In molecular biology , a displacement loop or Dloop is a DNA structure where the two strands of a double ... introducing the term illustrated the Dloop with a shape resembling a capital D , where the displaced strand formed the loop of the D . ref name Kasamatsu Kasamatsu, H et al. 1971 , A novel closed ... 1971 Sep 68 9 2252 7. PMID 5289384 ref An unrelated use of the term Dloop, but not displacement loop, is for the loop of RNA that forms the end of the D arm of a transfer RNA molecule. D loops occur ... The Dloop occurs in the main non coding area of the mitochondrial DNA molecule, a segment called the mtDNA control region control region or Dloop region. Replication of the mitochondrial DNA can occur in two different ways, both starting in the Dloop region. ref name fish Fish, J et al. 2004 , Discovery of a major Dloop replication origin reveals two modes of human mtDNA synthesis , Science 2004 ... strand begins. The more recently reported mode starts at a different origin within the Dloop region ... 100 515 524. PMID 10721989 ref Certain bases within the Dloop region are conserved, but large ... of the mtDNA DLoop Region in Rodents , J Mol Evol. 2002 Feb 54 2 145 55. PMID 11821908 ref The region ... strands of mitochondrial DNA immediately adjacent to the Dloop structure that is associated with initiation ... ref Dloop sequences are also of interest in the study of cancers. ref cite journal pmid 19333057 ... Diseases of the colon and rectum ref The function of the Dloop is not yet clear, but recent research ... ref ref Leslie, Mitch 2007 , Thrown for a Dloop , J Cell Biol. 2007 January 15 176 2 129. doi ... loop a special protein stabilizes the joint. The t loop which is completed by the Dloop splice protects the end of the chromosome from damage. ref Greider, CW 1999 , Telomeres do Dloop T loop , Cell ... chromosome and that strand is used to form a Dloop at that point, displacing the intact chromosome ... of the Dloop. In the bacterium Escherichia coli , a similar function is performed by the protein ... more details
Dloop replication is a process by which chloroplast s and mitochondria replicate their genetic material. An important component of understanding Dloop replication is that many chloroplast s and mitochondria have a single circular chromosome like bacterium bacteria instead of the linear chromosome s found in eukaryote s. However, many cloroplasts s and mitochondria have a linear chromosome, and Dloop replication is not important in these organelles. In many organisms, one strand of DNA in the plastid comprises heavier nucleotide s relatively more purine s adenine and guanine . This strand is called the H heavy strand. The L light strand comprises lighter nucleotides pyrimidine s thymine and cytosine . Replication begins with replication of the heavy strand starting at the Dloop also known as the control region . An origin of replication opens, and the heavy strand is replicated in one direction. After heavy strand replication has continued for some time, a new light strand is also synthesized, through the opening of another origin of replication. When diagramed, the resulting structure looks like the letter D. The Dloop region is important for phylogeography phylogeographic studies. Because the region does not code for any genes, it is free to vary with only a few natural selection selective limitations on size and heavy light strand factors. The mutation rate is among the fastest of anywhere in either the nuclear or mitochondrial genomes in animals. Mutation s in the Dloop can effectively track recent and rapid evolution ary changes such as within species and among very closely related species. See also Dloop Mitochondrial DNA useful in organisation of nucleoid of mitochondria Organelle References Russell, P. J. 2002. iGenetics . Benjamin Cummings, San Francisco. Category DNA Burger, et al. 2003. Unique mitochondrial genome architecture in unicellular relatives of animals . PNAS 100 3 892 897. genetics stub ... more details
In computer science a for loop is a programming language statement programming statement which allows code to be repeatedly execution computers executed . A for loop is classified as an iteration statement. Unlike many other kinds of Control flow Loops loops , such as the while loop , the for loop is often distinguished by an explicit loop counter or loop variable. This allows the body of the for loop ... are also typically used when the number of iterations is known before entering the loop. For loops are shorthand way to make loops when the number of iterations is known, as a for loop can be written as a while loop. The name for loop comes from the English word wiktionary for for , which is used as the Keyword computing keyword in most programming languages to introduce a for loop. The loop body is executed for the given values of the loop variable, though this is more explicit in the ALGOL ... and PL I though, the keyword DO is used and it is called a do loop , but it is otherwise identical to the for loop described here and is not to be confused with the Do while loop . Kinds of for loops A for loop statement is available in most imperative programming languages. Even ignoring ... based for loops Main Foreach This type of for loop is a generalization of the numeric range type of for loop ... characterized by the use of an implicit or explicit iterator , in which the loop variable takes ... languages have this in addition to another for loop syntax notably, PHP has this type of loop under the name code foreach code , as well as a three expression for loop see below under the name code for code . Vectorised for loops Some languages offer a for loop that acts as if processing all iterations ... for code loop in the following pseudocode fragment, when calculating the new value for code A i ... its size or dimensionality. The example loop could be rendered as A 2 N 1 A 1 N 2 A 2 N 1 A 3 N 3 But whether that would be rendered in the style of the for loop or the forall loop or something else ... more details
The Loop may refer to tocright Neighborhoods Chicago Loop , a district of downtown Chicago Delmar Loop , a district in St. Louis and University City, Missouri Transportation The Loop CTA , an elevated railroad circuit in downtown Chicago Interstate 610 Texas , a beltway in Houston, Texas Massachusetts Route 213 , a highway between I 93 and I 495 in Massachusetts Loop Parkway , a spur of the Meadowbrook State Parkway on Long Island in New York Other uses The Loop Methuen, Massachusetts , a shopping center in Massachusetts The Loop Australian TV series The Loop , an Australian music television show The Loop TV series The Loop TV series , a comedy television show on the FOX network WLUP FM The Loop, a classic rock radio station in Chicago The Loop , a novel by Nicholas Evans The Loop, a music remix group formed in 1993 by members of Celebrate the Nun The Loop , a song by Morrissey from World of Morrissey The Loop , a segment on Attack of the Show See also In the Loop disambiguation Out of the Loop disambiguation disambiguation es The Loop Metro de Chicago nl The Loop ... more details
Wiktionary loopLoop or LOOP may refer to TOC right Technology Loop telecommunication , sending a signal on a channel and receiving it back at the sending terminal Loop computing , a method of control flow in computer science Loop device , a Unix device node that allows a file to be mounted on a directory Audio induction loop , an aid for the hard of hearing Mathematics Loop algebra , a quasigroup with an identity element Loop graph theory , an edge that begins and ends on the same vertex Loop topology , a path that starts and ends at the same point Sports Loop jump , a figure skating jump Flight cricket or loop, an aspect of bowling in cricket Aerobatic loop , a type of aircraft aerobatic maneuver Loop, a type of Table tennis Loop offensive shot in table tennis Loop, a type of Playboating Loops playboating maneuver Transportation Loop Texarkana , a proposed roadway loop around Texarkana, Arkansas Loop route , a main route or highway that forms a closed loop Ring road or loop, a main route or highway that encircles a town or city Rail Balloon loop , section of track that allows reversal of direction without stopping Loop line railway , branch line that deviates from a direct route and rejoins it at another location Passing loop , short section of track that allows trains to pass on a single ... Loop, Germany , a municipality in Schleswig Holstein, Germany London Outer Orbital Path , a signed walk around the edge of Outer London, England Chicago Loop , the downtown neighborhood of Chicago, Illinois bounded by the elevated railway The Loop CTA Loop Retail Historic District , a shopping district in the Chicago Loop Louisiana Offshore Oil Port , a deep water port in the Gulf of Mexico off the coast of Louisiana Delmar Loop , an entertainment district in St. Louis, Missouri Music Loop music , a finite element of sound which is repeated by technical means Loop band , a London rock band Loop album Loop album , a 2002 album by Keller Williams Loop song Loop song , a song by Maaya ... more details
wiktionary In the Loop is an idiom meaning informed or up to date . It may also refer to In The Loop , a radio and internet program produced by Minnesota Public Radio In the Loop film In the Loop film , a 2009 feature film directed by Armando Iannucci In The Loop , an episode of 2004 TV series Powers TV series Powers In the Loop with iVillage , a 2006 08 American television series See Also The Loop disambig ... more details
LOOP may refer to London Outer Orbital Path , a signed walk around the edge of Outer London, England Louisiana Offshore Oil Port , a deep water port in the Gulf of Mexico off the coast of Louisiana See also Loop disambiguation disambig ... more details
Loop the loop may refer to Aerobatic maneuver , Aircraft special maneuvers Slitherlink , game to connect links dab Long comment to avoid being listed on short pages ... more details
Infobox Single Name Loop the Loop Cover Gncv 0025.gif Artist Kotoko singer Kotoko from Album B side Raimei ga Naku Koro Released October 20, 2010 Format Maxi single Maxi Recorded Genre J pop Length Label Geneon Writer Producer Certification Last single Hekira no Sora e Izanaedo br 2010 This single Loop the Loop br 2010 Next single Light My Fire br 2011 Loop the Loop is the 16th single of the J pop singer KOTOKO , release on October 20, 2010. The title track is used as the opening theme for the anime series Motto To Love Ru , the sequel to the anime adaptation of To Love Ru . This single was released in two editions The CD DVD edition GNCV 0025 ref name cdjapan cite web title TV Anime Motto To Love Ru Intro Theme Loop the Loop KOTOKO CD url http www.cdjapan.co.jp detailview.html?KEY GNCV 25 accessdate 2010 10 25 language Japanese ref and CD only edition GNCV 0026 . The DVD contains the PV for Loop the Loop . Track listing Loop the Loop 4 13 Lyrics KOTOKO Composition Tomoyuki Nakazawa Arrangement Tomoyuki Nakazawa, Takeshi Ozaki nihongo Raimei ga Naku Koro 5 55 Lyrics KOTOKO Composition Arrangement C.G mix Loop the Loop Instrumental nihongo Raimei ga Naku Koro Instrumental Charts and sales Daily chart 14 Weekly chart 18 First week sales 4,304 units References reflist Kotoko Category 2010 singles Category Kotoko songs ko Loop the Loop ja Loop the Loop ... more details
Infobox single See Wikipedia WikiProject Songs Name Loop & Loop Cover Loop & Loop.jpg Caption Artist ASIAN KUNG FU GENERATION from Album Sol fa album Sol fa Released May 19, 2004 Format CD single Recorded Genre Alternative rock Length 3 45 Label Ki oon br small KSCL 919 small Writer Masafumi Got Producer Asian Kung Fu Generation Certification Chart position Last single Siren Asian Kung Fu Generation song Siren br 2004 This single Loop & Loop br 2004 Next single Rewrite song Rewrite br 2004 Nihongo Loop & Loop & R pu&R pu is a song by Japanese rock band Asian Kung Fu Generation . It was released as the second single of their second full length studio album, Sol fa album Sol fa , on May 19, 2004. ref http www.sonymusic.co.jp eng Arch ASIANKUNG FU KSCL 919 ASIAN KUNG FU GENERATION Loop & Loop . Sony Music Japan Sony Music Online Japan . Retrieved on 2008 10 25. Language icon en English ref The song was used as the theme song for the drama Dame Nari . The following year, the song was used in Osu Tatakae Ouendan , a Japanese Music video game Rhythm games rhythm game released on Nintendo DS . ref cite web url http www.eurogamer.net articles osu tatakae ouendan 2 review?page 2 title Osu Tatakae Ouendan 2 Review accessdate 2007 10 17 author Fahey, Rob date 2007 06 05 work Eurogamer publisher Eurogamer Network Ltd ref Music video The music video for Loop & Loop was co directed by Kazuyoshi Oku and Masafumi Got . ref http www.spaceshowertv.com search artist.cgi?ac 010577&ch 0 SPACE SHOWER Music Video Search . SPACE SHOWER TV. Retrieved on 2008 11 07. Language icon ja Japanese ref The PV takes place within a classroom populated by four young boys. Over the course of the video, the students ride bikes, play jumprope, and pretend to be a band using brooms for guitars. All the while, they listen to headphones and lip sync the lyrics to the song. Track listing Nihongo Loop & Loop ... drama theme songs hr Loop & Loop ja & pl Loop & Loop zh ... more details
In computer science , a loop invariant is an invariant computer science invariant used to prove properties of Loop computing loop s. Informally, a loop invariant is a statement of the conditions that should be true on entry into a loop and that are guaranteed to remain true on every iteration of the loop. This means that on exit from the loop both the loop invariant and the loop termination condition ... ref the partial correctness of a while loop is governed by the following rule of inference ... loop does not have the side effect of falsifying math I math if the loop s body does not change ... be true after the loop has run as long as it was true before. math while C ... math runs as long as the condition math C math is true after the loop has run, if it terminates, math C math is false ... math lnot C land I math holds. The boolean formula I in this rule is known as the loop invariant ... C of the code while code loop is math x 10 math . A useful loop invariant I is math x leq10 math ... , which is what we wanted to show. The loop invariant plays an important role in the intuitive argument for soundness of the Floyd Hoare rule for code while code loops. The loop invariant has to be true before each iteration of the loop body, and also after each iteration of the loop body. Since a code while code loop is precisely the repeated iteration of the loop body, it follows that if the invariant is true before entering the loop, it must also be true after exiting the loop. Because of the fundamental ... induction induction . In fact, the loop invariant is often the inductive property one has to prove of a recursive program that is equivalent to a given loop. Programming language support Eiffel The Eiffel programming language Eiffel programming language provides native support for loop invariants. ref Bertrand Meyer Meyer, Bertrand , Eiffel The Language, Prentice Hall , 1991, pp. 129 131. ref A loop invariant is expressed with the same syntax used for a class invariant . In the sample below, the loop ... more details
About the programming term the street on which Apple Inc. s campus is located Infinite Loop street An infinite loop also known as an endless loop or unproductive loop is a sequence of instructions in a computer program which loops endlessly, either due to the control flow Loops loop having no terminating condition, having one that can never be met, or one that causes the loop to start over. In older .... Busy wait loop s are also sometimes misleadingly called infinite loops . One possible cause of a computer hang computing freezing is an infinite loop others include deadlock and segmentation fault ... a specific condition is met. An infinite loop occurs when the condition will never be met, due to some inherent characteristic of the loop. Intentional looping There are a few situations when this is desired ... in their main loop, as there is no operating system for the program to exit to the loop runs ... level there is an infinite processing idle loop that must continue until the device is turned ..., and enter an infinite loop waiting for the user to either respond to a prompt to continue ... known as an unproductive loop. Such errors are most common among novice programmers, but can ... main while 1 printf Infinite Loop n source This is a loop that will print Infinite Loop without halting ... for syntax highlighting. freebasic does the same thing in this case source lang freebasic DO LOOP UNTIL 0 source A similar example in X86 assembly language source lang asm loop Code to loop here jmp loop source A third example is in MS DOS source lang asm A START goto A source Here the loop is quite ... , executing the loop code once for each item. Improperly formed links can create a reference loop ... of the list into a circle, causing the program to loop forever. Mathematical errors Here is one example of an infinite loop in Visual Basic source lang vb dim x as integer do until x 5 x 1 x x 1 loop source This creates a situation where x will never be greater than 5, since at the start of the loop ... 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 ... on VLIW and superscalar compilation, including ref Cite journal author Callahan, D author2 Kennedy, K ... publisher Morgan Kaufmann year 2001 isbn 1 55860 286 0 Reflist See also Loop unwinding DEFAULTSORT Loop Splitting Category Compiler optimizations ... more details
In mathematics and abstract algebra , a Bol loop is an algebraic structure generalizing the notion of Group mathematics group . Bol loops are named for the Dutch mathematician Gerrit Bol who introduced them in harv Bol 1937 . A loop algebra loop , L , is said to be a left Bol loop if it satisfies the Identity mathematics identity math a b ac a ba c math , for every a , b , c in L , while L is said to be a right Bol loop if it satisfies math ca b a c ab a math , for every a , b , c in L . These identities can be seen as weakened forms of associativity . A loop is both left Bol and right Bol if and only if it is a Moufang loop . Different authors use the term Bol loop to refer to either a left Bol or a right Bol loop. Bruck loops A Bol loop satisfying the automorphic inverse property, ab sup &minus 1 sup a sup &minus 1 sup b sup &minus 1 sup for all a,b in L , is known as a left or right Bruck loop or K loop named for the American mathematician Richard Bruck . The example in the following section is a Bruck loop. Bruck loops have applications in special relativity see Ungar 2002 . Left Bruck loops are equivalent to Ungar s 2002 gyrocommutative gyrogroup s , even though the two structures are defined differently. Example Let L denote the set of n x n Positive definite matrix positive definite , Hermitian matrix Hermitian Matrix mathematics matrices over the complex numbers. It is generally not true that the Matrix multiplication matrix product AB of matrices A , B in L is Hermitian, let alone positive definite. However, there exists a unique P in L and a unique unitary matrix U such that AB PU this is the polar decomposition of AB . Define a binary operation on L by A B P . Then L , is a left Bruck loop. An explicit formula for is given by A B A B sup 2 sup A sup 1 2 sup , where the superscript 1 2 indicates the unique positive definite Hermitian Square root of a matrix square ... VI is about Bol loops. Robinson, D. A. 1966 Bol loops, Trans. Amer. Math. Soc. 123 341 354. Ungar ... more details
Knot details name Span loop names image Span loop ABOK 1049.jpg caption type loop type2 strength origin related Alpine butterfly knot , Farmer s loop , Artillery loop releasing Non jamming uses caveat abok number 1049 A span loop is a non jamming loop knot loop that can be tied away from the ends of the rope . External links http notableknotindex.webs.com spanloop.html Span Loop Knots knot stub Category Loop knots ... more details
In loop knitting , long, dangling loops are introduced into the middle of a knitting knitted fabric or along an edge fringe border . The loops may appear singly or in large clusters. An overall array of such loops may be used to give a shaggy look to the fabric and or make it warmer, e.g., tufting the inside of mittens. After they re made, the loops may be cut or left intact two adjacent loops tied together in a bow knot is an attractive pattern as well. Techniques A fringe border can be made by dropping stitches along the border from the top to bottom of the knitted fabric. This is the same as producing a vertical stripe in drop stitch knitting . A common method for producing one or more loops is as follows. The yarn is formed into the desired number of loops with the desired length. These loop s are held behind the work, drawn through the desired stitch using the right hand needle and placed on the left hand needle next to the desired stitch. The loops and the desired stitch are knit together to secure the loops. Another method for producing a dangling loop is to knit twice into the same stitch, leaving a long loop in between the two stitches are knit together to secure the loop. this is very common in the name of the weft and warp References Nofootnotes date February 2008 Robinson D. 1986 The Encyclopedia of Knitting Techniques , Viking Penguin. ISBN 0 7181 3124 X June Hemmons Hiatt 1988 The Principles of Knitting , Simon and Schuster, pp. 39 41. ISBN 0 671 55233 3 knitting Category Knitting stitches textile arts stub ... more details
Knot details name Dropper loop knot image Dropper loop knot.jpg names type loop strength origin related releasing uses Fishing caveat abok number The Dropper loop is a type of Loop knot loop knot which is often used on multi hook fishing lines. It can be created in the middle of a long line and forms a loop which is off to the side of the line. Techniques There are two main methods of tying the dropper loop. Gather a loop and then twist it around the overlap a few times Form the loop and then use a matchstick to twist up the overlap. Finally drop the loop through the central twist. Image Dropperloop.jpg thumb Dropper Loop being formed See also List of knots External links http www.animatedknots.com dropperloop Animated Knots by Grog Dropper Loop Knots knot stub ... more details
In mathematics , a Moufang loop is a special kind of algebraic structure . It is similar to a group mathematics ... . Definition A Moufang loop is a loop mathematics loop Q that satisfies the following equivalent ... identities . Examples Any group mathematics group is an associative loop and therefore a Moufang loop. The nonzero octonion s form a nonassociative Moufang loop under octonion multiplication. The subset ... forms a Moufang loop. The basis octonions and their additive inverses form a finite Moufang loop of order 16. The set of invertible split octonion s forms a nonassociative Moufang loop, as does the set ... over a field mathematics field F forms a Moufang loop, as does the subset of unit norm elements. The set of all invertible elements in an alternative ring R forms a Moufang loop called the loop of units in R . For any field F let M F denote the Moufang loop of unit norm elements in the unique split ... of F is 2 then Z e , otherwise Z e . The Paige loop over F is the loop M F M F Z . Paige loops ... loops over finite field s. The smallest Paige loop M 2 has order 120. A large class of nonassociative ... u 2 1 math and math ug g 1 u math . With the above product M G ,2 is a Moufang loop. It is associative if and only if G is abelian. The smallest nonassociative Moufang loop is M S sub 3 sub ,2 which has order 12. Richard A. Parker constructed a Moufang loop of order 2 sup 13 sup , which was used by Conway in his construction of the monster group . Parker s loop has a center of order 2 with elements ... sup , identified with the binary Golay code . The loop is then defined up to isomorphism by the equations ... in that they need not be associative . A Moufang loop that is associative is a group. The Moufang identities ... elements x , y , and z in a Moufang loop obey the associative law xy z x yz then they generate an associative ... i.e. the subloop generated by any two elements of a Moufang loop is associative and therefore a group ... Q math . Inverse properties All Moufang loops have the inverse property loop inverse property , which ... more details
Unreferenced date February 2008 A loop line or loop around is a telephone company test circuit. The circuit has two associated phone numbers. When one side of the loop is called side A , the caller receives a test tone of approximately 1000 hertz Hz milliwatt test . When the second number side B is called, it produces dead silence, but the party on side A hears the milliwatt test tone drop, and is connected to the person on side B. The purpose of the loop around test is to allow circuit testing to a distant central office without needing a person at the far end. The technician can send a tone down either line and measure the response tone on the second line to determine the path loss parameters. When a line is connected to side A, multiple telephone lines, within limits, may connect to side B and thus be connected into a conference with the person on side A. The function of the tone on side A was to alert those already connected, when somebody called the B side and connected. Teenagers Citation needed date August 2009 discovered that the test facility could be used as party line telephony party lines or chat room s and would dial up the primary number and wait for someone at random to call its mate. Phreaks would use the loop around in a similar manner, to exchange information that they had learned about the phone company. http www.lospadres.info thorg lbb.html Loop lines are far less common today than they were in the 1960s , however they reportedly continued to exist past the turn of the century. One such loop line is certain to exist it is a TPI 560P located at 416 981 0001 ... make the line appear out of service Selective loop activation by operators Restrictions on which lines may call Using uncommon DTMF tones A through D in the telephone number Eventually, telephone companies designed devices to prevent this misuse of the loop around. Some devices blocked the audio ... end. See also Loopback DEFAULTSORT Loop Around Category Telephone numbers Category Communication circuits ... more details
In mathematics, in the topology of 3 manifold s, the loop theorem is a generalization of Dehn s lemma . The loop theorem was first proven by Christos Papakyriakopoulos in 1956, along with Dehn s lemma and the Sphere theorem 283 manifolds 29 Sphere theorem . A simple and useful version of the loop theorem states that if there is a map math f colon D 2, partial D 2 to M, partial M , math with math f partial D 2 math not nullhomotopic in math partial M math , then there is an embedding with the same property. The following version of the loop theorem, due to John Stallings , is given in the standard 3 manifold treatises such as Hempel or Jaco Let math M math be a 3 manifold and let math S math be a connected surface in math partial M math . Let math N subset pi 1 S math be a normal subgroup such that math mathop mathrm ker pi 1 S to pi 1 M N neq emptyset math . Let math f colon D 2 to M , math be a continuous map such that math f partial D 2 subset S , math and math f partial D 2 notin N. , math Then there exists an embedding math g colon D 2 to M , math such that math g partial D 2 subset S , math and math g partial D 2 notin N. , math Furthermore if one starts with a map f in general position, then for any neighborhood U of the singularity set of f , we can find such a g with image lying inside the union of image of f and U. Stalling s proof utilizes an adaptation, due to Whitehead and Shapiro, of Papakyriakopoulos tower construction . The tower refers to a special sequence of coverings designed to simplify lifts of the given map. The same tower construction was used by Papakyriakopoulos to prove the sphere theorem 3 manifolds , which states that a nontrivial map of a sphere into a 3 manifold implies the existence of a nontrivial embedding of a sphere. There is also a version ... construction. A proof not utilizing the tower construction exists of the first version of the loop ... to the word problem for Haken manifold s although he recognized this gave a proof of the loop theorem ... more details
Exhibition Loop may refer to Exhibition Loop TTC , a streetcar turning loop and station in Toronto, Canada Exhibition railway line , Brisbane, Australia dab ... more details
Refimprove date February 2008 Loop unwinding , also known as loop unrolling , is a loop transformation ... compiler . The goal of loop unwinding is to increase a program s speed by reducing or eliminating instructions that control the loop, such as pointer arithmetic and end of loop tests on each iteration ref cite book author Ullman, Jeffrey D. Aho, Alfred V. title Principles of compiler ... . ref cite journal author Nicolau, Alexandru title Loop Quantization Unwinding for Fine Grain Parallelism ... , as well as end of loop tests. If an optimizing compiler or assembler is able to pre calculate offsets ... of the program. Branch predictor branch penalty is minimised. If the statements in the loop are independent of each other i.e. where statements that occur earlier in the loop do not affect statements ... programming readable . If the code in the body of the loop involves function calls, it may not be possible ... performance is far away.html Code unwinding performance is far away ref Static Manual Loop Unrolling Manual or static loop unrolling involves the programmer analyzing the loop and interpreting the iterations into a sequence of instructions which will reduce the loop overhead. This is in contrast to dynamic ... by means of a code for code loop which calls the function delete item number . If this part of the program is to be optimized, and the overhead of the loop requires significant resources compared to those for delete x loop, unwinding can be used to speed it up. class wikitable border 1 cellpadding 1 Normal loop After loop unrolling source lang c int x for x 0 x 100 x delete x source source lang ... significant decrease in the loop administration overhead. To produce the optimal benefit ... hand, this manual loop unrolling expands the source code size from 3 lines to 7, that have to be produced ... in the expanded loop iteration Dubious date December 2009 . In addition, the loop control variables and number of operations inside the unrolled loop structure have to be chosen carefully so that the result ... more details
A Costas loop is a phase locked loop used for carrier wave carrier phase Carrier recovery recovery from suppressed carrier modulation signals, such as from double sideband suppressed carrier signals. It was invented by John P. Costas engineer John P. Costas at General Electric in the 1950s. Its invention was described as having had a profound effect on modern digital communications . The primary application of Costas loops is in wireless receivers. Its advantage over the PLL based detectors is that at small deviations the Costas loop error voltage is sin 2 sub i sub sub f sub vs sin sub i sub sub f sub . This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking doppler shifted carriers esp. in OFDM and GPS receiver s ref cite journal url http ieeexplore.ieee.org iel5 5 22249 01037569.pdf?arnumber 1037569 title Introduction to Synchronous Communications , A Classic Paper by John P. Costas engineer John P. Costas author D. Taylor journal Proceedings of the IEEE volume 90 issue 8 pages pp. 1459 1460 year 2002 month August ref Implementation In the usual implementation of a Costas loop, ref cite journal url http rfdesign.com images archive 0102Feigin20.pdf format PDF title Practical Costas loop design author Jeff Feigin date January 1, 2002 journal RF Design pages pp. 20 36 ref a local voltage controlled oscillator provides Quadrature phase quadrature outputs, one to each of two phase detector s, e.g. , Product detector product detectors. The same phase of the input signal information theory signal is also applied to both phase detectors and the output of each phase detector is passed through a low pass filter . The outputs of these low pass filters are inputs to another phase detector, the output of which passes through noise reduction filter before being used to control the voltage controlled oscillator. The overall loop ... Loop pt Costas loop ... more details
Java programming language Java , C Sharp programming language C , D programming language D The code for the loop is the same for Java, C and D source lang csharp int counter 5 long factorial 1 while ...Unreferenced date December 2009 File While loop diagram.svg thumb right While loop diagram In most computer programming languages, a while loop is a control flow statement programming statement that allows code to be executed repeatedly based on a given Boolean datatype boolean condition. The while loop ... . Because while loop checks the condition before the block is executed, the control structure is often also known as a pre test loop . Compare with the do while loop , which tests the condition after the loop has executed. For example, in the C programming language C programming language as well as Java ... lang c int x 0 while x 5 printf x d n , x x source first checks whether x is less than 5, which it is, so then the loop body is entered, where the printf function is run and x is incremented by 1. After completing all the statements in the loop body, the condition, x 5 , is checked again, and the loop ... to true, creating an infinite loop . When such a loop is created intentionally, there is usually another control structure such as a Control flow break statement that controls termination of the loop ... programming language C and its descendants, a while loop is a for loop Three expression for loops for loop ... is Counter Integer 5 Factorial Integer 1 begin while Counter 0 loop Factorial Factorial Counter Counter Counter 1 end loop Ada.Integer Text IO.Put Factorial end Factorial source Bash Unix shell Bash ... init variable and set value Do While counter 0 counter counter 1 Loop program goes here, until counter ... source And finally in D source lang d writefln factorial source JavaScript source lang javascript var ... loop factorial counter Multiply counter Decrement factorial Oberon programming language Oberon , Oberon ... While Loop source lang Python while True print Help I am Lost in this Loop. source Racket programming ... more details
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