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Mathematical concept
In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes
Spectral_gap
Conjecture in ergodic theory
mathematics, the spectral gap conjecture of Alexander Lubotzky, Ralph S. Phillips, and Peter Sarnak is a statement on the spectral gaps of certain actions
Spectral_gap_conjecture
Energy difference between ground and first excited states
mechanics, the spectral gap of a system is the energy difference between its ground state and its first excited state. The mass gap is the spectral gap between
Spectral_gap_(physics)
Millennium Prize Problem
The general problem of determining the presence of a mass gap (a special case of a spectral gap) in a system is known to be undecidable, meaning no computer
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Proven conjecture in probability theory
In probability theory, Aldous' spectral gap conjecture is the statement that two Markov chains associated to a graph, namely the random walk and the interchange
Aldous' spectral gap conjecture
Aldous'_spectral_gap_conjecture
Difference between successive eigenvalues
or noise in the data. In spectral clustering, the eigengap is often referred to as the spectral gap; although the spectral gap may often be defined in
Eigengap
Binary operation in graph theory
graph can be measured by its spectral gap, with an important property of the zigzag product the preservation of the spectral gap. That is, if H {\displaystyle
Zig-zag_product
Sparse graph with strong connectivity
is the degree of the vertices of G. The spectral gap of G is defined to be d − λ2, and it measures the spectral expansion of the graph G. If we set λ =
Expander_graph
Forbidden energy state in solid state physics
an energy gap is often known more abstractly as a spectral gap, a term which need not be specific to electrons or solids. If an energy gap exists in the
Energy_gap
Linear algebra aspects of graph theory
the graph G is d-regular, there is a relationship between h(G) and the spectral gap d − λ2 of G. An inequality due to Dodziuk and independently Alon and
Spectral_graph_theory
Computational problems no algorithm can solve
belongs to Rn+1. Determining whether a quantum mechanical system has a spectral gap. In the ray tracing problem for a 3-dimensional system of reflective
List_of_undecidable_problems
Short-term auditory illusion
as follows: while listening to broadband noise ("white noise") with a spectral gap, if it is switched off, a faint tone lasting for several seconds can
Zwicker_tone
Type of quantum information processing
the gap in the energy eigenvalues (spectral gap) of the Hamiltonian. Specifically, if the system is to be kept in the ground state, the energy gap between
Adiabatic_quantum_computation
Electromagnetic effect in physics
electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy
Quantum_Hall_effect
Largest absolute value of an operator's eigenvalues
iteration Spectral gap The Joint spectral radius is a generalization of the spectral radius to sets of matrices. Spectrum of a matrix Spectral abscissa
Spectral_radius
Eigenvalue algorithm
section). In other words, convergence is exponential with base being the spectral gap. The power iteration algorithm starts with a vector b 0 {\displaystyle
Power_iteration
Spectral graph theory concept
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal
Ramanujan_graph
Square matrix used to represent a graph or network
_{1}-\lambda _{2}} is called the spectral gap and it is related to the expansion of G. It is also useful to introduce the spectral radius of A {\displaystyle
Adjacency_matrix
South African-born mathematician
Faculty, 2007–present, Institute for Advanced Study Sarnak, P. (1982). "Spectral Behavior of Quasi Periodic Potentials". Commun. Math. Phys. 84 (3): 377–401
Peter_Sarnak
Constant in Riemannian geometry
2a(n-1)h(M)+10h^{2}(M).} Cheeger constant (graph theory) Isoperimetric problem Spectral gap Cheeger 1971. Brooks 1981. Buser 1978. Buser 1982. Brooks, Robert (1981)
Cheeger_constant
Mathematical inequality in Sobolev space theory
{\displaystyle R^{s}} as a result. Friedrichs' inequality Korn's inequality Spectral gap Poincaré, H. (1890). "Sur les Equations aux Dérivées Partielles de la
Poincaré_inequality
S2CID 815023. Hastings, Matthew B.; Koma, Tohru (22 April 2006). "Spectral Gap and Exponential Decay of Correlations". Communications in Mathematical
Gapped_Hamiltonian
Electronic method of transmitting information with a carrier wave
sideband appears at higher frequency. This initial translation creates a spectral gap (in the speech example, from 1.7 kHz to 2.3 kHz), which simplifies low-pass
Single-sideband_modulation
Measure of whether or not a graph has a "bottleneck"
spectral gap of the Laplacian matrix of the graph. The Cheeger inequality is a fundamental result and motivation for spectral graph theory. Spectral graph
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Structure used in waveguides
Rutgers University. Osting, B. (2012). "Bragg structure and the first spectral gap". Applied Mathematics Letters. 25 (11): 1926–1930. doi:10.1016/j.aml
Distributed_Bragg_reflector
Graph defined from a mathematical group
use Cheeger's inequality to bound the edge expansion ratio using the spectral gap. Representation theory can be used to construct such expanding Cayley
Cayley_graph
Statistical description for the behavior of fermions
fermion, provided it is in a neighbourhood of positive spectral density. In the case of a spectral gap, such as for electrons in a semiconductor, the point
Fermi–Dirac_statistics
Matrix representation of a graph
the 0 eigenvalue. The smallest non-zero eigenvalue of L is called the spectral gap. The second smallest eigenvalue of L (could be zero) is the algebraic
Laplacian_matrix
Type of mathematical group
established via the notion of cusp form. The spectral gap of the surface S {\displaystyle S} is by definition the gap between the smallest eigenvalue λ 0 = 0
Arithmetic_Fuchsian_group
Quantum algorithm
steps on the graph, where the parameter δ {\displaystyle \delta } is the spectral gap associated to the stochastic matrix P {\displaystyle P} of the graph
Quantum_walk_search
μ {\displaystyle \mu } as an invariant measure, but also possesses a spectral gap that is independent of the dimension of H {\displaystyle {\mathcal {H}}}
Preconditioned Crank–Nicolson algorithm
Preconditioned_Crank–Nicolson_algorithm
221 Singmaster's conjecture binomial coefficients David Singmaster 8 Spectral gap conjecture ergodic theory Standard conjectures on algebraic cycles algebraic
List_of_conjectures
Basic circuit in quantum computing
theory methods and/or relation to (approximate) unitary t-designs. The spectral gap conjecture, if true, would imply that a generically chosen set of quantum
Quantum_logic_gate
Austrian mathematician
Society. In 2008 he was an invited speaker (Effective equidistribution and spectral gap) at the European Mathematical Congress in Amsterdam. In 2010 he was an
Manfred_Einsiedler
Classification of stars based on spectral properties
stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by
Stellar_classification
Material designed to manipulate sound waves
sonic crystals, which exhibit spectral gaps two orders of magnitude smaller than the wavelength of sound. The spectral gaps prevent the transmission of
Acoustic_metamaterial
Israeli mathematician and theoretical physicist (born 1980)
ISSN 0179-5376. S2CID 16096886. Eldan, Ronen (22 March 2013). "Thin Shell Implies Spectral Gap Up to Polylog via a Stochastic Localization Scheme". Geometric and Functional
Ronen_Eldan
Energy range in a solid where no electron states exist
solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states
Band_gap
Analog of the continuous Laplace operator
American Mathematical Society. pp. 51–86. ISBN 978-0-8218-9384-5. Ollivier, Yann (2004). "Spectral gap of a graph". Archived from the original on 2007-05-23.
Discrete_Laplace_operator
Soviet mathematician
of spectral gaps. In the early 1960s, while studying this inverse spectral problem for Schrödinger operators with a finite number of spectral gaps, he
Naum_Akhiezer
Northern Irish mathematician
(2022). "A random cover of a compact hyperbolic surface has relative spectral gap 3/16 − ε". Geometric and Functional Analysis. 32 (3): 595–661. arXiv:2003
Michael_Magee_(mathematician)
2009 non-fiction book discussing mathematics
The final chapter of this part discusses the connection between the spectral gap of a Markov chain and its mixing time. The second part of the book includes
Markov Chains and Mixing Times
Markov_Chains_and_Mixing_Times
American award for mathematical analysis
in a novel direction." Including: 1. Semyon Dyatlov and Joshua Zahl, Spectral gaps, additive energy, and a fractal uncertainty principle. Geometric and
Bôcher_Memorial_Prize
Speed limit of quantum information
MR 0312860. S2CID 122298337. Hastings, Matthew B.; Koma, Tohru (2006-04-22). "Spectral Gap and Exponential Decay of Correlations". Communications in Mathematical
Lieb–Robinson_bounds
spectral gap results. The spectrum in question is that of the Laplacian matrix associated to a family of quotients of a discrete group Γ; and the gap
Superstrong_approximation
2010 Sorin Popa for "On the superrigidity of malleable actions with spectral gap," J. Amer. Math. Soc. (2008) 2013 Michael J. Larsen and Richard Pink
E. H. Moore Research Article Prize
E._H._Moore_Research_Article_Prize
in S to the number of vertices in S. 4. The spectral expansion of a d-regular graph G is the spectral gap between the largest eigenvalue d of its adjacency
Glossary_of_graph_theory
vehicle speed and load. Additionally, the lack of engine noise leaves a spectral gap (empty space) between wind and road noise and amplifies individual vehicle
Active_sound_design
American mathematician
Graduate Center of the City University of New York known for his work in spectral problems in number theory, probability, and Arithmetic combinatorics. He
Alexander_Gamburd
Hungarian mathematician (born 1982)
Princeton University, where he defended his thesis Random walks and spectral gaps in linear groups in 2011 under the supervision of Jean Bourgain. He
Péter_Varjú
depends upon the system. This spectral gap condition requires that the spectrum of A {\displaystyle A} must contain large gaps to be guaranteed of existence
Inertial_manifold
Theorem in quantum information theory
the length of the gate sequence optimal up to a constant factor. The spectral gap conjecture, if true, would imply that it is possible to take c = 1 {\displaystyle
Solovay–Kitaev_theorem
\lambda )} -graphs form a family of expander graphs with a constant spectral gap. Let G = ( V , E ) {\displaystyle G=(V,E)} be an ( n , d , λ ) {\displaystyle
Expander_mixing_lemma
American mathematician
Michigan (Ph.D.) UCLA Known for Lumer-Phillips theorem Scattering theory Spectral gap conjecture Awards Leroy P. Steele Prize (1997) Scientific career Fields
Ralph_S._Phillips
Potential cancer therapy using ultrasound harmonic excitation
membrane and nuclear envelope. A modal analysis reveals the existence of a spectral gap between the resonant growth rates of healthy and cancerous cells along
Oncotripsy
Romanian-American mathematician
Popa, Sorin (2008). "On the superrigidity of malleable actions with spectral gap". Journal of the American Mathematical Society. 21 (4): 981–1000. arXiv:math/0608429
Sorin_Popa
Energy difference between ground state and lightest excited state(s)
In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy
Mass_gap
Feature of the Hertzsprung-Russell diagram
regions to the gap. The gap is named after Ejnar Hertzsprung, who first noticed a gap in the Hertzsprung–Russell diagram between A5 and G0 spectral type and
Hertzsprung_gap
2003 mathematics text
r} . The spectral expansion of the graph is defined from the difference between the largest and second-largest eigenvalues, the spectral gap, which controls
Elementary Number Theory, Group Theory and Ramanujan Graphs
Elementary_Number_Theory,_Group_Theory_and_Ramanujan_Graphs
Stellar classification
dwarf") is a main-sequence (core hydrogen-burning) star of spectral type K. The spectral luminosity class is V. These stars are intermediate in size
K-type_main-sequence_star
Engineering the global environment of Venus to make it suitable for humans
"escape" to space through partially transparent atmospheric "windows" – spectral gaps between strong CO2 and H2O absorption bands in the near infrared range
Terraforming_of_Venus
Stellar classification
A G-type main-sequence star is a main-sequence star of spectral type G. The spectral luminosity class is V. Such a star has about 0.9 to 1.1 solar masses
G-type_main-sequence_star
Function used in signal processing
coefficients and expansion order, the GAP window can mimic all the known window functions, reproducing accurately their spectral properties. w 0 [ n ] = a 0 +
Window_function
Periodicity computation method
Least-squares spectral analysis (LSSA) is a class of methods for estimating a frequency spectrum by fitting sinusoids to data using a least-squares fit
Least-squares spectral analysis
Least-squares_spectral_analysis
Photographic light source capable of producing sub-microsecond light flashes
energy discharge. Since the spark gap discharges in air generating a plasma, the spectrum shows both a continuum and spectral lines, mainly of nitrogen since
Air-gap_flash
Russian mathematician
on the theory of positive operators, in particular results in which spectral gaps were estimated. His work on integral operators and superposition operators
Mark_Krasnoselsky
Concept relating to waves and signals
discrete set over the independent variable, with band gaps between pairs of spectral bands or spectral lines. The classical example of a continuous spectrum
Spectrum_(physical_sciences)
Spectral density of light emitted by a black body
In physics, Planck's law (also Planck radiation law) describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium
Planck's_law
Scatter plot of stars showing the relationship of luminosity to stellar classification
the main sequence by the Hertzsprung gap, populated by subgiants and located in the region between A5 and G0 spectral type and between +1 and −3 absolute
Hertzsprung–Russell_diagram
Polynomial Matrix Spectral Factorization or Matrix Fejer–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices. Polynomial
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
Dim, low mass stars on the main sequence
the Sun, with masses about 7.5% that of the Sun. These red dwarfs have spectral types of L0 to L2. There is some overlap with the properties of brown dwarfs
Red_dwarf
American engineer and intelligent design advocate (born 1950)
interesting multidimensional construction ... exploit[s] the [required] spectral gaps that occur when sampling multidimensional signals. Their approach is
Robert_J._Marks_II
Stellar classification
main-sequence star is a main-sequence (core hydrogen burning) star of spectral type A. The spectral luminosity class is V. These stars have spectra defined by strong
A-type_main-sequence_star
Transparent optical element with flat, polished surfaces that refract light
dispersive prism can be used to break white light up into its constituent spectral colors (the colors of the rainbow) to form a spectrum as described in the
Prism_(optics)
Moon of Saturn
and orbits within the Encke Gap in Saturn's A Ring. Pan is a ring shepherd and is responsible for keeping the Encke Gap free of ring particles. It is
Pan_(moon)
Stellar classification
main-sequence star is a main-sequence, core-hydrogen-fusing star of spectral type F. The spectral luminosity class is V. They have from around 1.1 to 1.6 times
F-type_main-sequence_star
Range 300-3000 GHz of the electromagnetic spectrum
materials of interest have unique spectral "fingerprints" in the terahertz range. This offers the possibility to combine spectral identification with imaging
Terahertz_radiation
Light emitted by the Sun
change. Since 2003, the SORCE Spectral Irradiance Monitor (SIM) has monitored Spectral solar irradiance (SSI) – the spectral distribution of the TSI. Data
Sunlight
which the spectral lines of an alloy are broadened by the random distribution of atoms within the alloy. It is one of a number of spectral line broadening
Alloy_broadening
Illustrative organization of color hues
circle based on spectral wavelengths appears with red at one end of the spectrum and is 100% mixable violet at the other. A wedge-shaped gap represents colors
Color_wheel
Type of star larger than main-sequence but smaller than a giant
in the Hertzsprung Gap and are likely evolutionary subgiants, but both are often assigned giant luminosity classes. The spectral classification can be
Subgiant
Substellar object
can fuse lithium (7Li). Astronomers classify self-luminous objects by spectral type, a distinction intimately tied to the surface temperature -- brown
Brown_dwarf
Range of frequencies or wavelengths of electromagnetic radiation
radiation Optical window Ozone layer Radiant energy Radiation Radio window Spectral imaging Spectroscopy V band W band Mehta, Akul (25 August 2011). "Introduction
Electromagnetic_spectrum
Type of polarizer
are available with divergence angles from less than 1° to about 45°. The spectral range of operation depends on the selected birefringent material and its
Wollaston_prism
Study of underwater depth of lake or ocean floors
produced by hyper-spectral (HS) sensors tend to range between 100 and 200 spectral bands of approximately 5–10 nm bandwidths. Hyper-spectral sensing, or imaging
Bathymetry
Main-sequence star of spectral type O
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
O-type_main-sequence_star
Applied Spectral Imaging or ASI is a multinational biomedical company that develops and manufactures microscopy imaging and digital analysis tools for
Applied_Spectral_Imaging
Types of noise
power spectral density Gaussian noise, with a probability density function equal to that of the normal distribution Pink noise, with spectral density
Noise_(spectral_phenomenon)
Continuous band of stars that appears on plots of stellar color versus brightness
red giant, or directly to a white dwarf. Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main
Main_sequence
Area of the Solar System beyond the planets, comprising small bodies
its own unique spectroscopic signature, and by reading an object's full spectral "fingerprint", astronomers can determine its composition. Analysis indicates
Kuiper_belt
Self-adjoint operator that arises in physical transition problems
(It is known that almost surely can not be replaced by surely.) That the spectral measures are singular when λ ≥ 1 {\displaystyle \lambda \geq 1} follows
Almost_Mathieu_operator
Brightest star in the constellation Auriga
hotter and of spectral class G0III; it is 72.7±3.6 times as luminous as the Sun and 8.83±0.33 times its radius. It is in the Hertzsprung gap, corresponding
Capella
Deep-red spectral line of hydrogen
deep-red visible spectral line of the hydrogen atom with a wavelength of 656.28 nm in air and 656.46 nm in vacuum. It is the first spectral line in the Balmer
Hydrogen-alpha
Semiconductor light source
emit light. Unlike a laser, the light emitted from an LED is neither spectrally nor spatially coherent nor even highly monochromatic. Its spectrum is
Light-emitting_diode
US military surveillance aircraft
updated from EQ. Features a new sensor turret with high definition, multi-spectral imaging, full-motion video camera, offering better range from previous
Pilatus_U-28_Draco
Effect of a hole in a camera causing excess diffusion of light and overexposure
A light leak is a hole or gap in the body of a camera, or other optical instrument, where light is able to "leak" into the normally light-tight chamber
Light_leak
Stellar classification distinguished by bright blue luminosity
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
B-type_main-sequence_star
Black hole formed by a collapsed star
"upper" mass gaps, roughly representing the ranges of 2 to 5 and 50 to 150 solar masses (M☉), respectively. Another range given for the upper gap is 52 to
Stellar_black_hole
Stellar core remnant
Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. This would become known as the first white dwarf. The
White_dwarf
Chemical element with atomic number 91 (Pa)
naming in 1949. The discovery of protactinium completed one of the last gaps in early versions of the periodic table, and brought fame to the involved
Protactinium
SPECTRAL GAP
SPECTRAL GAP
Girl/Female
Bengali, Indian, Modern
Special
Girl/Female
Bengali, Indian, Telugu
Special
Girl/Female
Indian
Special
Girl/Female
Hindu, Indian, Tamil
Special
Girl/Female
Greek, Indian, Marathi, Turkish
Special
Boy/Male
Hindu, Indian
Special
Boy/Male
Indian
Special
Boy/Male
Hindu
Special
Girl/Female
Indian
Special
Girl/Female
Hindu, Indian, Tamil
Special
Boy/Male
Tamil
Special
Boy/Male
Hindu, Indian
Special
Boy/Male
Tamil
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Special
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Tamil, Telugu
Special
Girl/Female
Hindu, Indian, Tamil
Special
Girl/Female
Indian, Telugu
Special
Girl/Female
Tamil
Special
Boy/Male
Hindu, Indian
Special
Boy/Male
Indian, Telugu
Special
Girl/Female
Bengali, Indian, Telugu
Special
SPECTRAL GAP
SPECTRAL GAP
Surname or Lastname
English
English : variant of Shreeves.
Girl/Female
Indian
Beautiful, Lovely
Male
Russian
Variant spelling of Russian Innokentiy, INNOKENTI means "harmless, innocent."
Boy/Male
Hindu
Beloved
Girl/Female
British, English
Mud
Boy/Male
American, British, English
Safety
Female
Hebrew
(מֵ×ִירָה) Feminine form of Hebrew Meir, MEIRA means "giving light."
Girl/Female
Indian, Sanskrit
Shining Forth
Boy/Male
Latin
Dragon.
Boy/Male
Muslim
Graceful, Good looking
SPECTRAL GAP
SPECTRAL GAP
SPECTRAL GAP
SPECTRAL GAP
SPECTRAL GAP
n.
A clasp or a cross worn on the breast.
a.
Relating to, or good for, diseases of the chest or lungs; as, a pectoral remedy.
a.
Limited in range; confined to a definite field of action, investigation, or discussion; as, a special dictionary of commercial terms; a special branch of study.
a.
Of or pertaining to the breast, or chest; as, the pectoral muscles.
a.
Having the breast conspicuously colored; as, the pectoral sandpiper.
n.
A medicine for diseases of the chest organs, especially the lungs.
pl.
of Spectrum
a.
Of or pertaining to a specter; ghosty.
n.
A luminous appearance, or an image seen after the eye has been exposed to an intense light or a strongly illuminated object. When the object is colored, the image appears of the complementary color, as a green image seen after viewing a red wafer lying on white paper. Called also ocular spectrum.
a.
Of or pertaining to the spectrum; made by the spectrum; as, spectral colors; spectral analysis.
n.
A breastplate, esp. that worn by the Jewish high person.
n.
A covering or protecting for the breast.
n.
One appointed for a special service or occasion.
a.
Appropriate; designed for a particular purpose, occasion, or person; as, a special act of Parliament or of Congress; a special sermon.
a.
Of or pertaining to a scepter; like a scepter.
n.
The tarsius, or spectral lemur.
n.
An apparition; a specter.
n.
The several colored and other rays of which light is composed, separated by the refraction of a prism or other means, and observed or studied either as spread out on a screen, by direct vision, by photography, or otherwise. See Illust. of Light, and Spectroscope.
adv.
In the form or manner of a specter.
a.
Of or pertaining to a sector; as, a sectoral circle.