Infobox Disease Name PAGENAME Image Leftbundlebranchblock ECG characteristics.png Caption ECG characteristics of a typical LBBB showing wide QRS complexes with abnormal morphology in leads V1 and V6. DiseasesDB 7352 ICD10 ICD10 I 44 4 i 30 ICD10 I 44 7 i 30 ICD9 ICDO OMIM MedlinePlus eMedicineSubj ped eMedicineTopic 2501 MeshID Leftbundlebranchblock LBBB is a cardiac conduction abnormality seen on the electrocardiogram ECG . ref name urlConduction Blocks 2006 KCUMB cite web url http courses.kcumb.edu physio blocks index.htm title Conduction Blocks 2006 KCUMB format work accessdate 2009 01 20 ref In this condition, activation of the left ventricle is delayed, which results in the left ventricle contracting later than the right ventricle . EKG diagnosis Image Leftbundlebranchblock supraventricular extrasystole.jpg right thumb Electrocardiogram showing leftbundlebranchblock and irregular rhythm due to supraventricular extrasystole s. Image LBBB2009.JPG thumb A leftbundlebranchblock The criteria to diagnose a leftbundlebranchblock on the electrocardiogram The heart rhythm must be supraventricular in origin The QRS duration must be 120 ms ref name urlLesson VI ECG Conduction Abnormalities cite web url http library.med.utah.edu kw ecg ekg outline Lesson6 index.html LBBB title Lesson VI EKG Conduction Abnormalities format work accessdate 2009 01 07 ref There should be a QS ... DEFAULTSORT LeftBundleBranchBlock Category Cardiac dysrhythmia de Linksschenkelblock es Bloqueo ... with bundlebranchblock. A concordant T wave may suggest ischemia or myocardial infarction. Causes ... rapid left ventricular contractions. Classification There are also partial blocks of the leftbundlebranchleft anterior fascicular block LAFB ref GPnotebook x20050921122910832459 ref and a left posterior fascicular block LPFB . ref GPnotebook x20050921123129832459 ref This refers to the bifurcation of the leftbundlebranch . See also Bundlebranchblock Right bundlebranchblock References ... more details
V1 and a slurred S wave in lead I. Leftbundlebranchblock widens the entire QRS, and in most cases ... Heart block s First degree AV block Second degree AV block Third degree AV block Right bundlebranchblockLeftbundlebranchblockLeft anterior fascicular block Bifascicular block Trifascicular ...Infobox Disease Name Bundlebranchblock Image Bundlebranch block.svg Caption ECG Showing changes in bundlebranchblock DiseasesDB 7352 DiseasesDB mult DiseasesDB2 11620 ICD10 ICD10 I 44 4 i 30 ICD10 ... 2501 eMedicine mult eMedicine2 ped 2500 MeshName BundleBranchBlock MeshNumber C14.280.067.558.323 A bundlebranchblock refers to a defect of the heart s electrical conduction system of the heart ... travels next through the left and right atria and summates at the atrioventricular node . From the AV node the electrical impulse travels down the Bundle of His and divides into the right and leftbundle branches. The right bundlebranch contains one wikt fascicle fascicle . The leftbundlebranch subdivides into two fascicles the left anterior fascicle and the left posterior fascicle. Other sources divide the LeftBundlebranch into three 3 fascicles, the left anterior, the left posterior, and the left ... and perhaps tweaking up the Ejection Fraction . Diagnosis and treatment A bundlebranchblock can ... bundlebranchblock typically causes prolongation of the last part of the QRS complex, and may ... R wave in lead I. Another normal finding with bundlebranchblock is appropriate T wave ... complex. Unfortunately, some individuals will exhibit both left and right bundlebranch blocks ... physiologic depolarization of the ventricles. Bundlebranch blocks When a bundlebranch ... across the bundlebranch, it may move instead through muscle fibers in a way that both slows the electrical ... may lead to Ventricular Dyssynchrony . Some people with bundlebranch blocks are born with this condition. Many other acquire it as a consequence of heart disease. People with bundlebranch blocks may ... more details
AV block image RBBB.JPG RBBB with associated tachycardia Image RBBB2010.JPG A RBBB gallery See also BundlebranchblockLeftbundlebranchblock References Reflist Circulatory system pathology Category ...Infobox disease Name Right bundlebranchblock Image Right bundlebranchblock ECG characteristics.png Caption ECG characteristics of a typical RBBB showing wide QRS complexes with a terminal R wave in lead V1 and slurred S wave in lead V6. DiseasesDB 11620 ICD10 ICD10 I 45 1 i 30 ICD9 ICDO OMIM MedlinePlus eMedicineSubj ped eMedicineTopic 2500 MeshID multiple image direction horizontal width 155 footer ... in RBBB Schematic With a blockage in the right bundlebranch red , the left ventricle is excited in time purple , while the excitation of the right ventricle takes a detour via the leftbundlebranch blue arrows . A right bundlebranchblock RBBB is a defect in the heart s Electrical conduction system ... 2009 01 20 ref During a right bundlebranchblock, the right ventricle heart ventricle is not directly activated by impulses travelling through the right bundlebranch. The left ventricle however, is still normally activated by the leftbundlebranch. These impulses are then able to travel through the myocardium of the left ventricle to the right ventricle and depolarise the right ventricle this way. As conduction through myocardium is slower than conduction through the Bundle of His Purkinje fibres ... cite journal pmc 1122450 ref ECG diagnosis The criteria to diagnose a right bundlebranchblock on the electrocardiogram ... deflection of the QRS complex. This is known as appropriate T wave discordance with bundlebranchblock. A concordant T wave may suggest ischemia or myocardial infarction. A mnemonic to remember the ECG changes is WiLLiaM MaRRoW, i.e. with Leftbundlebranchblock there is a W in V1 and a M in V6 ... the rapid depolarisation of the left ventricle followed by the slower depolarisation of the right ... duration must be more than 100 ms incomplete block or more than 120 ms complete block ref name ... more details
Infobox disease Name Left posterior fascicular block Image Caption DiseasesDB ICD10 ICD10 I 44 5 i 30 ICD9 ICDO OMIM MedlinePlus eMedicineSubj eMedicineTopic MeshID A left posterior fascicular block is a condition where the left posterior fascicle, i.e. the backside part of the left cardiac bundle, does not conduct the electrical impulses from the atrioventricular node . The electricity then has to go through the other fascicle, and thus is a frontal right axis deviation seen on the ECG . ref name urlLesson VI ECG Conduction Abnormalities cite web url http library.med.utah.edu kw ecg ecg outline Lesson6 index.html LPFB title Lesson VI ECG Conduction Abnormalities format work accessdate 2009 01 07 ref The deviation should be greater than 120 degrees and it is not a pathognomonic sign there are other conditions that can give the same picture. ref name urlConduction Blocks 2006 KCUMB cite web url http courses.kcumb.edu physio blocks index.htm title Conduction Blocks 2006 KCUMB work accessdate 2009 01 20 ref See also Leftbundlebranchblock References reflist Further reading cite journal author Ma FS, Ma J, Tang K, et al. title Left posterior fascicular block a new endpoint of ablation for verapamil sensitive idiopathic ventricular tachycardia journal Chin. Med. J. volume 119 issue 5 pages 367 72 year 2006 month March pmid 16542578 doi url http www.cmj.org Periodical LinkIn.asp?journal Chinese 20Medical 20Journal&linkintype pubmed&year 2006&vol 119&issue 5&beginpage 367 Heart diseases Category Cardiac dysrhythmia medicine stub ... more details
from leftbundlebranchblock . It is caused by only the anterior half of the bundle of His being defective. It is manifest on the electrocardiogram ECG by left axis deviation. It is much more common than left posterior fascicular block . Characteristics Normal activation of the left ventricle proceeds down the leftbundlebranch, which consist of two fascicles the left anterior fascicle and left posterior fascicle. Left Anterior Fascicular Block LAFB , which is also known as Left Anterior Hemiblock LAHB , occurs when a cardiac impulse spreads first through the left posterior fascicle, causing a delay in activation of the anterior and lateral walls of the left ventricle which are normally activated via the left anterior fascicle. Although there is a delay or block in activation of the left anterior fascicle there is still preservation of initial left to right septal activation as well as preservation of the inferior activation of the left ventricle preservation of septal Q waves in I ... of the cardiac skeleton. See also Bundlebranchblock References reflist 2 External links http ...Infobox disease ICD10 ICD10 I 44 4 i 30 Left anterior fascicular block is a cardiac condition, ref name ... by left anterior fascicular block during exercise journal Br Heart J volume 54 issue 1 pages 107 ... HC, Anand IS title Left anterior fascicular block an ischaemic response during treadmill testing ... T title Electrocardiographic criteria for the diagnosis of left anterior fascicular block. Left ... activation of the remainder of the left ventricle now results in a shift in the QRS axis leftward and superiorly, causing marked left axis deviation. This delayed activation also results in a widening of the QRS complex, although not to the extent of a complete LBBB Criteria Abnormal left axis deviation ... left axis deviation due to theinitial forces Q wave in a Qr complex in leads II, III, and aVF. As opposed to LAHB, the left axis shift is due to terminal forces i.e., the S wave in an rS complex ... more details
Infobox Artery Name Circumflex branch of left coronary artery Latin ramus circumflexus arteriae coronariae ... form the posterior left ventricular branch or posterolateral artery . The circumflex artery ends at the point ... circumflex branch of left coronary artery http www.merck.com media mmhe2 figures fg020 ... of heart. Circumflex branch not visible, but would be near the coronary sinus . Image2 Gray495.png Caption2 Base of ventricles exposed by removal of the atria. Circumflex branch not visible, but bifurcation of left coronary artery visible at left. BranchFrom left coronary artery BranchTo left atrial branch BR left marginal artery BR posterolateral artery BR sinuatrial nodal artery in some people BR posterior interventricular artery in some people Vein Supplies posterolateral left ventricle , anterolateral ... r 02 DorlandsSuf 12689380 The LCX , or left circumflex artery or circumflex artery , or circumflex branch of the left coronary artery is an artery of the heart . Course It follows the left part of the coronary sulcus , running first to the left and then to the right, reaching nearly as far as the posterior longitudinal sulcus . Branches The circumflex artery curves to the left around the heart within the coronary sulcus , giving rise to one or more diagonal or left marginal arteries also ... the posterolateral left ventricle and the anterolateral papillary muscle . It also supplies the sinoatrial nodal artery in 38 of people. It supplies 15 25 of the left ventricle in right dominant systems. If the coronary anatomy is left dominant, the LCX supplies 40 50 of the left ventricle. See coronary ... images File Coronary arteries.png thumb 300px left Coronary arteries labeled in red text and other major landmarks in blue text . Left circumflex artery is labeled at right. gallery Image Cardiac ... arteries Image Heart coronary territories.jpg Heart coronary territories Image Heart left lateral coronaries diagram.svg Heart left lateral coronaries diagram gallery External links SUNYAnatomyFigs ... more details
images File Coronary arteries.png thumb 300px left Coronary arteries labeled in red text and other major landmarks in blue text . Left anterior descending or interventricular artery is labeled ... gallery External links eMedicineDictionary anterior interventricular branch 20of 20left 20coronary 20artery SUNYAnatomyLabs 20 09 01 02 Heart The Left Coronary Artery and its Branches SUNYAnatomyFigs ... more details
Wiktionary bundleBundle or Bundling may refer to In marketing Product bundling , a marketing strategy that involves offering several products for sale as one combined product Bundling fundraising , when donations from many individuals are collected by one person and presented to the recipient Bundling political economy , a similar concept to product bundling that occurs in electoral republics In mathematics Bundle mathematics , a generalization of a fiber bundle dropping the condition of a local product structure Fiber bundle , a topology space that looks locally like a product space seealso Category Fiber bundles In medicine Bundle of His , a collection of heart muscle cells specialized for electrical conduction Bundle of Kent , an extra conduction pathway between the atria and ventricles in the heart In Computing Bundle NEXTSTEP , a type of directory in NEXTSTEP and Mac OS X Bundle software distribution , a package containing a software and everything it needs to operate Other uses Bundle adjustment , a photogrammetry computer vision technique Bundle conductor power engineering Bundle of rights property law Bundle theory philosophy Bundled payment , a method for reimbursing health care providers Bundles album Bundles album , a 1975 album by Soft Machine, including a song of the same title Bundling packaging , the process of using straps to bundle up items Bundling tradition , the traditional practice of wrapping one person in a bed accompanied by his her courter Optical fiber bundle , a cable consisting of a collection of fiber optics Bundle Brent Eileen Bundle Brent , an Agatha Christie character disambig Category Dutch loanwords de Bundle ko ... more details
. The intrinsic rate of the Bundle of His is between 40 60 bpm. ref http sprojects.mmi.mcgill.ca cardiophysio anatomybundlehis.htm AnatomyBundleHis Bot generated title ref The bundle of His branches into the three bundlebranch es the right, left anterior and left posterior bundle branches that run ... 1469382599 UMichAtlas ht rt vent Right atrioventricular bundlebranch, anterior view eMedicineDictionary ...Infobox Anatomy Name Bundle of His Latin fasciculus atrioventricularis GraySubject GrayPage Image ConductionsystemoftheheartwithouttheHeart.png Caption Isolated Heart conduction system showing Bundle of His Image2 bundleofhis.png Caption2 Heart cut away showing Bundle of His Schematic representation of the atrioventricular bundle of His. The bundle, represented in red, originates near the orifice of the coronary sinus , undergoes slight enlargement to form the AV node . The AV node tapers down into the bundle of His, which passes into the ventricular septum and divides into two bundle branches, the left and right bundles. Sometimes the left and right bundles of His are called Purkyn or Purkinje ... DorlandsPre b 26 DorlandsSuf 12200650 The bundle of His , known as the AV bundle or atrioventricular bundle, is a collection of heart muscle cells specialized for electrical conduction that transmits ... medizinischen Klinik zu Leipzig, Jena, 1893 14 50. ref Function This bundle is an important part of the electrical ... . These fibers distribute the impulse to the ventricular muscle. Together, the bundle branches and Purkinje ... to travel from the bundle of His to the ventricular muscle. Pathology If the Bundle of His is blocked ... called a third degree heart block . The other cause of a third degree block would be a block of the right, left anterior, and left posterior bundlebranch es. A third degree block is a very serious medical condition that will most likely require an artificial pacemaker . His Bundle Pacing Direct His Bundle pacing has produced synchronous ventricular depolarization and improved cardiac function ... more details
&prime be a specified topological space, equipped with a continuous left action of G . Then the bundle ... homogeneous space for the left action of G on itself, then the associated bundle E &prime is called ... G bundle and let G Homeo F be a continuous group action left action of G on a space F in the smooth ... as a reduction of the tangent bundle to a block matrix subgroup but here the reduction is only ...In mathematics , the theory of fiber bundle s with a structure group math G math a topological group allows an operation of creating an associated bundle , in which the typical fiber of a bundle changes ... G math . For a fibre bundle F with structure group G , the transition functions of the fibre i.e. ... a fibre bundle F as a new fibre bundle having the same transition functions, but possibly a different ... in G . The associated bundle construction is just the observation that this data does just as well ... from a bundle with fiber math F math , on which math G math acts, to the associated principal bundle namely the bundle where the fiber is math G math , considered to act by translation on itself . For then we can go from math F 1 math to math F 2 math , via the principal bundle. Details in terms ... is organized as follows. We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle. This then specializes to the case when the specified fibre is a principal homogeneous space for the left action of the group on itself, yielding the associated principal bundle. If, in addition, a right action is given on the fibre of the principal bundle, we describe how to construct any associated bundle by means of a fibre product construction ... 1951 page 36 ref Associated bundles in general Let &pi E &rarr X be a fibre bundle over a topological ... left action of G as a transformation group on the fibre F . Suppose furthermore that this action is group ... of the principal bundle associated to E . ref There is a locally trivial local trivialization of the bundle ... more details
by left multiplication on S . Such a spinor bundle is said to be real , complex , graded or ungraded ... which is given by left multiplication on each fiber. The spinor bundle S M is therefore a bundle of Clifford ...In mathematics , a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford ... bundle associated to any pseudo Riemannian manifold pseudo Riemannian manifold M which is called the Clifford bundle of M . General construction Let V be a real number real or complex number complex ... vector bundle . Let E be a smooth vector bundle over a smooth manifold M , and let g be a smooth symmetric bilinear form on E . The Clifford bundle of E is the fiber bundle whose fibers are the Clifford ... structure topology of C E is determined by that of E via an associated bundle construction. One ... nondegenerate form nondegenerate that is, when E , g is a Riemannian or pseudo Riemannian vector bundle. For concreteness, suppose that E , g is a Riemannian vector bundle. The Clifford bundle of E can ... are all vectors in R sup n sup . The Clifford bundle of E is then given by math C ell E F E times rho C ell n mathbb R math where F E is the orthonormal frame bundle of E . It is clear from this construction ... n sub R it follows that C E is a bundle of superalgebra Z sub 2 sub graded algebras over M . The Clifford bundle C E can then be decomposed into even and odd subbundles math C ell E C ell 0 E oplus C ell 1 E . math If the vector bundle E is orientability orientable then one can reduce the structure group of C E from O n to SO n in the natural manner. Clifford bundle of a Riemannian manifold If M is a Riemannian manifold with metric tensor metric g , then the Clifford bundle of M is the Clifford bundle generated by the tangent bundle TM . One can also build a Clifford bundle out of the cotangent bundle T M . The metric induces a natural isomorphism TM T M and therefore an isomorphism C TM C T M . There is a natural vector bundle morphism vector bundle isomorphism between the Clifford bundle ... more details
image ConductionsystemoftheheartwithouttheHeart.png right thumb 350px Image showing Bachmann s bundle Refimprove date December 2009 Bachmann s bundle , also known as the anterior interatrial band, is a broad band of atrial muscle that runs just behind the ascending aorta and connects the top of the right atrium with the top of the left atrium . Bachmann s bundle is, during normal sinus rhythm, the preferential path for electrical activation of the left atrium. It is therefore considered as part of the atrial conduction system of the heart . Interatrial conduction The normal cardiac rhythm originates in the sinoatrial node , which is located in the right atrium near the superior caval vein. From there, the electrical activation spreads over the right atrium. There are at least four different locations where the activation can pass to the left atrium. Apart from Bachmann s bundle these are the anterior interatrial septum, posterior interatrial septum, and the coronary sinus . ref Cite journal author Sakamoto, S I, et al. title Interatrial Electrical Connections The Precise Location and Preferential Conduction journal Journal of Cardiovascular Electrophysiology volume 16 pages 1077 1086 year 2005 doi 10.1111 j.1540 8167.2005.40659.x ref Because it originates close to the sinoatrial node and consists of long parallel fibers, Bachmann s bundle is, during sinus rhythm, the first of these connections to activate the left atrium. Bachmann s bundle and the atrial conduction system Besides Bachmann s bundle, the other three conduction tracts that constitute the atrial conduction system are known as the anterior , middle, and Posterior anatomy posterior tracts, which run from the sinoatrial node to the atrioventricular node , converging in the region near the coronary sinus . Atrial .... See also Electrical conduction system of the heart Bundle of His References Reflist Heart DEFAULTSORT Bachmann s Bundle Category Cardiac anatomy Circulatory stub id Berkas Bachmann nl Bundel van ... more details
distinguish2 an optical fiber bundle File Roundhairbrush.JPG thumb A cylindrical hairbrush showing the intuition behind the term fiber bundle . This hairbrush is like a fiber bundle in which the base space ... topology , a fiber bundle or, in British English , fibre bundle is intuitively a space ... structure. Specifically, the similarity between the fiber bundle E and a product space B F is defined ... regions of B F to B . The map , called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E is known as the total space of the fiber bundle ... the projection from the product space to the first factor. This is called a trivial bundle . Examples ... bottle , as well as nontrivial covering space s. Fiber bundles such as the tangent bundle of a manifold and more general vector bundle s play an important role in differential geometry and differential topology , as do principal bundle s. Mappings which factor over the projection map are known as bundle maps , and the set of fiber bundles forms a category theory category with respect to such mappings. A bundle map from the base space itself with the identity mapping as projection to E is called a section fiber bundle section of E . Fiber bundles can be generalized in a number of ways, the most ... A fiber bundle consists of the data E , B , , F , where E , B , and F are topological spaces ... below. The space B is called the base space of the bundle, E the total space , and F the fiber . The map is called the projection map or bundle projection . We shall assume in what follows that the base .... The set of all U sub i sub , sub i sub is called a local trivialization of the bundle. Thus for any ... is and is called the fiber over p . Every fiber bundle E B is an open map , since projections ... bundle E , B , , F is often denoted math F longrightarrow E xrightarrow , pi B math that, in analogy ... as the map from total to base space. A smooth fiber bundle is a fiber bundle in the category mathematics ... more details
Infobox Disease Name Bifascicular block Image RBBB with first degree AV block.jpg Caption Right bundlebranchblock with first degree AV block . DiseasesDB ICD10 ICD10 I 45 2 i 30 ICD9 ICD9 426.53 ICDO OMIM MedlinePlus eMedicineSubj eMedicineTopic MeshID Bifascicular block is a conduction abnormality in the heart where two of the three main wikt fascicle fascicle s of the Electrical conduction system of the heart His Purkinje system are blocked. Most commonly, it refers to a combination of right bundlebranchblock RBBB and either left anterior fascicular block LAFB or left posterior fascicular block LPFB , with the former being more common. ref name urlLesson VI ECG Conduction Abnormalities cite web url http library.med.utah.edu kw ecg ecg outline Lesson6 index.html bifasc title Lesson VI ECG Conduction Abnormalities format work accessdate 2009 01 07 ref Some authors consider leftbundlebranchblock LBBB to be a technical bifascicular block, since the block occurs above the wikt bifurcation bifurcation of the left anterior and left posterior fascicles of the leftbundlebranch. Treatment In those with bifasciular block and no symptoms little with respect to treatment is needed. In those with syncope a pacemaker is recommended. Image gallery Image Bifascicular block ECG.png Bifascicular block on an electrocardiogram . gallery References reflist External links GPnotebook 1584070658 Circulatory system pathology Category Cardiac dysrhythmia disease stub ... more details
In mathematics , a frame bundle is a principal fiber bundle F E associated to any vector bundle E . The fiber ... x sub . The general linear group acts naturally on F E via a change of basis , giving the frame bundle the structure of a principal GL sub k sub R bundle where k is the rank of E . The frame bundle of a smooth manifold is the one associated to its tangent bundle . For this reason it is sometimes called the tangent frame bundle . Definition and construction Let E X be a real vector bundle of rank ... . The space F sub x sub is said to be a GL sub k sub R torsor . The frame bundle of E , denoted by F ... . The frame bundle F E can be given a natural topology and bundle structure determined by that of E ... maps sup &minus 1 sup U sub i sub F E . With all of the above data the frame bundle F E becomes a principal fiber bundle over X with structure group GL sub k sub R and local trivializations U sub ... . The above all works in the smooth category as well if E is a smooth vector bundle over a smooth manifold M then the frame bundle of E can be given the structure of a smooth principal bundle over M . Associated vector bundles A vector bundle E and its frame bundle F E are associated bundle s. Each one determines the other. The frame bundle F E can be constructed from E as above, or more abstractly using the fiber bundle construction theorem . With the latter method, F E is the fiber bundle with same ... k sub R is that of left multiplication. Given any linear representation GL sub k sub R V there is a vector bundle math mathrm F E times rho V , math associated to F E which is given by product F E × ... classes by p , v . The vector bundle E is naturally isomorphic to the bundle F E × sub ... E sub x sub is a frame at x . One can easily check that this map is well defined . Any vector bundle associated to E can be given by the above construction. For example, the dual bundle of E is given .... Tensor bundle s of E can be constructed in a similar manner. Tangent frame bundle The tangent ... more details
Image Tangent bundle.svg right thumb Informally, the tangent bundle of a manifold in this case a circle ... bundle of a differentiable manifold M is the disjoint union ref group note name disjoint The disjoint ... picture for tangent bundle of circle S sup 1 sup , see Tangent bundle Examples Examples section ... . That is, math TM bigsqcup x in M T xM bigcup x in M left x right times T xM. math where T sub ... . The tangent bundle to a manifold is the prototypical example of a vector bundle a fiber bundle whose fibers are vector space s . A Section fiber bundle section of TM is a vector field on M , and the dual bundle to TM is the cotangent bundle , which is the disjoint union of the cotangent space s of M ... bundle is trivial bundle trivial . By definition, a manifold M is Framed mathematics framed if and only if the tangent bundle TM is stably trivial, meaning that for some trivial bundle E the Vector bundle Whitney sum nowrap 1 TM &oplus E is trivial. For example, the n dimensional sphere S sup n sup ... The main role of the tangent bundle is to provide a domain and range for the derivative of a smooth ... . Topology and smooth structure The tangent bundle comes equipped with a natural topology not the disjoint ... sup , then the tangent bundle is said to be trivial . Trivial tangent bundles usually occur for manifolds ... group . The tangent bundle of the unit circle is trivial because it is a Lie group under multiplication ... tangent bundles are Lie groups manifolds which have a trivial tangent bundle are called parallelizable ... smooth maps between open subsets of R sup 2 n sup . The tangent bundle is an example of a more general construction called a vector bundle which is itself a specific kind of fiber bundle . Explicitly, the tangent bundle to an n dimensional manifold M may be defined as a rank n vector bundle .... Examples The simplest example is that of R sup n sup . In this case the tangent bundle is trivial. Another simple example is the unit circle , S sup 1 sup see picture above . The tangent bundle ... more details
Unreferenced date December 2009 In mathematics , a surface bundle is a fiber bundlebundle in which the fiber is a surface . When the base space is a circle the total space is 3 manifold three dimensional and is often called a surface bundle over the circle . See also Mapping torus DEFAULTSORT Surface Bundle Category Geometric topology es Surface Bundle ... more details
normal subgroup normal . Then G is a principal H bundle over the left coset space G H . Here the action of H on G is just right multiplication. The fibers are the left cosets of H in this case there is a distinguished ...In mathematics , a principal bundle ref cite book last Steenrod first Norman title The Topology of Fibre ... group G . In the same way as with the Cartesian product, a principal bundle P is equipped with An group ... of the space. A common example of a principal bundle is the frame bundle F E of a vector bundle ... bases. Since there is no preferred way to choose an ordered basis of a vector space, a frame bundle ... group G determine a unique principal G bundle from which the original bundle can be reconstructed. Formal definition A principal G bundle, where G denotes any topological group , is a fiber bundle P ... the fibers of P and acts freely and transitively on them. This implies that the fiber of the bundle ... definition of a principal G bundle is as a G bundle P X with fiber G where the structure group acts on the fiber by left multiplication. Since right multiplication by G on the fiber commutes with the action ... example of a smooth principal bundle is the frame bundle of a smooth manifold M , often denoted ... bundle over M . Variations on the above example include the orthonormal frame bundle of a Riemannian ... bundle if E is any vector bundle of rank k over M , then the bundle of frames of E is a principal GL k , R bundle, sometimes denoted F E . A normal regular covering space p C X is a principal bundle where the structure group math pi 1 X p pi 1 C math acts on the fibres of p via the Covering space Monodromy action monodromy action . In particular, the universal cover of X is a principal bundle ... bundle is the associated bundle of the M bius strip . Besides the trivial bundle, this is the only principal Z sub 2 sub bundle over S sup 1 sup . Projective space s provide some more interesting examples ... O 1 bundle over RP sup n sup . Likewise, S sup 2 n 1 sup is a principal U 1 bundle over ... more details
Refimprove date September 2009 Bundle theory , originated by the 18th century Scottish philosopher David ... consists only of a collection bundle of properties, relations or trope philosophy tropes . According to bundle theory, an object consists of its properties and nothing more thus neither can there be an object without properties nor can one even conceive of such an object for example, bundle theory claims ... theory substance in which the properties inherence inhere . Arguments for the bundle theory ... properties is a common justification for bundle theory, especially among current philosophers in the Anglo ... of bare particulars leaves a bundle of properties and nothing more as the only possible conception of an object, thus justifying bundle theory. Objections to the bundle theory Objections to bundle theory concern the nature of the bundle of properties , the properties wikt compresence compresence ... on understanding reality. Compresence objection Bundle theory maintains that properties are bundled together in a collection without describing how they are tied together. For example, bundle theory ... . The apple is said to be a bundle of properties including redness, being four inches 100 mm wide, and juiciness. Critics question how bundle theory accounts for the properties wikt compresence ... if there is no substance in which they both inhere . Traditional bundle theory, according to Professor ... of a bundle of properties located on the table, one of which is the looks like an apple property .... The bundle theory of substance explains compresence . Specifically, it maintains that properties ... strata. The bundle theory of substance thus rejects the substance theories of Aristotle , Descartes ... reality objection Section OR date May 2012 The language reality objection to bundle theory relates ... that supports bundle theory. Per the objection, properties are synthetic constructions of language ..., includes at least six concepts and would best be left as dead end logical propositions. Since the objection ... more details
Image Bundle adjustment sparse matrix.png right thumb A sparse matrix obtained when solving a modestly sized bundle adjustment problem. This is the sparsity pattern of a 992× 992 normal equations i.e. approximate Hessian matrix. Black regions correspond to nonzero blocks. Given a set of images depicting a number of 3D points from stereoscopy different viewpoints , bundle adjustment can be defined ... problem corresponding image projections of all points. Bundle adjustment is almost always used ... is zero mean Gaussian noise Gaussian , then bundle adjustment is the Maximum likelihood Maximum Likelihood ... categorical bundle mathematics bundle seems a pure coincidence . Bundle adjustment was originally conceived ... researchers during recent years. Bundle adjustment boils down to minimizing the reprojection error ... equations . When solving the minimization problems arising in the framework of bundle adjustment, the normal equations have a Sparse matrix sparse block structure owing to the lack of interaction among .... Mathematical definition Bundle adjustment amounts to jointly refining a set of initial camera and structure ... math by a vector math mathbf b i math . Bundle adjustment minimizes the total reprojection error with respect ... . Clearly, bundle adjustment is by definition tolerant to missing image projections and minimizes a physically meaningful criterion. Software http www.ics.forth.gr lourakis sba sba A Generic Sparse Bundle ... Matlab http www.inf.ethz.ch personal chzach opensource.html ssba Simple Sparse Bundle Adjustment ... projects mcba mcba Multi Core Bundle Adjustment CPU GPU . https github.com dkogan libdogleg ... equation References cite conference title Bundle Adjustment A Modern Synthesis author B. Triggs ... Bundle Adjustment author M.I.A. Lourakis and A.A. Argyros journal ACM Transactions on Mathematical ... pubs 2000 TMHF00 Triggs va99.pdf B. Triggs, P. McLauchlan, R. Hartley and A. Fitzgibbon, Bundle Adjustment ... rbf CVonline LOCAL COPIES ZISSERMAN bundle bundle.html Bundle adjustment . CV Online ... more details
In mathematics , an algebra bundle is a fiber bundle whose fiber s are algebra over a field algebra s and local trivialization s respect the algebra structure. It follows that the transition function s are algebra isomorphism s. Since algebras are also vector space s, every algebra bundle is a vector bundle . Examples include the tensor bundle , exterior bundle , and symmetric bundle associated to a given vector bundle , as well as the Clifford bundle associated to any Riemannian vector bundle. See also Lie algebra bundle References 1. W. Greub, S. Halperin and R. Vanstone, Connections, Curvature and Cohomology, Vo. 2, Academic Press, New Yark, 1973 2. C. Chidambara and B.S. Kiranagi, On Cohomology of Associative algebra bundles, J. Ramanujan Math. Soc., Vol. 9 1 , 1994. pp. 1 12 3. B.S. Kiranagi and R. Rajendra, Revisiting Hochschild Cohomology for Algebra Bundles, Journal of Algebra and Its Applications Vol. 7, No. 6 2008 685 715. DEFAULTSORT Algebra Bundle Category Vector bundles topology stub algebra stub ... more details
Unreferenced date August 2008 In mathematics , the tensor bundle of a manifold is the direct sum of vector bundles direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold. To do calculus on the tensor bundle a connection mathematics connection is needed. Category Vector bundles geometry stub ru ... more details
Unreferenced date December 2010 Infobox musical artist See Wikipedia WikiProject Musicians name Bundle of Hiss image caption image size background group or band alias origin Seattle , Washington U.S. state Washington , United States instrument genre Hard rock , grunge , heavy metal music heavy metal occupation years active 1980&ndash 1988 label Loveless associated acts Mudhoney , Tad band Tad website current members past members Jamie Lane br Kurt Danielson br Dan Peters notable instruments Bundle of Hiss were an United States American grunge band formed in 1980 in Stanwood, Washington by pre Tad band Tad member Kurt Danielson , guitarist Jeff Hopper, vocalist Kurt Schonberg and drummer Russ Bartlett. Schonberg left the band after they had recorded a couple of demo tapes. Russ Bartlett then moved from drums to vocals. They featured various drummers before finding Dan Peters . Hopper later left the band and was replaced by Jamie Lane, whom met Kurt Danielson at the University of Washington . In 1986, Russ Bartlett left the band to pursue a solo career. Jamie Lane then took up vocals and guitar. The band recorded demo tapes and passed them on to fans at their shows and fellow Seattle bands, such as Soundgarden , Mudhoney , and The Melvins . In 1988, the band split up to go separate ways. Kurt Danielson formed his new band Tad band Tad with former drummer Tad Doyle. Dan Peters became drummer in a somewhat short lived local band project called Feast, which disbanded shortly after he joined. After Feast broke up, Peters met up with Mark Arm and Steve Turner guitarist Steve Turner to form Mudhoney band Mudhoney . In 2000, Bundle of Hiss re released an old demo tape on Loveless Records called Sessions 1986 88 . External links http www.lovelessrecords.com boh Band Website DEFAULTSORT Bundle Of Hiss Category Musical groups from Washington state Category Grunge musical groups US alternative rock band stub ... more details
Unreferenced date November 2006 In mathematics , the dual bundle of a vector bundle E X is a vector bundle E X whose fibers are the dual space s to the fibers of E . The dual bundle can be constructed using the associated bundle construction by taking the dual representation of the structure group . Specifically, given a local trivialization of E with Topology transition functions t sub ij sub , a local trivialization of E is given by the same open cover of X with transition functions t sub ij sub t sub ij sub sup T sup sup &minus 1 sup the inverse matrix inverse of the transpose . The dual bundle E is then constructed using the fiber bundle construction theorem . For example, the dual to the tangent bundle of a differentiable manifold is the cotangent bundle . If the base space X is paracompact and Hausdorff space Hausdorff then a finite rank vector bundle E and its dual E are isomorphic as vector bundles. However, just as for vector space s, there is no natural isomorphism canonical choice of isomorphism unless E is equipped with an inner product . DEFAULTSORT Dual Bundle Category Vector bundles ... more details
In mathematics, the inverse bundle of a fibre bundle is its inverse with respect to the Whitney sum operation. Let math E rightarrow M math be a fibre bundle . A bundle math E rightarrow M math is called the inverse bundle of math E math if their Whitney sum is a trivial bundle, namely if math E oplus E cong M times mathbb R n. , math Any vector bundle over a compact space compact Hausdorff space Hausdorff base has an inverse bundle. References Citation last Hatcher first Allen author link Allen Hatcher title Vector Bundles & K Theory url http www.math.cornell.edu hatcher VBKT VBpage.html edition 2.0 year 2003 Category Differential topology Category Algebraic topology Category Vector bundles ... more details
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