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Integral transform
In mathematics the longitudinal ray transform (LRT) is a generalization of the X-ray transform to symmetric tensor fields Let f i 1 . . . i m {\displaystyle
Longitudinal_ray_transform
derivative. This work, and Sharafutdinov's, stem from the study of the longitudinal ray transform, of symmetric tensor fields. Here the null space is exactly symmetric
Saint-Venant's compatibility condition
Saint-Venant's_compatibility_condition
Wave that remains in a constant position
waves in a pipe demonstrates how the same principles can be applied to longitudinal waves with analogous boundary conditions. Standing waves can also occur
Standing_wave
Mathematical function in general imaging
estimating the deviation of a defocused ray from the ideal by stating the longitudinal aberration; a measure of how much a ray deviates from the focal point along
Contrast_transfer_function
Medical imaging procedure
radiocontrast. The history of X-ray computed tomography goes back to at least 1917 with the mathematical theory of the Radon transform. In October 1963, William
CT_scan
movements List of waves named after people Long wavelength limit Longitudinal mode Longitudinal wave Longwave Love wave Mach wave Mach–Zehnder interferometer
Index_of_wave_articles
Dynamic disturbance in a medium or field
transfer); or longitudinal wave if those vectors are aligned with the propagation direction. Mechanical waves include both transverse and longitudinal waves;
Wave
Study of classical optics using Fourier transforms
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination
Fourier_optics
Scientific phenomenon
\gamma =1/{\sqrt {1-\beta ^{2}}}} . Relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each
Relativistic_Doppler_effect
Medical diagnostic method
trade-off in terms of noise and longitudinal resolution. In cone-beam computed tomography (commonly abbreviated CBCT), the X-ray beam is conical. Helical (or
Operation of computed tomography
Operation_of_computed_tomography
opposed to X-ray photons. However, essential mathematics and reconstruction algorithms used for CT and OPT are similar; for example, radon transform or iterative
Optical_projection_tomography
Girl who behaves boyishly
Hines, M.; Golombok, S.; Rust, J.; Johnston, K. J.; Golding, J.; Avon Longitudinal Study of Parents and Children Study Team (2002). "Testosterone during
Tomboy
Laser using electron beam in vacuum as gain medium
} factor to the above formula. In an X-ray FEL the typical undulator wavelength of 1 cm is transformed to X-ray wavelengths on the order of 1 nm by γ {\displaystyle
Free-electron_laser
Bony skin-covered spines or rays protruding from the body of a fish
structures among different clades: in ray-finned fish (Actinopterygii), fins are mainly composed of spreading bony spines or "rays" covered by a thin stretch of
Fish_fin
the sharpest pictures of both through X-ray diffraction technique. The first calculations of the Fourier transform of an atomic helix were reported one year
Molecular_models_of_DNA
Physical phenomenon
observations, spin–lattice relaxation is the mechanism by which the longitudinal component of the total nuclear magnetic moment vector (parallel to the
Spin–lattice_relaxation
dialing – Direct ray – Directional antenna – Directional coupler – Directive gain – Direct-sequence spread spectrum – Discrete Fourier transform – Discrete
Index_of_electronics_articles
Measurement method using interference of waves
highest-precision length measuring instruments in existence. In Fourier transform spectroscopy they are used to analyze light containing features of absorption
Interferometry
Controversial psychological typology
typology is a controversial theory proposed by American-Canadian sexologist Ray Blanchard which classifies transgender women into two groups: "homosexual
Blanchard's transsexualism typology
Blanchard's_transsexualism_typology
Theory of interwoven space and time by Albert Einstein
independent of any medium. Nevertheless, relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each
Special_relativity
Complete reflection of a wave
in terms of "rays" rather than waves; in a medium whose properties are independent of direction, such as air, water or glass, the "rays" are perpendicular
Total_internal_reflection
Portrayal of sexual subject matter
society, while others oppose censorship efforts insisting it is benign. A longitudinal study ascertained pornography use is not a predictive factor in intimate
Pornography
Medical condition featuring permanent bending of fingers
myofibroblasts, an involution stage in which these cells align along longitudinal stress lines in the hand, and a residual stage in which dense, relatively
Dupuytren's_contracture
Medical imaging technique
is sometimes stated in literature. The recovery of longitudinal magnetization is called longitudinal or T1 relaxation and occurs exponentially with a time
Physics of magnetic resonance imaging
Physics_of_magnetic_resonance_imaging
Lion population in India
The Asiatic lion has a ruddy-tawny to sandy grey fur, a distinctive longitudinal skin fold along its belly, and a larger tail tuft. The males are distinguishable
Asiatic_lion
Type of mathematical relation
relations are known by the names Sokhotski–Plemelj theorem and Hilbert transform. Let χ ( ω ) = χ 1 ( ω ) + i χ 2 ( ω ) {\displaystyle \chi (\omega )=\chi
Kramers–Kronig_relations
Spectroscopic technique based on change of nuclear spin state
for radiation damping alongside the conventional relaxation terms. The longitudinal relaxation time of radiation damping ( T R D {\displaystyle T_{RD}} )
Nuclear_magnetic_resonance
theorem and can be used to derive integral identities. For an example see Longitudinal and transverse vector fields. This identity implies that the Fourier
Common integrals in quantum field theory
Common_integrals_in_quantum_field_theory
Device used in television cameras
Video camera tubes are devices based on the cathode-ray tube that were used in television cameras to capture television images, prior to the introduction
Video_camera_tube
Method of microscopic imaging
breaks down for thicker samples where electron or X-ray wavefronts undergo significant longitudinal evolution. The conceptual origin for using a single
Ptychography
Semiconductor light source
filament consists of multiple LED chips connected in series on a common longitudinal substrate that forms a thin rod reminiscent of a traditional incandescent
Light-emitting_diode
Response if an optical system to a point source of light
functional terms, it is the spatial domain version (i.e., the inverse Fourier transform) of the optical transfer function (OTF) of an imaging system. It is a
Point_spread_function
X-Ray diffraction microscopy Feature detection Canny edge detector: detect a wide range of edges in images Generalised Hough transform Hough transform Marr–Hildreth
List_of_algorithms
Differential equation important in physics
results the designation "two-way wave equation". It can be shown for plane longitudinal wave propagation that the synthesis of two one-way wave equations leads
Wave_equation
Mathematical model combining space and time
the source and/or receiver are exactly along the line connecting them (longitudinal Doppler effect), and (2) the motions are at right angles to the said
Spacetime
Type of radioactive decay
energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission
Beta_decay
Frank, Amanda; Naseer, Mahwish (2021-02-10). "A systematic review of longitudinal risk factors for loneliness in older adults". Aging & Mental Health.
Loneliness_in_old_age
Anime and manga pornography
to another." Literal one-to-one English translations for this would be transform and metamorph, wherein trans- and meta- correspond to 變, while form and
Hentai
Sports car produced by Dodge (1992–2017)
the normal Viper's spartan nature) that can, at the flick of a switch, transform from a red RT/10 (later a blue GTS) into a grey/silver weaponized armored
Dodge_Viper
Sports car manufactured by Japanese automobile manufacturer Nissan
screen on the centre dash confirms the test equipment's assertion that longitudinal acceleration of at least 1.0 g persists for almost two seconds. No wonder
Nissan_GT-R
Electric charge generated in certain solids due to mechanical stress
sensor, different "modes" to load the piezoelectric element can be used: longitudinal, transversal and shear. Detection of pressure variations in the form
Piezoelectricity
Physical characteristic of oscillating systems
frequencies. The standing wave patterns produced are called "modes". Longitudinal modes differ only in frequency while transverse modes differ for different
Resonance
Subcompact car produced by American Motors Corporation
as its corporate race livery. Dick Arons built the engines. The team "transformed the brand's staid grocery-getter reputation from the ground up into that
AMC_Gremlin
Cancer of the colon or rectum
present. Eventually, a cell line acquires a mutation in the TP53 gene and transforms the tissue from a benign epithelial tumor into an invasive epithelial
Colorectal_cancer
Russian nuclear energy research and development laboratory
endorsed the invasion, claiming that the neighboring country had been transformed "primarily due to the efforts of our Western partners, into a neo-Nazi
Kurchatov_Institute
Magnetic phenomenon
to 37% (1/e) of its initial value after its generation by tipping the longitudinal magnetization towards the magnetic transverse plane. Hence the relation
Spin–spin_relaxation
Property of a charged particle beam
direction. Motion along this design trajectory is referred to as the longitudinal axis, and the two axes perpendicular to this trajectory (usually oriented
Beam_emittance
Secular meditation practice
indicate that mindfulness promotes prosocial behaviour although more longitudinal studies are needed to confirm this. Difficult experiences encountered
Mindfulness
First-person shooter
Burkhardt, Johanna; Lenhard, Wolfgang (2022). "A Meta-Analysis on the Longitudinal, Age-Dependent Effects of Violent Video Games on Aggression". Media Psychology
Doom_(1993_video_game)
Sauropod dinosaur genus from the late Jurassic Period
have denticles. It was somewhat spatulate (spoon-shaped), and had a longitudinal ridge. Each dentary had space for about fourteen teeth. The maxillary
Brachiosaurus
1974 James Bond film by Guy Hamilton
a broken bridge and spinning around 360 degrees in mid-air about the longitudinal axis, doing an "aerial twist"; Willert successfully completed the jump
The Man with the Golden Gun (film)
The_Man_with_the_Golden_Gun_(film)
Elementary particle involved with rest mass
the SU(2) and U(1) gauge bosons (the Higgs mechanism) to become the longitudinal components of the now-massive W and Z bosons of the weak force. The remaining
Higgs_boson
Device that emits light via optical amplification
divergence to concentrate their power at a great distance. Temporal (or longitudinal) coherence implies a polarized wave at a single frequency, whose phase
Laser
Type of sexual assault involving sexual intercourse without consent
2011.622355. PMID 22126112. S2CID 20570694. Foubert J.D. (2000). "The Longitudinal Effects of a Rape-prevention Program on Fraternity Men's Attitudes, Behavioral
Rape
Reversible transition in amorphous materials
series whose physical interpretation consists of a superposition of longitudinal and transverse waves of atomic displacement with varying directions and
Glass_transition
Evaluation by peers with similar expertise
Good Development Thing: A Longitudinal Analysis of Peer Review and Authority in Undergraduate Writing," conducted a longitudinal study comparing two groups
Peer_review
Cathedral church in Venice, Italy
double-tiered arcades surrounded the interior on all sides. In contrast, the longitudinal axis was emphasized to create a space appropriate for processions associated
St_Mark's_Basilica
Abnormal condition of the mind
adjusted association hardly decays with time: a meta-analysis on 59 longitudinal/prospective studies with 443 313 participants". Psychological Medicine
Psychosis
E and B modes (Polarisation)
dispersion relation: It is partly transverse (with E1⊥B0) and partly longitudinal. There are two directions in a polarization pattern - its orientation
Polarization_(cosmology)
Major earthquake in Northern California
retrofitted to the Cypress Viaduct in 1977. The added elements were longitudinal restraints at transverse expansion joints in the box girder spans, but
1989_Loma_Prieta_earthquake
Optical device with parallel mirrors
Physically, the Airy distribution is the sum of mode profiles of the longitudinal resonator modes. Starting from the electric field E c i r c {\displaystyle
Fabry–Pérot_interferometer
Monochrome light beam whose amplitude envelope is a Gaussian function
coordinate ρ = r / w 0 {\displaystyle \rho =r/w_{0}} and the normalized longitudinal coordinate Z = z / z R {\displaystyle Z=z/z_{\mathrm {R} }} as follows:
Gaussian_beam
Skeletal disorder
Other Features of the Female Athlete Triad in Elite Endurance Runners: A Longitudinal and Cross-Sectional Observational Study". International Journal of Sport
Osteoporosis
Rapid transit system in Bengaluru, Karnataka, India
Features include stainless steel body fully air-conditioned coaches, longitudinal bank of wide seats, wide vestibules between coaches, non-skid and non-slip
Namma_Metro
Aesthetic assessment of physical traits
subjective to the eye of the beholder. Recent results from the Wisconsin Longitudinal Study confirmed the positive link between psychological well-being and
Physical_attractiveness
Rigid organs of the skeleton of vertebrates
the marrow cavity, chondrocytes multiply and arrange themselves into longitudinal columns of flattened lacunae. Zone of cell hypertrophy. Next, the chondrocytes
Bone
Type of therapy to improve mental health
Richey JA (2007). "Anxiety Sensitivity Amelioration Training (ASAT): a longitudinal primary prevention program targeting cognitive vulnerability". Journal
Cognitive_behavioral_therapy
Large flightless bird endemic to Australia
responded by throwing a boomerang, severing the arms of the man and transforming him into a flightless emu. The Kurdaitcha man of Central Australia is
Emu
Aircraft without any human pilot on board
images of various landslide features, such as transverse, radial, and longitudinal cracks, ridges, scarps, and surfaces of rupture, even in inaccessible
Unmanned_aerial_vehicle
Physics concept expressed as E = mc²
direction as well. Lorentz in 1904 gave the following expressions for longitudinal and transverse electromagnetic mass: m L = m 0 ( 1 − v 2 c 2 ) 3 , m
Mass–energy_equivalence
Theoretical framework in physics
that at high energy, the amplitude for emission or absorption of a longitudinally polarized massive gauge boson becomes equal to the amplitude for emission
Quantum_field_theory
Lower torso of the human body
The anterior sacrococcygeal ligament is an extension of the anterior longitudinal ligament (ALL) that run down the anterior side of the vertebral bodies
Pelvis
Color reproduction capability
many systems. However, as optoelectronic technology matures, single-longitudinal-mode diode lasers are becoming less expensive, and many applications
Gamut
conventional interferometer. The spectrum is reconstructed taking the Fourier transform of the recorded interferogram. Similar to other cavity enhanced spectroscopic
Incoherent broad-band cavity-enhanced absorption spectroscopy
Incoherent_broad-band_cavity-enhanced_absorption_spectroscopy
Marine phylum of animals often with radial symmetries
like the Apodida lack tube feet and canals along the body; others have longitudinal canals. The arrangement in crinoids is similar to that in asteroids,
Echinoderm
Family of flowering plants
dorsifixed, or basifixed with poricide dehiscence or through small longitudinal cracks. The stamen's filament can be filiform or flat. The stamens can
Solanaceae
Structure at the rear of the vertebrate brain, beneath the cerebrum
narrow in the mediolateral direction, but much more extended in the longitudinal direction. Different markers generate different sets of stripes, the
Cerebellum
Developmental disorder
"Risk factors for conduct disorder and delinquency: Key findings from longitudinal studies". The Canadian Journal of Psychiatry. 55 (10): 633–642. doi:10
Conduct_disorder
2009–2010 pandemic of swine influenza caused by H1N1 influenza virus
characteristics of 2009 (H1N1) pandemic influenza based on paired sera from a longitudinal community cohort study". PLOS Medicine. 8 (6) e1000442. doi:10.1371/journal
2009_swine_flu_pandemic
Species of insect
as a commensal of humans. Adults are gray to black, with four dark, longitudinal lines on the thorax, slightly hairy bodies, and a single pair of membranous
Housefly
Minor basilica in Bogotá, Colombia
Heart of Jesus. The basilica is built in the Neo-baroque style, with a longitudinal nave, 16 side chapels, and a transept. At the crossing rises a double
Basilica of the Sacred Heart of Jesus, Bogotá
Basilica_of_the_Sacred_Heart_of_Jesus,_Bogotá
Classification of irreducible representations of the Poincaré group
introduction of transversely and longitudinally-polarized photons, and of the related concept of transverse and longitudinal structure functions, when considering
Wigner's_classification
City in Merseyside, England
and is known as one of the first cathedrals to break the traditional longitudinal design. In the 21st century, many parts of Liverpool's city centre have
Liverpool
Class of marine invertebrates
grooves separated by five wider interambulacral areas. Each of these ten longitudinal columns consists of two sets of plates (thus comprising 20 columns in
Sea_urchin
Genus of gastropods
restricted to a smaller number of species than formerly, most of which have longitudinal black lines on the mantle. Many former members of Chromodoris were transferred
Chromodoris
Nuclear magnetic resonance spectroscopy effect
was awarded the 1991 Nobel Prize in Chemistry for developing Fourier transform and two-dimensional NMR spectroscopy, which was soon adapted to the measurement
Nuclear_Overhauser_effect
Infectious disease
COVID-19 pandemic on tuberculosis control in Indonesia: a nationwide longitudinal analysis of programme data". The Lancet Global Health. 11 (9): e1412–e1421
Tuberculosis
Insects of the order Blattodea
hind wings, which are used in flight. All four wings have branching longitudinal veins, as well as multiple cross-veins. The three pairs of legs are sturdy
Cockroach
Human disease
type 18. The Ludwig-McGill HPV Cohort is one of the world's largest longitudinal studies of the natural history of human papillomavirus (HPV) infection
Human papillomavirus infection
Human_papillomavirus_infection
Central nervous system stimulant
December 2006. Halkitis PN, Pandey Mukherjee P, Palamar JJ (2008). "Longitudinal Modeling of Methamphetamine Use and Sexual Risk Behaviors in Gay and
Methamphetamine
Capital and largest city of Bangladesh
Nazimud-Doula, S.; Rezawana, N. (2010). Social Formation in Dhaka, 1985-2005: A Longitudinal Study of Society in a Third World Megacity. Routledge. pp. 6, 12.
Dhaka
Dwarf planet in the Kuiper belt
and cosmic rays, which break down the methane and trigger photochemical reactions. These photochemical reactions can cascade: transforming methane into
Makemake
Major river in the western United States and Mexico
& Cushing 2005, p. 490. Pitlick, John; Cress, Robert (March 2000). "Longitudinal Trends in Channel Characteristics of the Colorado River and Implications
Colorado_River
Fundamental color in color mixing
His spherical model of colors equally spaced red, yellow, and blue longitudinally with orange, green, and violet between them, and white and black at
Primary_color
reformat, reformation, reformatory, transform, transformable, transformation, transformational, transformative, triform, triformity, uniform, uniformity
List of Latin words with English derivatives
List_of_Latin_words_with_English_derivatives
Reptiles of the superfamily Chelonioidea
determine their position relative to a goal with both latitudinal and longitudinal information, and requires the detection and interpretation of more than
Sea_turtle
which is subjected to an external load applied perpendicularly to a longitudinal axis of the element. bending moment The reaction induced in a structural
Glossary_of_physics
interventions on travel behaviour and health: Results from a five-year longitudinal travel survey in Outer London". Journal of Transport & Health. 35 101771
2024_in_science
Rapid transit system in the US
June 10, 2025. Williams, Elliot (April 19, 2019). "This Local Artist Transforms DC Metro Stations Into Beautiful Nature Scenes". Washingtonian. Archived
Washington_Metro
Japanese anime television series
consumed by frequent alien use of Inflation Drive technology. Three giant longitudinal rings surround what is dubbed as the Quantum Core, and ruins exist upon
Divergence_Eve
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
Girl/Female
American, German, Hebrew, Latin, Scandinavian
Female Sheep; Ewe; Nickname of Rachel
Boy/Male
American, Australian, British, Christian, English, German
Gray-haired
Girl/Female
Scandinavian American
Doe.
Male
Scandinavian
 Variant spelling of Scandinavian Kai, CAY means "lord." Compare with another form of Cay.
Boy/Male
English Teutonic Biblical Sanskrit
Ram.
Girl/Female
Australian, Christian
Sunshine; Bright; Day
Male
Hebrew
 Variant spelling of Hebrew Rav, RAB means "great" or "teacher." Compare with another form of Rab.
Surname or Lastname
English
English : variant spelling of Ray 1–4.
Male
English
Short form of English Raymond, RAY means "wise protector."
Female
English
 English name derived from the vocabulary word, DAY means "day." Feminine form of Middle English Daye, meaning "day."
Boy/Male
American, British, Christian, Danish, English, Finnish, French, German, Gujarati, Hindu, Indian, Kannada, Latin, Malayalam, Marathi, Scottish, Swedish, Tamil, Telugu
Regal; Counsellor; Abbreviation of Raymond; Advice; Beam of Light; Grace; Well Advised Protector; Wise Protector; Dear Brook; Abbreviation of R
Boy/Male
Indian, Telugu
Lord Ram
Boy/Male
Hindu
Beam of light
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : nickname denoting someone who behaved in a regal fashion or who had earned the title in some contest of skill or by presiding over festivities, from Old French rey, roy ‘king’. Occasionally this was used as a personal name.English : nickname for a timid person, from Middle English ray ‘female roe deer’ or northern Middle English ray ‘roebuck’.English : variant of Rye (1 and 2).English : habitational name, a variant spelling of Wray.Scottish : reduced and altered form of McRae.French : from a noun derivative of Old French raier ‘to gush, stream, or pour’, hence a topographic name for someone who lived near a spring or rushing stream, or a habitational name from a place called Ray.Indian : variant of Rai.
Boy/Male
Shakespearean
Henry VI, Part 2' Lord Say.
Female
English
English name derived from the vocabulary word, GAY means "happy." Compare with masculine Gay.
Boy/Male
Scottish American Latin French German English
Grace.
Female
English
English name, possibly derived from the vocabulary word ray, RAE means "sunbeam."
Female
Hebrew
(רֵעַ) Hebrew name RAYA means "friend." Compare with another form of Raya.
Male
English
Variant spelling of English Ray, RAE means "wise protector."Â
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
Boy/Male
Arabic, Muslim
Full Moon
Girl/Female
Arabic
Invention; Discovery
Boy/Male
British, English
From the Stone Fortification
Surname or Lastname
English (West Midlands)
English (West Midlands) : unexplained.German : variant of Roden.
Boy/Male
French American English
Prosperous protector. A FrenchOld English name Eadmund, meaning rich or happy, and protection.
Boy/Male
Hindu, Indian
Full of Light
Female
Egyptian
, a priestess of the goddess Nut.
Boy/Male
Muslim
Ways, Paths, Pieces, Parts
Male
English
Variant spelling of English Mattaniah, MATANIA means "gift of God."Â
Girl/Female
Muslim
Good health
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
LONGITUDINAL RAY-TRANSFORM
n.
One of a number of lines or parts diverging from a common point or center, like the radii of a circle; as, a star of six rays.
n.
A railway sleeper lying parallel with the rail.
a.
Extending in length; in the direction of the length; running lengthwise, as distinguished from transverse; as, the longitudinal diameter of a body.
a.
Of or pertaining to the laity, as distinct from the clergy; as, a lay person; a lay preacher; a lay brother.
n.
A line of light or heat proceeding from a radiant or reflecting point; a single element of light or heat propagated continuously; as, a solar ray; a polarized ray.
n.
The longitudinal guides, or guiding surfaces, on the bed of a planer, lathe, or the like, along which a table or carriage moves.
n.
Length of space; distance; interval; as, a great way; a long way.
superl.
Gray-haired; gray-headed; of a gray color; hoary.
n.
To send forth or shoot out; to cause to shine out; as, to ray smiles.
n.
A longitudinal sleeper.
n.
A crack, or longitudinal fissure.
v. i.
To shine, as with rays.
a.
Having four prominent longitudinal angles.
a.
Of or pertaining to longitude or length; as, longitudinal distance.
n.
Right of way. See below.
n.
One of a system of diverging lines passing through a point, and regarded as extending indefinitely in both directions. See Half-ray.
n.
In a restricted sense, any of the broad, flat, narrow-tailed species, as the skates and sting rays. See Skate.
n.
One of the component elements of the total radiation from a body; any definite or limited portion of the spectrum; as, the red ray; the violet ray. See Illust. under Light.
n.
The merrymaking of May Day.
a.
Striped longitudinally.