle x in V, y in W math , and a smooth function h on W such that math f circ Phi x,y textstyle frac12 x TBx h y . math This result is often referred to as the parametrized Morse lemma , which can be seen by viewing y as the parameter. It is the gradient version of the implicit function theorem . Extensions There are extensions to infinite dimensions, to complex analytic functions, to functions invariant under the action of a compact group, . . . References citation first1 Tim last1 Poston first2 Ian last2 Stewart authorlink2 Ian Stewart mathematician title Catastrophe Theory and Its Applications publisher Pitman year 1979 ISBN 978 0273084297 . citation first Th last Brocker title Differentiable Germs and Catastrophes publisher Cambridge University Press year 1975 ISBN 978 0521206815 . Category Singularity theory Category Functions and mappings ... more details
In the theory of causal structure on Lorentzian manifold s, Geroch s theorem or Geroch s splitting theorem first proved by Robert Geroch gives a topological characterization of globally hyperbolic spacetimes. The theorem Let math M, g ab math be a globally hyperbolic spacetime. Then math M, g ab math is strongly causal and there exists a global time function on the manifold, i.e. a continuous, surjective map math f M rightarrow mathbb R math such that For all math t in mathbb R math , math f 1 t math is a Cauchy surface , and math f math is strictly increasing on any causal curve . Moreover, all Cauchy surfaces are homeomorphic, and math M math is homeomorphic to math S times mathbb R math where math S math is any Cauchy surface of math M math . relativity stub differential geometry stub Category General relativity Category Lorentzian manifolds Category Theorems in mathematical physics ... more details
In mathematical logic , proof compression by splitting is an algorithm that operates as a post process on resolution logic resolution proofs. It was proposed by Scott Cotton in his paper Two Techniques for Minimizing Resolution Proof ref name Cotton Cotton, Scott. Two Techniques for Minimizing Resolution Proofs . 13th International Conference on Theory and Applications of Satisfiability Testing, 2010. ref . The Splitting algorithm is based on the following observation Given a proof of unsatisfiability math pi math and a variable math x math , it is easy to re arrange split the proof in a proof of math x math and a proof of math neg x math and the recombination of these two proofs by an additional resolution step may result in a proof smaller than the original. Note that applying Splitting in a proof math pi math using a variable math x math does not invalidates a latter application of the algorithm using a differente variable math y math . Actually, the method proposed by Cotton ref name Cotton generates a sequence of proofs math pi 1 pi 2 ldots math , where each proof math pi i 1 math is the result of applying Splitting to math pi i math . During the construction of the sequence, if a proof math pi j math happens to be too large, math pi j 1 math is setted to be the smallest proof in math pi 1, pi 2, ldots, pi j math . For achieving a better compression time ratio, a heuristic for variable selection is desirable. For this purpose, Cotton ref name Cotton defines the additivity of a resolution step with antecedents math p math and math n math and resolvent math r math math operatorname add r max r max p , n , 0 , math Then, for each variable math v math , a score is calculated summing the additivity of all the resolution steps in math pi math with pivot math v math together with the number of these resolution steps. Denoting each score calculated this way by math add v, pi math , each variable is selected with a probability proportional to its score math p v frac operatorname ... more details
The R word is a euphemism used when referring to the word mental retardation retard to avoid causing potential offense. See Also Anarchism The A word B word disambiguation The B word The c word The C word Penis The D word Extremism The E word The F word disambiguation The F word Gook The G word H word The H word Lesbian The L word Marxism The M word The n word The N word S word The S word The T word The T word Vagina The V word W word The W word X word The X word External links http www.r word.org R Word.org Spread the word to end the word http therword.org the r word campaign, when you say retard, somebody hurts Category Euphemisms ... more details
In mathematics , the splitting circle method is a numerical analysis numerical algorithm for the numerical factorization of a polynomial and, ultimately, for finding its complex number complex Root of a function roots . It was introduced by Arnold Sch nhage in his 1982 paper The fundamental theorem of algebra in terms of computational complexity Technical report, Mathematisches Institut der Universit t T bingen . A revised algorithm was presented by Victor Pan in 1998. An implementation was provided by Xavier Gourdon in 1996 for the Magma computer algebra system Magma and PARI GP computer algebra systems. General description The fundamental idea of the splitting circle method is to use methods of complex analysis , more precisely the residue theorem , to construct factors of polynomials. With those methods it is possible to construct a factor of a given polynomial math p x x n p n 1 x n 1 cdots p 0 math for any region of the complex plane with a piecewise smooth boundary. Most of those factors will be trivial, that is constant polynomials. Only regions that contain roots of p x result in nontrivial factors that have exactly those roots of p x as their own roots, preserving multiplicity. In the numerical realization of this method one uses disks D c , r center c , radius r in the complex ... that all roots are well separated from the boundary circle of the disk. So to obtain a good splitting ... and 2 around the origin. But, not every polynomial admits such a splitting annulus. To remedy this situation ... 2 j math th dyadic powers of the roots of the initial polynomial p . By splitting math p j x ... finally finds a splitting annulus of relative width 4 around the origin. The approximate factorization ... greater than 11 4, as required for the initial splitting described above see Sch nhage 1982 . After ... simplified initial splitting see Malajovich Zubelli 1997 To locate the best root free annulus one uses ... author Gregorio Malajovich and Jorge P. Zubelli title A fast and stable algorithm for splitting polynomials ... more details
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