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The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. The VMS framework has been
Variational_multiscale_method
of small parameters. VAM is the synergy of variational principles and asymptotic approaches. Variational principles are applied to the defined functional
Variational_asymptotic_method
Numerical method for solving physical or engineering problems
procedures. Examples of the variational formulation are the Galerkin method, the discontinuous Galerkin method, mixed methods, etc. A discretization strategy
Finite_element_method
form Smoothed finite element method Variational multiscale method List of finite element software packages Spectral method — based on the Fourier transformation
List of numerical analysis topics
List_of_numerical_analysis_topics
Probabilistic problem-solving algorithm
Carlo method". Monte Carlo Methods and Applications. 22 (1): 73–79. doi:10.1515/mcma-2016-0102. S2CID 30198383. Baeurle, Stephan A. (2009). "Multiscale modeling
Monte_Carlo_method
Partitioning a digital image into segments
speeds) in an approach called the generalized fast marching method. The goal of variational methods is to find a segmentation which is optimal with respect
Image_segmentation
Method of solving differential equations
(2002). "Multiscale scientific computation: review". In Timothy J. Barth; Tony Chan; Robert Haimes (eds.). Multiscale and multiresolution methods: theory
Multigrid_method
Measure of local oscillation behavior
- Variational, PDE, Wavelet, and Stochastic Methods, SIAM, ISBN 0-89871-589-X (with in-depth coverage and extensive applications of Total Variations in
Total_variation
D.; Singha, K.; Minsley, B. J.; Holbrook, W. S.; Slater, L. (2015). "Multiscale geophysical imaging of the critical zone: Geophysical Imaging of the Critical
Geophysical_imaging
Signal processing technique
forward-backward splitting". Multiscale Model Simul. 4 (4): 1168–200. doi:10.1137/050626090. S2CID 15064954. Hestenes, M; Stiefel, E (1952). "Methods of conjugate gradients
Compressed_sensing
Design method of discrete wavelet transforms
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms
Multiresolution_analysis
Simulation of multiple aspects of physics
variation of the stress and temperature distributions would be considered a multiphysics simulation. Multiphysics simulation is related to multiscale
Multiphysics_simulation
Cell from a primary tumor carried by blood circulation
PMID 21863182. Chen P, Huang YY, Hoshino K, Zhang X (February 2014). "Multiscale immunomagnetic enrichment of circulating tumor cells: from tubes to microchips"
Circulating_tumor_cell
Variation in the time intervals between heartbeats
pointwise correlation dimension, approximate entropy, sample entropy, multiscale entropy analysis, sample asymmetry and memory length (based on inverse
Heart_rate_variability
Neural network that learns efficient data encoding in an unsupervised manner
autoencoder, to be detailed below. Variational autoencoders (VAEs) belong to the families of variational Bayesian methods. Despite the architectural similarities
Autoencoder
Subfield of materials science
components, so do its computational sub-disciplines. While many methods and variations have been and continue to be developed, seven main simulation techniques
Computational materials science
Computational_materials_science
3D reconstruction technique
Martin-Brualla, Ricardo; Srinivasan, Pratul P. (2021-04-07). "Mip-NeRF: {A} Multiscale Representation for Anti-Aliasing Neural Radiance Fields". arXiv:2103.13415
Neural_radiance_field
German mathematician
Bethuel, Huisken, Steffen: Variational models for microstructure and phase transitions. In: Hildebrandt, Struwe: Calculus of Variations and geometric evolution
Stefan_Müller_(mathematician)
Mathematics award
contributions of Pierre de Fermat have been decisive: Statements of variational principles Foundations of probability and analytic geometry Number theory
Fermat_Prize
Measurement of small-scale features on surfaces
superimposed onto one another that deriving conclusions in a multiscale method is relevant. Multiscale analysis facilitates the understanding of relations between
Surface_metrology
Molecular simulation method
Chemistry for "the development of multiscale models for complex chemical systems". An important advantage of QM/MM methods is their efficiency. The cost of
QM/MM
Optimization algorithm
Andina, D. (2009). "Edge detection using ant colony search algorithm and multiscale contrast enhancement". 2009 IEEE International Conference on Systems,
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
French physicist
1991), then showed in 1995 that Ponte Castañeda's (1991) variational method is a secant method using the second moment by phase of local fields. In 1994
Pierre_Suquet
Global meteorological forecasting mathematical model
numerical weather prediction system containing a global computer model and variational analysis run by the United States' National Weather Service (NWS). The
Global_Forecast_System
Biomedical and genomics research institute in New York, US
neurodegeneration. The institute was formed in 2011 as the Institute for Genomics and Multiscale Biology, as part of Mount Sinai's Department of Genetics and Genomic Sciences
Icahn_Genomics_Institute
Carlo, Kinetic More-Carlo (KMC), and other methods. Contemporary numerical tools include also hybrid multiscale approaches allowing concurrent or sequential
Nanomechanics
Prediction of digital video quality
called Multiscale SSIM (MS-SSIM) is conducted over multiple scales through a process of multiple stages of sub-sampling, reminiscent of multiscale processing
Structural similarity index measure
Structural_similarity_index_measure
Classes of computational models
are related to multiscale modeling. One mathematical technique for multiscale modeling of nanomaterials is based upon the use of multiscale Green's function
Microscale and macroscale models
Microscale_and_macroscale_models
Computational quantum mechanical modelling method to investigate electronic structure
ground-state observables. The variational problems of minimizing the energy functional E[n] can be solved by applying the Lagrangian method of undetermined multipliers
Density_functional_theory
Active and non-equilibrium materials: DDM is increasingly used to quantify multiscale dynamics in active and out-of-equilibrium soft materials, including gels
Differential dynamic microscopy
Differential_dynamic_microscopy
Chemical reaction between a fuel and oxygen
equilibrium edge preimage curve method. A few variational approaches The Computational Singular perturbation (CSP) method and further developments. The
Combustion
Deep learning method
self-attention modules to the generator and discriminator. Variational autoencoder GAN (VAEGAN): Uses a variational autoencoder (VAE) for the generator. Transformer
Generative adversarial network
Generative_adversarial_network
Low-Density Gases
discrete velocity method applied to the Boltzmann equation or to its model is more efficient than the DSMC method. More recent multiscale kinetic approaches
Rarefied_gas_dynamics
Function used in signal processing
the design of finite impulse response filters, merging multiscale and multidimensional datasets, as well as beamforming and antenna design
Window_function
Function for integral Fourier-like transform
Jianhong (2005). Image processing and analysis: variational, PDE, wavelet, and stochastic methods. Philadelphia: Society for Industrial and Applied
Wavelet
Algorithm for measuring similarity between temporal sequences
Meinard Müller, Henning Mattes, and Frank Kurth (2006). An Efficient Multiscale Approach to Audio Synchronization. Proceedings of the International Conference
Dynamic_time_warping
Very small scale structure of material
107. Tahmasebi, Pejman; Sahimi, Muhammad (2018-06-29). "A stochastic multiscale algorithm for modeling complex granular materials". Granular Matter. 20
Microstructure
Synchrotron X-ray diffraction-based imaging technique
Dark-field X-ray microscopy (DFXM or DFXRM) is an imaging technique used for multiscale structural characterisation. It is capable of mapping deeply embedded
Dark-field_X-ray_microscopy
Academic association dedicated to the use of mathematics in industry
since 1991 SIAM Journal on Applied Dynamical Systems (SIADS), since 2002 Multiscale Modeling and Simulation (MMS), since 2003 SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
Society_for_Industrial_and_Applied_Mathematics
Computer graphics method
and non-local means filters. Techniques based on wavelets and other multiscale filters have been tried, which can handle the varying frequency characteristics
Path_tracing
Jianke; Zhang, Liang; Zhang, Hongwu (2022-03-01). "An adaptive multiscale finite element method for strain localization analysis with the Cosserat continuum
Metallurgical failure analysis
Metallurgical_failure_analysis
Process of removing noise from a signal
Abrishami-Moghaddam, H.; Ghadimi, S. (July 2008). "Locally adaptive multiscale Bayesian method for image denoising based on bivariate normal inverse Gaussian
Noise_reduction
Software for statistical analysis of molecular evolution
Monte Carlo Approximations of Classically Scaled Population Processes". Multiscale Modeling & Simulation. 16 (3): 1206–1226. arXiv:1512.01588. doi:10.1137/17M1138169
Molecular Evolutionary Genetics Analysis
Molecular_Evolutionary_Genetics_Analysis
Type of image noise
reduction in medical ultrasound images using a new multiscale bivariate Bayesian MMSE-based method," IEEE 15th Signal Processing and Communication Applications
Speckle_(interference)
Object categorization problem
that the transforms from one can be applied to another. Variational Bayesian methods Variational message passing Expectation–maximization algorithm Bayesian
One-shot learning (computer vision)
One-shot_learning_(computer_vision)
Technology for RNA sequencing
Grotewold, Erich; Thompson, Addie; Lundquist, Peter K (2023-10-31). "Multiscale physiological responses to nitrogen supplementation of maize hybrids"
BRB-seq
Computer simulations to discover and understand chemical properties
implementations Monte Carlo method Molecular design software Molecular mechanics Multiscale Green's function Car–Parrinello method Comparison of software for
Molecular_dynamics
Photoacoustic microscopy Photoacoustic effect Wang, Lihong V. (2009-08-29). "Multiscale photoacoustic microscopy and computed tomography". Nature Photonics. 3
Deep learning in photoacoustic imaging
Deep_learning_in_photoacoustic_imaging
Type of electron microscope
three-step, multiscale, multiresolution reconstruction method is presented that directly uses 2D images in order to develop 3D models. This method, based on
Scanning_electron_microscope
Sequence of data points over time
transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred
Time_series
Mathematical technique used in data compression and analysis
can be extended to two dimension, while a more general term - shiftable multiscale transforms - is proposed. As mentioned earlier, impulse response can be
Wavelet_transform
Topics referred to by the same term
sequences Multiple system atrophy, a degenerative neurological disorder Multiscale approximation or multiresolution analysis Morphosyntactic alignment (linguistics)
MSA
contourlet used the Laplacian Pyramid for multiscale decomposition. This new method as proposed by Lu and Do uses a multiscale pyramid that can be adjusted by applying
Contourlet
Branch of chemistry
Warshel received the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems". Computational chemistry has a wide
Computational_chemistry
Variance-stabilizing transformation Variance-to-mean ratio Variation ratio Variational Bayesian methods Variational message passing Variogram Varimax rotation Vasicek
List_of_statistics_articles
Statistical model used in time series analysis
Fractional ARIMA, FARIMA) model time-series that exhibits long memory. Multiscale AR (MAR) is indexed by the nodes of a tree instead of integers. The notation
Autoregressive moving-average model
Autoregressive_moving-average_model
Particle with size less than 100 nm
nucleation and the rates associated with nucleation were modelled through multiscale computational modeling. This included exploration into an improved kinetic
Nanoparticle
Method for finding largest (or smallest) eigenvalues
Computer Society. pp. 59–62. Knyazev, Andrew V. (2006). Multiscale Spectral Image Segmentation Multiscale preconditioning for computing eigenvalues of graph
LOBPCG
Soviet-American mathematician (born)
introducing a concept of polyharmonic homogenization which led to a new type of multiscale finite elements. Together with H. Owhadi, he introduced a "transfer-of-approximation"
Leonid_Berlyand
Concept in mathematics
Equation and the Model of Thomas and Windle". International Journal for Multiscale Computational Engineering. 7 (6): 523–543. doi:10.1615/IntJMultCompEng
Stefan_problem
Multivariate statistical technique
F.; Oksanen, J. (2012). "Community ecology in the age of multivariate multiscale spatial analysis". Ecological Monographs. 82 (3): 257–275. Bibcode:2012EcoM
Spatial Analysis of Principal Components
Spatial_Analysis_of_Principal_Components
Genetic characteristic of tumorous tissue
calculated. TMB can be calculated directly from histopathology images using a multiscale deep learning pipeline, avoiding the need for sequencing and variant calling
Tumor_mutational_burden
Framework to describe phase transitions
ISBN 978-0-521-84223-5. Baeurle SA, Usami T, Gusev AA (2006). "A new multiscale modeling approach for the prediction of mechanical properties of polymer-based
Statistical_field_theory
Swedish cell biologist
Co-Founder and Chief Scientific Advisor at GenBio AI, an AI company developing multiscale AI foundation models for biology. Lundberg was an undergraduate and postgraduate
Emma_Lundberg_(scientist)
Weber et al. A Complex View of Barycentric Mappings Raif M. Rustamov Multiscale Biharmonic Kernels 2010 Keenan Crane et al. Trivial Connections on Discrete
Symposium on Geometry Processing
Symposium_on_Geometry_Processing
understanding of the structure and function of ribosomes. Development of multiscale models for complex chemical systems by Arieh Warshel and Michael Levitt
List of Israeli inventions and discoveries
List_of_Israeli_inventions_and_discoveries
Study of biochemical processes in an individual cell
H, Kong S, Wang T, Ho Y (September 2019). "Technological Advances in Multiscale Analysis of Single Cells in Biomedicine". Advanced Biosystems. 3 (11)
Single-cell_analysis
Signal processing algorithm
ISBN 978-1-4244-1483-3. S2CID 18226941. David Looney and Danilo P. Mandic, "Multiscale Image Fusion Using Complex Extensions of EMD", IEEE transactions on signal
Multidimensional empirical mode decomposition
Multidimensional_empirical_mode_decomposition
Infinitely detailed mathematical structure
Silva, C. M.; Philip, J.; Chauhan, K.; Meneveau, C.; Marusic, I. (2013). "Multiscale Geometry and Scaling of the Turbulent–Nonturbulent Interface in High Reynolds
Fractal
Israeli physicist
advanced dimensional analysis (extensions of the Buckingham theorem), variational analysis of "free ends" physical problems, enabling application of the
Edward_Bormashenko
British chemist
domain of multiscale modelling and simulation. Working initially with Eirik Flekkøy on foundations of the dissipative particle dynamics method and then
Peter_Coveney
Research field that applies to methods of studying issues in social science
actors (institutions). The purpose of the project is to build a generic multiscale platform which is planned to deal with water conflict-related issues.
Social_simulation
Type of functional magnetic resonance imaging
Wang X, Kantola J, Nikkinen J, et al. (November 2014). "Synchronous multiscale neuroimaging environment for critically sampled physiological analysis
Resting_state_fMRI
Primary organ of the respiratory system
February 2016. Miura T (2008). "Modeling Lung Branching Morphogenesis". Multiscale Modeling of Developmental Systems. Current Topics in Developmental Biology
Lung
Barrancos, Jose; Padilla, German D.; Perez, Nemesio M. (2021). "A nonlinear multiscale inversion approach for ambient noise tomography". Geophysical Journal
Subsurface mapping by ambient noise tomography
Subsurface_mapping_by_ambient_noise_tomography
Transform in numerical harmonic analysis
used for interlacing in the Portable Network Graphics (PNG) format, is a multiscale model of the data which is similar to a DWT with Haar wavelets. Unlike
Discrete_wavelet_transform
mfem/mfem: Lightweight, general, scalable C++ library for finite element methods". github.com. Retrieved December 17, 2025. "GitHub - idaholab/moose: Multiphysics
List of computational physics software
List_of_computational_physics_software
Iranian-American neuroscientist
Abbaspourazad H, Choudhury M, Wong YT, Pesaran B, Shanechi MM (January 2021). "Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp
Maryam_Shanechi
System with multiple fractal dimensions
h ) {\displaystyle D(h)} . Rather, data analysis gives access to the multiscaling exponents ζ ( q ) , q ∈ R {\displaystyle \zeta (q),\ q\in {\mathbb
Multifractal_system
Aspect of meteorological history
April 22, 1986. It was followed by the Canadian Global Environmental Multiscale Model (GEM) mesoscale model on February 24, 1997. The German Weather Service
History of numerical weather prediction
History_of_numerical_weather_prediction
Biological analysis approach
Joel T (21 January 2014). "Unifying immunology with informatics and multiscale biology". Nature Immunology. 15 (2): 118–127. doi:10.1038/ni.2787. ISSN 1529-2908
Multiomics
Spectroscopy of Biological Systems". In Tomar V, Qu T, Dubey DK, Verma D (eds.). Multiscale Characterization of Biological Systems: Spectroscopy and Modeling. Springer
Droplet-based_microfluidics
Weather prediction using mathematical models of the atmosphere and oceans
Integrated Forecast System and Environment Canada's Global Environmental Multiscale Model both run out to ten days into the future, and the Global Forecast
Numerical_weather_prediction
Sum of all the energy required to produce any goods or services
Bunster, Victor; Warren-Myers, Georgia; Moosavi, Sareh (2022). "Towards a multiscale framework for modeling and improving the life cycle environmental performance
Embodied_energy
Science of rubbing surfaces
Popov, Valentin L.; Shilko, Evgeny V.; Vasiljeva, Olga S., eds. (2021). "Multiscale Biomechanics and Tribology of Inorganic and Organic Systems". Springer
Tribology
Type of statistics
MR 2371990. Rosen, C.; Lennox, J.A. (October 2001), "Multivariate and multiscale monitoring of wastewater treatment operation", Water Research, 35 (14):
Robust_statistics
State of matter
method: principles and practice. Switzerland: Springer. ISBN 978-3-319-44649-3. OCLC 963198053. Steinhauser, M. O. (2022). Computational multiscale modeling
Liquid
Mechanism of spontaneous phase separation
(27 April 2022). "Optimally-Tailored Spinodal Architected Materials for Multiscale Design and Manufacturing". Advanced Materials. 34 (26) 2109304. Bibcode:2022AdM
Spinodal_decomposition
Hexagonal lattice made of carbon atoms
Bagci, Hakan (2020). "Numerical Methods for Electromagnetic Modeling of Graphene: A Review". IEEE Journal on Multiscale and Multiphysics Computational
Graphene
Probability distribution
because when doing inference over such models using methods such as Gibbs sampling or variational Bayes, Dirichlet prior distributions are often marginalized
Dirichlet_distribution
Scientific study of digital information
Yuanyuan; Wang, Ying; Li, Xin; Li, Xiaoli; Xie, Ping (2023-12-01). "Multiscale information interaction at local frequency band in functional corticomuscular
Information_theory
American chemical engineer
materials at the particle scale. He derived the overpotential from a variational principle and provide a thermodynamically consistent basis for phase
Martin_Z._Bazant
Predictive chemical model
at the Wayback Machine, Drug Theoretics and Cheminformatics Laboratory Multiscale Conceptual Model Figures for QSARs in Biological and Environmental Science
Quantitative structure–activity relationship
Quantitative_structure–activity_relationship
Chinese mathematician
Jian-Feng; Osher, Stanley; Shen, Zuowei, "Split Bregman methods and frame based image restoration". Multiscale Model. Simul. 8 (2009/10), no. 2, 337–369. Cai,
Zuowei_Shen
American physicist and climatologist
Henry F.; Markgraf, Vera (eds.). El Niño and the southern oscillation : multiscale variability and global and regional impact. Cambridge & New York: Cambridge
Michael_E._Mann
English meteorologist and mathematician (1881–1953)
extrapolation Richardson number Modified Richardson iteration Richards equation Multiscale turbulence Takebe Kenko Frederick W. Lanchester List of peace activists
Lewis_Fry_Richardson
Class of chemical substance
(2016-07-27). "The Impact of Mesopores on the Mechanical Stability of HKUST-1: A Multiscale Investigation". European Journal of Inorganic Chemistry. 2016 (27): 4517–4523
Metal–organic_framework
Han Chinese subdivision
theoretical models of turbulence, electronic structure analysis, multiscale methods, computational fluid dynamics, and weak KAM theory. Zhiwei Yun (1982–)
Wu_Chinese-speaking_people
Prolonged period of excessively hot weather
J.; de Jeu, R. A. M. (2012). "Soil moisture-temperature coupling: A multiscale observational analysis". Geophysical Research Letters. 39 (21) L21707
Heat_wave
Branch of geophysics, primarily seismology
2835157. G.-P. Ostermeyer, V.L. Popov, E. Shilko, O. Vasiljeva (2021). Multiscale Biomechanics and Tribology of Inorganic and Organic Systems. In memory
Earthquake_prediction
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
Boy/Male
Tamil
Variation to Shanti meaning peacefulness
Boy/Male
Australian, Danish, Dutch, German, Hebrew
Variation of Jenny; Diminutive of Jane and Jennifer
Boy/Male
Hindu, Indian
Variation
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Irish, Latin
Pearl; Child of Light; Variation of Margaret
Girl/Female
American, British, English, French, German
Truthful; Variation of Alice; Noble
Girl/Female
Indian
Angel, Variation of anaitis
Girl/Female
Muslim
Angel, Variation of anaitis
Girl/Female
American, Australian, Christian, French, German, Irish
Truthful; Noble; Nobility; Honest; Noble Sort; Variation of Alice
Boy/Male
British, English
The Gaelic Harvest Festival; A Variation of Samhain
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Variation of the Name Sukumaran
Girl/Female
American, Australian, British, Chinese, Christian, English, German, Hebrew, Scandinavian
Doe; Ewe; Wise Protection; Variation of Raymond; Female Sheep
Girl/Female
Indian, Kannada
Most Highly Adored; Most Praised; Variation of Muhammad
Boy/Male
African, American, Arabic, Bengali, French, Hebrew, Hindu, Indian, Latin, Muslim, Spanish, Tamil
Variation of Adam from the Red Earth; Earth; Man; Heaven
Girl/Female
Tamil
Variation of Jenny which is a diminutive of jane and jennifer
Boy/Male
Indian
First; Variation of Pratham
Girl/Female
Christian, Indian, Spanish
Dedicated to God; Variation of Isabel
Boy/Male
Hindu
Variation to Shanti meaning peacefulness
Boy/Male
Hindu, Indian
Variation of Lord Vishnu
Girl/Female
American, Australian, Greek
Protector of Men; Variation of Sandra or Chandra
Girl/Female
American, British, English, French
Fair-haired; Variation of the Spanish Blandina; Flattering
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
Girl/Female
Arabic, Australian, Muslim
Night Journey; Variant of Isra
Boy/Male
English Irish
Surname derived from a medieval given name.
Boy/Male
Indian, Tamil
King of Heart
Girl/Female
Tamil
Laalitya | லாலீதà¯à®¯à®¾Â
Loveliness, Grace, Beauty
Girl/Female
Assamese, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit, Traditional
Beautiful Flowers; Flower; Cheerful and Wise; One who has a Good Mind
Surname or Lastname
English
English : habitational name from Chilson in Oxfordshire, named with Old English cild ‘young man’ (see Child) + tūn ‘farmstead’, ‘settlement’.It is not known when this surname was first brought to America, but it was well established in CT in the early 18th century. Daniel Chilson of Weathersfield, CT, was born about 1720 and on 4 October 1745 married Sybil Stanclift in Middlesex County, CT.
Boy/Male
Tamil
Avigyan | அவிஜà¯à®žà®¾à®¨Â
Recollection
Girl/Female
Muslim
One who has a face like Moon
Boy/Male
Arabic
Loving; Friendly
Girl/Female
Scottish American
used as a woman's name.
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
VARIATIONAL MULTISCALE-METHOD
a.
Not given to variation or change; unalterable; unchangeable; always uniform.
a.
Of the same tenor or tone; equable; without variation.
n.
An instrument for recording automatically the variations of atmospheric pressure.
adv.
Without variation.
n.
State of diversity or variation; variegation; modification; change; alternation.
n.
The state or quality of being abnormal; variation; irregularity.
n.
Fluctuation; variation; change back and forth.
n.
The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.
v. i.
To sing a variation or accomplishment.
n.
The variation of words by declension, comparison, or conjugation; inflection.
n.
A suite; a set of variations.
n.
The succession and variation of leaves during different seasons.
n.
The observation of the state and variations of the atmosphere.
adv.
Without variation of termination.
n.
Extent to which a thing varies; amount of departure from a position or state; amount or rate of change.
n.
Change of termination of words, as in declension, conjugation, derivation, etc.
n.
One of the different arrangements which can be made of any number of quantities taking a certain number of them together.
n.
Variability in chemical constitution without variation in crystalline form.
n.
Repetition of a theme or melody with fanciful embellishments or modifications, in time, tune, or harmony, or sometimes change of key; the presentation of a musical thought in new and varied aspects, yet so that the essential features of the original shall still preserve their identity.
n.
A reading; a variation in the text.