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Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector_bundle
Mathematical concept in particularly differential topology
topology, the secondary vector bundle structure refers to the natural vector bundle structure (TE, p∗, TM) on the total space TE of the tangent bundle of a smooth
Secondary vector bundle structure
Secondary_vector_bundle_structure
second order jet bundle. Since (TM,πTM,M) is a vector bundle in its own right, its tangent bundle has the secondary vector bundle structure (TTM,(πTM)*,TM)
Double_tangent_bundle
In mathematics, a double vector bundle is the combination of two compatible vector bundle structures, which contains in particular the tangent T E {\displaystyle
Double_vector_bundle
Characteristic class of oriented, real vector bundles
oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth
Euler_class
Construct allowing differentiation of tangent vector fields of manifolds
the simplest methods of defining differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry
Affine_connection
and then take a vector bundle direct sum with a sufficient number of trivial line bundles; this corresponds exactly to the normal bundle of the stabilized
Stable_normal_bundle
Reproductive structure in flowering plants
as blossoms and blooms, are the reproductive structures of flowering plants. Typically, they are structured in four circular levels around the end of a
Flower
Mathematical theories
independent vectors. Obstruction theory turns out to be an application of cohomology theory to the problem of constructing a section of a bundle. The older
Obstruction_theory
a vector bundle over M {\displaystyle {\mathcal {M}}} , with n {\displaystyle n} -dimensional fiber V {\displaystyle V} . Equip this vector bundle with
First-class_constraint
British-Lebanese mathematician (1929–2019)
projective 3-space have a holomorphic structure. Horrocks had previously found some non-trivial examples of such vector bundles, which were later used by Atiyah
Michael_Atiyah
Examination of the heart's electrical activity
through the bundle of His and bundle branches. After the Bundle of His, the conduction system splits into the left bundle branch and the right bundle branch
Electrocardiography
Device to couple energy between circuits
descriptor: Step-up, step-down, isolation. General winding configuration: By IEC vector group, two-winding combinations of the phase designations delta, wye or
Transformer
Small DNA molecule within a cell
Bacteriophage DNA recombination Plasmidome Provirus Secondary chromosome Segrosome Transposon Triparental mating VectorDB Lloyd GS, Thomas CM (July 2023). "Microbial
Plasmid
Differential variety
{\displaystyle J^{k}(E)\to J^{k-1}E} are fibre bundles. As a particular case, when E {\displaystyle E} has a structure of fibred manifold over an n {\displaystyle
Diffiety
Open-source deep learning library
Francisco. It is supported commercially by the startup Skymind, which bundles DL4J, TensorFlow, Keras and other deep learning libraries in an enterprise
Deeplearning4j
Aligning molecular sequences using sequence and structural information
structures without the need for a predetermined alignment. Such algorithms have successfully identified canonical folds such as the four-helix bundle
Structural_alignment
References K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology it is an extraordinary
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
French mathematician (1869–1951)
modern terms, the method consists in associating to a fiber bundle E the principal fiber bundle having the same base and having at each point of the base
Élie_Cartan
pair with to form a full VSG. To dimerize, VSG N-terminal domains form a bundle of four alpha helices directed by hydrophobic interactions, around which
Variant_surface_glycoprotein
Open source widget toolkit and application development tools
Darling (software), a compatibility layer that relies on GNUstep GNUstep fat bundle Miller columns, the method of file tree browsing the GWorkspace File Viewer
GNUstep
Techniques in topology used to produce one finite-dimensional manifold from another
only if the Spivak normal fibration of X has a reduction to a stable vector bundle. If normal maps of degree one to X exist, their bordism classes (called
Surgery_theory
State of matter with insulating bulk but conductive boundary
assigning a matrix to each wave vector in the Brillouin zone. Mathematically, this assignment creates a vector bundle. Different materials will have different
Topological_insulator
Translator library for raster and vector geospatial data formats
(GDAL) is a computer software library for reading and writing raster and vector geospatial data formats (e.g. shapefile), and is released under the permissive
GDAL
Conversion process for computer data
the process of translating a data structure or object state into a format that can be stored (e.g. files in secondary storage devices, data buffers in
Serialization
Group of cytokines
required for its activity. Solution NMR suggests that the structure of IL2 comprises a bundle of 4 helices (termed A-D), flanked by 2 shorter helices and
Interleukin
Family of insects
The mouthparts of females are of the usual dipteran form and consist of a bundle of six chitinous stylets that, together with a fold of the fleshy labium
Tabanidae
Database software
combines the features and capabilities of Ingres and Vector, including column-based storage, vector processing, multi-core parallelism (and more): DataConnect
Ingres_(database)
overhead structures, for water and other growth-enhancing substances. These conduits consist of specialised tissues known as vascular bundles, which give
Glossary_of_plant_morphology
Programming language learning environment
The Costumes tab allows users to change the look of the sprite with a vector and bitmap editor in order to create various effects, including animation
Scratch (programming language)
Scratch_(programming_language)
List of versions of the Java programming language
Threads (Preview) JEP 426: Vector API (Fourth Incubator) JEP 427: Pattern Matching for switch (Third Preview) JEP 428: Structured Concurrency (Incubator)
Java_version_history
Infectious disease
migrate to the cell membrane with the aid of recycled endosomes and are bundled into the segments of the genome. Progeny viruses leave the cell by budding
Influenza
Domain of life whose cells have nuclei
shape. The nucleus stores the cell's DNA, which is divided into linear bundles called chromosomes; these are separated into two matching sets by a microtubular
Eukaryote
American annual mathematics conference
connections on SU(2) bundles over algebraic surfaces Dusa McDuff, Symplectic 4-manifolds Clifford Taubes, Anti-self dual conformal structures in 4 dimensions
Geometry_Festival
French mathematician (1928–2014)
Theorem on formal functions Ultrabornological space Weil conjectures Vector bundles on algebraic curves Zariski's main theorem Testimony by Pierre Cartier
Alexander_Grothendieck
games, for instance, skins of some characters may require the purchase of a bundle, while others are more easily accessible through spending diamonds acquired
Glossary_of_video_game_terms
biomacromolecules CD is particularly useful for determining the secondary structure. By way of contrast, in LD experiments the molecules need to have
Linear_dichroism
Suite of office software
charts and Gantt charts, not bundled in any Office suite. Microsoft Visio is a diagram and flowcharting app for Windows not bundled in any Office suite. Office
Microsoft_Office
Free and open-source wiki software
locales. For broader multilingual support, the MediaWiki Language Extension Bundle provides a curated set of extensions for adding language-related features
MediaWiki
1990s. There had been a number of arcade games that used simple wireframe vector graphics to simulate 3D, such as Battlezone, Tempest, and Star Wars. A unique
History_of_video_games
Chinese-American mathematician and poet
coherent sheaves" (PDF). Chern, S. S.; Bott, Raoul (1965). "Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections"
Shiing-Shen_Chern
Phylum of single-celled organisms
Cambrian onwards. Radiolarians have many needle-like pseudopods supported by bundles of microtubules, which aid in the radiolarian's buoyancy. The cell nucleus
Radiolaria
Business Process Management". bpmf.org. Future Strategies Inc. "Special 3-Book Bundle Spotlights the Annual BPM Awards". bpm-books.com. Future Strategies Inc
Workflow_Management_Coalition
Branch of mathematics
algebraic varieties, and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples of spaces studied
Geometry
Fusion device for physics experiments
position of the secondary beam; Auxiliary components and systems which include the primary beam detectors and the plasma/UV suppression structures, etc. FIR
Madison_Symmetric_Torus
Type of differential equation
boundary condition Robin boundary condition Cauchy problem Various topics Jet bundle Laplace transform applied to differential equations List of dynamical systems
Partial_differential_equation
Types of electrical transformer
the three secondary windings are connected together. Examples of connections are wye-delta, delta-wye, delta-delta, and wye-wye. A vector group indicates
Transformer_types
Mathematician
Stefano Ronchi (2025), whose dissertation was entitled Duals of higher vector bundles and cotangents of Lie 2-groupoids, and Hao Xu (2025), whose dissertation
Chenchang_Zhu
Air Vectors.net. Retrieved 23 June 2025. Goebel, Greg (1 June 2024). "Boeing B-52 Stratofortress - [3.1] B-52 IN THE 1970S & 1980S". Air Vectors.net.
List of military electronics of the United States: A–G
List_of_military_electronics_of_the_United_States:_A–G
Species of conifer tree
Carolina to Louisiana, and south to central Florida. Its leaves occur in bundles, fascicles of twos and threes, mostly threes, and the cones are larger
Pinus_elliottii
Electric current that periodically reverses direction
positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique is called Litz wire. This measure
Alternating_current
into heterologous hosts using recombinant vectors is a common biotechnology method for studying gene structure and function. high-throughput Describing
Glossary of cellular and molecular biology (0–L)
Glossary_of_cellular_and_molecular_biology_(0–L)
accessibility of Western media content. Departing from media offered in bundled content packages (magazines, CDs, television and radio slots), the Internet
Western_culture
Personal computer
PC Emulator and DR DOS 6, and the bundle was also made available in conjunction with the A4000. The Home Office bundle was updated with Iota's DataPower
Acorn_Archimedes
12 – (United States) A U.S. Air Force C-130 Hercules drops a record one-bundle 35,000 lb (15,876 kg) of equipment by parachute at El Centro, claimed as
1960s_in_air_cargo
State of matter with properties of both conventional liquids and crystals
approximately to one another. To describe this anisotropic structure, a dimensionless unit vector n called the director, is introduced to represent the direction
Liquid_crystal
Natural satellite orbiting Earth
Christoph (2023). "Constraints on Moon's Orbit 3.2 Billion Years Ago From Tidal Bundle Data". Journal of Geophysical Research: Planets. 128 (1) e2022JE007466.
Moon
Phylum of invertebrate animals
on both sides of the body are linked by commissures (relatively large bundles of nerves). The ganglia above the gut are the cerebral, the pleural, and
Mollusca
Siege engine using a long arm to throw projectiles
possessed knowledge of the traction trebuchet beforehand. Regardless of the vector of transmission, it appeared in the eastern Mediterranean by the late 6th
Trebuchet
Nonlinear two-terminal fundamental circuit element
based on the memristors physical parameters. The vector S → {\displaystyle {\vec {S}}} is the vector of voltage generators in series to the memristors
Memristor
Long narrow depression bordering the Aegean Sea to the south
nevertheless have slip vectors aligned with the western vectors over the entire arc in a wheel-spoke pattern; that is, the azimuths of the vectors decrease regularly
Hellenic_Trench
superstring revolution Secondary circulation Secondary electrons Secondary emission Secondary flow Secondary ion mass spectrometry Secondary mirror Sectional
Index_of_physics_articles_(S)
Algebra in algebraic topology
Let ν Y / X → Y {\displaystyle \nu _{Y/X}\to Y} be the associated Normal bundle to this immersion. The Steenrod squares of α {\displaystyle \alpha } can
Steenrod_algebra
Free and open-source compiler for various programming languages
system, selling them separately at a higher combined price than the previous bundle, which led many of Sun's users to buy or download GCC instead of the vendor's
GNU_Compiler_Collection
Interpretation of quantum mechanics
Broglie–Bohm theory on curved space with spin, the spin space becomes a vector bundle over configuration space, and the potential in the Schrödinger equation
De_Broglie–Bohm_theory
Warm-blooded animals with wings and feathers
atrioventricular bundle which communicates contraction to the ventricles. The avian heart also consists of muscular arches that are made up of thick bundles of muscular
Bird
Candidate unified theory of physics
derive spacetime as well as all the objects therein as secondary objects from the structures of an underlying causal fermion system. This concept also
Causal_fermion_systems
Class of ectothermic tetrapods
and by using internal fertilisation. In salamandrids, the male deposits a bundle of sperm, the spermatophore, and the female picks it up and inserts it into
Amphibian
Widely used standard for video compression
their own slice structures, macroblock modes, motion vectors, etc., allowing encoders to be designed with a simple parallelization structure (supported only
Advanced_Video_Coding
Sendai virus, virus of rodents
promotes the establishment of a stable six-helix bundle structure (6HB). The formation of the 6HB structure leads to the establishment of the pore and the
Murine_respirovirus
Species of bacteria
this bacteria. Lyme disease is a zoonotic, vector-borne disease transmitted by the Ixodes tick (also the vector for Babesia and Anaplasma). The infected
Borrelia_burgdorferi
Methods to prevent destructive asteroid hits
B83 physics packages, each set for their maximum 1.2-megatonne yield, bundled together and lofted by an Ares V vehicle sometime in the 2020s, with each
Asteroid_impact_avoidance
Tropical, edible, staple fruit
outer layer (a peel or skin) with numerous long, thin strings (Vascular bundles), which run lengthwise between the skin and the edible inner white flesh
Banana
Species of bacterium
they exhibit a "puzzling lack of antigenicity". The genome also revealed a bundle of 12 proteins and some putative hemolysins are potential virulence factors
Treponema_pallidum
Partial or total inability to hear
have introduced subscription-based hearing aid models. These typically bundle device costs, servicing, and follow-up care into a monthly fee, reducing
Hearing_loss
Enzyme
conformational change. This behavior is defined by the presence of a triple helical bundle formed by the N-termini of the hexameric protein in acidic environments
Glutamate_decarboxylase
Emissions, impacts and responses of the United States related to climate change
locations of concern are "coastal regions, islands, deserts in the southwest, vector-borne and zoonotic disease border regions, cities, and the U.S. Arctic (Alaska)"
Climate change in the United States
Climate_change_in_the_United_States
Class of animals with milk-producing glands
over the wing. This generates a lift force vector pointing forwards and upwards, and a drag force vector pointing rearwards and upwards. The upwards
Mammal
British quantum physicist (1935–2025)
age of twelve, where he attended secondary school. His interest in science was stimulated by his teachers at secondary school and by books, in particular
Basil_Hiley
Zircaloy family
for high flux zone reactor components and cladding for fuel pellet tube bundles in prototype submarine reactors in the late 1940s. The choice was owing
Zirconium_alloys
on complex birational geometry, Hodge theory, abelian varieties, and vector bundles Jane Cronin Scanlon (July 17, 1922 – June 19, 2018), mathematician;
List of University of Michigan alumni
List_of_University_of_Michigan_alumni
sinoatrial node dysfunction and may include atrioventricular node disease and bundle branch block. Electrocardiogram findings include sinus bradycardia, sinus
List_of_dog_diseases
Oïl language spoken in eastern Brittany, France
gradual, the transition with Poitevin to the south is more abrupt. A dense bundle of isoglosses crosses the former Marches of Brittany and Poitou [fr], near
Gallo_language
Neurosurgical treatment
Thomas E. (May 2017). "Deep brain stimulation to the medial forebrain bundle for depression- long-term outcomes and a novel data analysis strategy".
Deep_brain_stimulation
Quantification of bulk fluid movement
The primary flow element may consist of a single long capillary tube, a bundle of such tubes, or a long porous plug; such low flows create small pressure
Flow_measurement
Interpreter that enables users to enter and run programs in the BASIC language
product. After the MITS Altair 8800, microcomputers were expected to ship bundled with BASIC interpreters of their own (e.g., the Apple II, which had multiple
BASIC_interpreter
University of Mumbai Ushadevi Bhosle (born 1949), Indian expert on vector bundles Francesca Biagini (born 1973), Italian-German probability theorist and
List_of_women_in_mathematics
2015–16 concert tour by Madonna
from March 9, 2015, and the North American tickets purchased online were bundled with an exclusive digital download of Rebel Heart. Special access was granted
Rebel_Heart_Tour
Series of British microcomputers by Acorn
software, and the screen. Features specific to some versions of BASIC, like vector graphics, keyboard macros, cursor-based editing, sound queues, and envelopes
BBC_Micro
Class of molluscs
composed of two types of muscle fibres, striated muscle bundles for fast actions and smooth muscle bundles for maintaining a steady pull. Paired pedal protractor
Bivalvia
History of research by Augustin-Jean Fresnel
whereby sinusoidal functions are added like vectors. He acknowledged the directionality of the secondary sources and the variation in their distances
Fresnel's_physical_optics
Study of the toxicity of nanomaterials
composition, detailed shape, level of aggregation, combination with other vectors, etc. Above all, these properties would have to be determined not only
Nanotoxicology
delivering carbon nanotubes into cells is Cell squeezing, a high-throughput vector-free microfluidic platform for intracellular delivery developed at the Massachusetts
Potential applications of carbon nanotubes
Potential_applications_of_carbon_nanotubes
Interpretation of quantum mechanics
v ) {\displaystyle (x,v)} are coordinates in phase space (the tangent bundle), δ i j {\displaystyle \delta _{ij}} is the Kronecker delta describing the
Stochastic_quantum_mechanics
the brain develops abnormal clumps (amyloid plaques) and tangled fiber bundles (neurofibrillary tangles). Many genes associated with Alzheimer's disease
Role_of_microglia_in_disease
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Boy/Male
Spanish
Victor.
Surname or Lastname
German (Bünte)
German (Bünte) : most likely a variant of Bünde (see Bunde 2).English : variant spelling of Bunt.
Surname or Lastname
English
English : variant of Rundell.Respelling of German Rundel.
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Surname or Lastname
English (mainly Wales)
English (mainly Wales) : variant of Benthall.In some cases, probably an altered spelling of German Bendel.
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Male
English
Roman Latin name VICTOR means "conqueror."Â
Male
Arthurian
, sir Hector de Maris; (defender).
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Boy/Male
English American
Doctor; teacher.
Surname or Lastname
English
English : probably a metonymic occupational name for a hurdle maker, from Middle English herdle, hurdel ‘hurdle’.
Surname or Lastname
English
English : nickname from a diminutive of Rudd ‘red’.English : habitational name from a place called Ruddle, near Newnham in Gloucestershire.
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place in Lancashire named Brindle, from Old English burna ‘stream’ + hyll ‘hill’.Altered spelling of South German Brindl, Bründl, a topographic name for someone who lived by a spring or stream, from a diminutive of Middle High German brun(ne) ‘spring’, ‘stream’, or of Brendle or Brendel.
Surname or Lastname
English
English : variant spelling of Beadle.
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
Boy/Male
English American
From the spring farm.
Girl/Female
Arabic, Muslim
Pure Love
Boy/Male
Dutch Slavic French
Strong.
Surname or Lastname
English
English : metonymic occupational name for a maker or seller of boots, from Middle English, Old French bote (of unknown origin).Dutch and North German : metonymic occupational name for a boatman, from Dutch boot ‘boat’.
Male
German
Low German form of German Eckhard, EGGERT means "strong edge."
Female
Egyptian
, a XXVIth dynasty Egyptian lady.
Girl/Female
Tamil
Blessed
Male
Norse
Old Norse name composed of the elements hallr "rock" and steinn "stone," hence "rock stone."
Boy/Male
Australian, Hebrew, Jewish
Prophet and Judge; Heard by God
Boy/Male
Hindu
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
SECONDARY VECTOR-BUNDLE-STRUCTURE
a.
Possessing some quality, or having been subject to some operation (as substitution), in the second degree; as, a secondary salt, a secondary amine, etc. Cf. primary.
adv.
In a secondary manner or degree.
a.
Dependent or consequent upon another disease; as, Bright's disease is often secondary to scarlet fever. (b) Occuring in the second stage of a disease; as, the secondary symptoms of syphilis.
v. t.
To tie or bind in a bundle or roll.
adv.
Secondly; in the second place.
a.
Subsequent in origin; -- said of minerals produced by alteertion or deposition subsequent to the formation of the original rocks mass; also of characters of minerals (as secondary cleavage, etc.) developed by pressure or other causes.
v. t.
To release, as from a bundle; to disclose.
v. t.
To draw up into a bundle; to roll up.
n.
A number of things bound together, as by a cord or envelope, into a mass or package convenient for handling or conveyance; a loose package; a roll; as, a bundle of straw or of paper; a bundle of old clothes.
imp. & p. p.
of Bundle
a.
Pertaining to a rector or a rectory; rectoral.
n.
A secondary quill.
v. i.
To wash ore in a buddle.
a.
Acting by deputation or delegated authority; as, the work of secondary hands.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A secondary circle.
imp. & p. p.
of Bungle
n.
One who occupies a subordinate, inferior, or auxiliary place; a delegate deputy; one who is second or next to the chief officer; as, the secondary, or undersheriff of the city of London.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
Same as Radius vector.