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Description of a system using mathematical concepts and language
developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences
Mathematical_model
Scientific Journal
sciencedirect.com/journal/applied-mathematical-modelling/about/insights#abstracting-and-indexing "Applied Mathematical Modelling". MIAR: Information Matrix
Applied Mathematical Modelling
Applied_Mathematical_Modelling
Application of mathematical methods to other fields
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business,
Applied_mathematics
Academic association dedicated to the use of mathematics in industry
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science
Society for Industrial and Applied Mathematics
Society_for_Industrial_and_Applied_Mathematics
Study of discrete mathematical structures
finite settings. In applied mathematics, discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae
Discrete_mathematics
Mathematical practice
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility
Continuous_modelling
Mathematical modeling competition for students
The International Mathematical Contest in Modeling (MCM) is a multi-day mathematical modelling competition held annually in USA, during the first or second
Mathematical Contest in Modeling
Mathematical_Contest_in_Modeling
Using mathematical models to understand infectious disease transmission
programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. The modelling of infectious
Mathematical modelling of infectious diseases
Mathematical_modelling_of_infectious_diseases
Application of mathematical and statistical methods in finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling
Mathematical_finance
Informative representation of an entity
modulus, 'a measure'. Models can be divided into physical models (e.g. a ship model) and abstract models (e.g. a set of mathematical equations describing
Model
Branch of biology
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical modeling, and abstractions
Mathematical and theoretical biology
Mathematical_and_theoretical_biology
Technique in mathematical modeling
metamodeling, with applications in all areas of mathematical modelling. Many modern mathematical models of real-life processes pose challenges when used
Model_order_reduction
Field of knowledge
Nicola; Preziosi, Luigi (Dec 22, 1994). Modelling Mathematical Methods and Scientific Computation. Mathematical Modeling. Vol. 1. CRC Press. p. 1. ISBN 978-0-8493-8331-1
Mathematics
Matrix decomposition
"Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions". Applied Mathematical Modelling. 37 (20–21):
Singular_value_decomposition
Competitive algorithm for searching a problem space
the Boltzmann–BGK equation and evolutionary optimisation". Applied Mathematical Modelling. 52: 215–240. doi:10.1016/j.apm.2017.07.024. ISSN 0307-904X
Genetic_algorithm
Academic journal
Mathematical Models and Methods in Applied Sciences is a journal founded in 1991 and published by World Scientific. It covers: mathematical modelling
Mathematical Models and Methods in Applied Sciences
Mathematical_Models_and_Methods_in_Applied_Sciences
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description
Geometric_modeling
Equation of statistical mechanics
in collisionless and BGK forms for macroscopic gas flows". Applied Mathematical Modelling. 35 (3): 996–1015. doi:10.1016/j.apm.2010.07.027. Evans, B.;
Boltzmann_equation
Not-for-profit foundation for study and research in the mathematical sciences
been published, The Mathematical Scientist and Mathematical Spectrum. Journal of Applied Probability (since 1964) Advances in Applied Probability (since
Applied_Probability_Trust
Fibrous structure in the vestibular system of the inner ear
Twizell, E.H. (1980). "A variable gravity model of the otolith membrane". Applied Mathematical Modelling. 4 (2): 82–86. doi:10.1016/0307-904x(80)90110-9
Otolithic_membrane
Relationship between proficiency and experience
(2012), "Inventory models for imperfect quality items with shortages and learning in inspection", Applied Mathematical Modelling, 36 (11): 5334–5343
Learning_curve
Inventory management method
inventory model with fuzzy demand, backordering, and discount using a hybrid imperialist competitive algorithm". Applied Mathematical Modelling. 40 (15–16):
Vendor-managed_inventory
Branch of applied mathematics
Major areas of research in mathematical chemistry include chemical graph theory, which deals with topology such as the mathematical study of isomerism and
Mathematical_chemistry
completion time scheduling with a time-dependent deterioration, Applied Mathematical Modelling, 35(3), 1506–1511 Yin, Y., Liu, M., Hao, J., & Zhou, M., 2012
Machine-dependent_software
System for reasoning about vagueness
"The trapezoidal fuzzy soft set and its application in MCDM". Applied Mathematical Modelling. 36 (12): 5846–5847. doi:10.1016/j.apm.2012.01.036. ISSN 0307-904X
Fuzzy_logic
Type of wind turbine
aerodynamic optimisation of vertical axis wind turbine blades". Applied Mathematical Modelling. 40 (2): 1038–1051. doi:10.1016/j.apm.2015.07.001. ISSN 0307-904X
Vertical-axis_wind_turbine
Professor at IIT Kharagpur
Johann (December 2010). "Most Cited Applied Mathematical Modelling Articles Since 2010". Applied Mathematical Modelling. 34 (12): 3991–4011. doi:10.1016/j
Bhrigu_Nath_Singh
Modeling financial systems
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed
Financial_modeling
Methods used to generate sound waveforms using a computer
Physical modelling synthesis refers to sound synthesis methods in which the waveform of the sound to be generated is computed using a mathematical model, a
Physical_modelling_synthesis
Use of math in the study of cancer
Mathematical oncology is the use of mathematical models and computer simulations applied to the study of cancer (oncology). Teorell made preliminary efforts
Mathematical_oncology
Branch of applied mathematics
Engineering Mathematics is a branch of applied mathematics, concerning mathematical methods and techniques that are typically used in engineering and
Engineering_mathematics
Method for representing and evaluating partial differential equations
methods application in geometrically nonlinear stress analysis". Applied Mathematical Modelling. 24 (7): 439–455. doi:10.1016/S0307-904X(99)00047-5. ISSN 0307-904X
Finite_volume_method
Mathematics independent of applications
new mathematical objects or working out the mathematical consequences of basic principles. While the distinction between pure and applied mathematics has
Pure_mathematics
Optimization algorithm
Oliveira. "A cellular automata ant memory model of foraging in a swarm of robots." Applied Mathematical Modelling 47, 2017: 551-572. Russell, R. Andrew.
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, formulae are fit to discrete data—data that could potentially
Discrete_modelling
British computer scientist (1956–2025)
A transient model of thermoregulation in a clothed human. Applied Mathematical Modelling, 8(3), 211-216". Applied Mathematical Modelling. 8 (3): 211–216
Peter Smith (computer scientist)
Peter_Smith_(computer_scientist)
Israeli-American applied mathematician
Mathematicae, Frontiers in Systems Biology, Cancer Research, Applied Mathematics Modelling, PLoS One, and Differential Equations and Dynamical Systems
Doron_Levy
Numerical method for solving certain differential equations
elastoplasticity", Applied Mathematical Modelling, 29 (2): 235–252, doi:10.1016/j.apm.2004.09.004 "Trefftz method", Encyclopedia of Mathematics, EMS Press, 2001
Trefftz_method
Family of closed mathematical curves
super ellipsoid concept and its application in mechanics". Applied Mathematical Modelling. 40 (21): 9427–9444. doi:10.1016/j.apm.2016.06.011. ISSN 0307-904X
Superellipse
Predictive modelling technique
Uplift modelling, also known as incremental modelling, true lift modelling, or net modelling, is a predictive modelling technique that directly models the
Uplift_modelling
Research institute specializing in computational mathematics
schemes was developed by A. A. Samarskii. Samarskii considered mathematical modelling as an independent scientific discipline. Sergei Kurdyumov created
Keldysh Institute of Applied Mathematics
Keldysh_Institute_of_Applied_Mathematics
Theoretical framework
Outline for a Morphology of Modelling Methods: Contribution to a General Theory of Modelling Colette Rolland (1993). "Modeling the Requirements Engineering
Conceptual_model
The SAM is a center for research and teaching in numerical mathematics, mathematical modelling and computing in Science and Technology in the D-MATH of
Seminar for Applied Mathematics
Seminar_for_Applied_Mathematics
Mathematical model
A population model is a type of mathematical model that is applied to the study of population dynamics. Models allow a better understanding of how complex
Population_model
Study of mathematical algorithms for optimization problems
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria
Mathematical_optimization
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Mathematical model of a complex system
statistics-encoded neural network for poro/micro-mechanical modelling". Computer Methods in Applied Mechanics and Engineering. 441 117986. doi:10.1016/j.cma
Computational_model
Process in artificial intelligence and operations research
constraints satisfaction models for optimization problems in container terminals". Journal of Applied Mathematical Modelling. 37 (6): 3601–34. doi:10
Constraint_satisfaction
American chemical engineer
"Analysis of weak solutions for the phase-field model for lithium-ion batteries". Applied Mathematical Modelling. 78: 185–199. doi:10.1016/j.apm.2019.09.048
Martin_Z._Bazant
Mathematical Models and Methods in Applied Sciences Mathematical Notes Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Programming
List_of_mathematics_journals
Model simulating an emergency evacuation
Duvigneau, R. (2014-12-15). "Macroscopic modeling and simulations of room evacuation". Applied Mathematical Modelling. 38 (24): 5781–5795. arXiv:1308.1770
Evacuation_model
Area of mathematics
Computational mathematics is a field of study that focuses on the interaction of mathematical sciences, computer science, and algorithms. A large part
Computational_mathematics
"Studies of an infinite element method for acoustical radiation". Applied Mathematical Modelling. 30 (7): 641–655. doi:10.1016/j.apm.2005.08.022. ISSN 0307-904X
Infinite_element_method
Convex optimization problem
Applications models". Applied Mathematical Modelling. 36 (10): 5122–5134. doi:10.1016/j.apm.2011.12.053. ISSN 0307-904X. "MOSEK Modeling Cookbook - Conic
Second-order_cone_programming
Mathematical representation of economic system
analysis. Qualitative models often suffer from lack of precision. At a more practical level, quantitative modelling is applied to many areas of economics
Economic_model
Class of models in the behavioral sciences
where mathematical analysis of behavior is standard. However, they are widely used throughout the social sciences, and are commonly applied to cognitive
Rational_choice_model
Type of programming language
kind of mathematical problems like: linear problems integer problems (mixed integer) quadratic problems mixed complementarity problems mathematical programs
Algebraic_modeling_language
Evolution of the basic supply chain
chain network design using multi-objective fuzzy mathematical programming". Applied Mathematical Modelling. 36 (8): 3433–3446. doi:10.1016/j.apm.2011.10
Supply_chain_network
Educational qualification in the UK
subjects, mathematics is assessed by examination at the end of the course. The syllabus seeks to develop skills in mathematical modelling, problem-solving
Advanced_level_mathematics
Iranian mathematician (born 1972)
Mathematical Finance at the University of Oxford. He is known for contributions to probability theory, stochastic analysis and mathematical modelling
Rama_Cont
include: Practical Applied Mathematics Modelling, Analysis, Approximation Topics in Industrial Mathematics: Case Studies and Related Mathematical Methods Industrial
European Study Groups with Industry
European_Study_Groups_with_Industry
British mathematical biologist
formation, morphogenesis, and the mathematical modelling of cell biology and developmental biology. Baker read mathematics at Wadham College, Oxford, and
Ruth_Baker
Description of limiting behavior of a function
Practical Applied Mathematics: Modelling, Analysis, Approximation. Cambridge University Press. ISBN 978-0-521-84274-7. Miller, P. D. (2006), Applied Asymptotic
Asymptotic_analysis
Mathematical data production model with limited structure
In mathematics, statistics, and computational modelling, a grey box model combines a partial theoretical structure with data to complete the model. The
Grey_box_model
Branch of applied mathematics
Example applications of mathematical linguistics Mathematical linguistics is the application of mathematics to model phenomena and solve problems in general
Mathematical_linguistics
Mathematical modeling of psychological theories and phenomena
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes
Mathematical_psychology
Branch of applied mathematics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods
Mathematical_economics
Point in evolutionary space where selection always leads
crop diseases. The case of the Maize Lethal Necrosis Disease". Applied Mathematical Modelling. 90: 912–942. doi:10.1016/j.apm.2020.09.036. Fabre, Frédéric;
Evolutionary_attractor
mathematics. These include mathematical research, mathematics education, the history and philosophy of mathematics, public outreach, and mathematics contests
List_of_women_in_mathematics
in 5 research areas:[citation needed] Computational mathematics Mathematical modelling Mathematical physics Partial differential equations, control and
Basque Center for Applied Mathematics
Basque_Center_for_Applied_Mathematics
Optimization algorithm
aerodynamic shape optimisation using Modified Cuckoo Search". Applied Mathematical Modelling. 40 (7–8): 4543–4559. doi:10.1016/j.apm.2015.11.023. ISSN 0307-904X
Cuckoo_search
Optimization algorithm
global optimisation with application to modelling of a flexible system" (PDF). Applied Mathematical Modelling. 40 (9–10): 5442–5461. doi:10.1016/j.apm
Spiral_optimization_algorithm
Russian mathematical physicist
Khrennikov (born 1958) is a Russian-Swedish mathematical physicist. He is a professor of applied mathematics at the Linnaeus University in Växjö, Sweden
Andrei_Khrennikov
Flow of gas and liquid in the same conduit
dynamic instabilities Additional exhaustive information, like applied mathematical models can be found in. Gurgling is a characteristic sound made by unstable
Two-phase_flow
1960 article by Eugene Wigner
published in Communication in Pure and Applied Mathematics in 1960. In it, Wigner observes that pure mathematical concepts that have been developed and
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Mathematical measure of transient behavior
In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady
Resilience_(mathematics)
Decision-making strategy
method for decision making problem with interval numbers". Applied Mathematical Modelling. 33 (5): 2257–2262. doi:10.1016/j.apm.2008.06.002. Heydari,
VIKOR_method
Syllabus in college and university mathematics
(1975) American Mathematical Monthly 82(6): 681–4 G.M. Kaufman (1963) American Mathematical Monthly 70(10): 1116 G. C. Dorner (1971) Mathematics Magazine 44(4):
Finite_mathematics
encountered in several areas of mathematical biology – for example, demography and cell proliferation modeling; it is applied when age structure is an important
Von_Foerster_equation
New Zealand mathematical modeller
of contributions to the field of applied mathematics, particularly for his explanations of how mathematical modelling can benefit social and ecological
Michael_Plank
1989 textbook by James D. Murray
Mathematical Biology is a two-part monograph on mathematical biology first published in 1989 by the applied mathematician James D. Murray. It is considered
Mathematical_Biology
Aphorism in statistics
thing Scientific modelling – Scientific activity that produces models Statistical model – Type of mathematical model Statistical model validation – Evaluating
All_models_are_wrong
Person with an extensive knowledge of mathematics
Analyst Mathematical Statistician Mathematical Technician Actuary Applied Statistician Weight Analyst There is no Nobel Prize in mathematics, though sometimes
Mathematician
Testing a predictive model on historical data
prediction – Weather prediction using mathematical models of the atmosphere and oceans Predictive modelling – Form of modelling that uses statistics to predict
Backtesting
Mathematical model
log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which
Log-linear_model
Concept in probability theory
approach for the computation of sums of Erlang random variables". Applied Mathematical Modelling. 39 (16): 4971–4977. doi:10.1016/j.apm.2015.04.013. Bolch, Gunter;
Hypoexponential_distribution
Measure of linear correlation
stochastic processes". In Yang, Fengshan (ed.). Progress in Applied Mathematical Modeling. Nova Science Publishers, Inc. pp. 223–260. ISBN 978-1-60021-976-4
Pearson correlation coefficient
Pearson_correlation_coefficient
River in Taiwan
routing model and a three-dimensional ocean model to predict overbank flows in a complex river–ocean system". Applied Mathematical Modelling. 37 (9):
Maoluo_River
Italian-British mathematician
to interpret and model extreme events. He is currently a Professor of Applied Mathematics at the School of Computing and Mathematical Sciences of the University
Valerio_Lucarini
Branch of mathematics
Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through quantitative methods of approximation and convergence
Mathematical_analysis
Form of modelling that uses statistics to predict outcomes
Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to
Predictive_modelling
Rediscovery of the trapezoidal rule in 1994
Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves". In the paper, Tai proposes "Tai's model"
Tai's_model
Environmental modelling is the creation and use of mathematical models of the environment. Environmental modelling may be used purely for research purposes
Environmental_modelling
Preziosi, Luigi (December 22, 1994). Modelling Mathematical Methods and Scientific Computation. Mathematical Modeling. Vol. 1. CRC Press. p. 1. ISBN 978-0-8493-8331-1
Philosophy_of_mathematics
Mathematical optimization approach to deal with optimization problems under uncertainty
Mohamadreza (2016-01-01). "Novel robust fuzzy mathematical programming methods". Applied Mathematical Modelling. 40 (1): 407–418. doi:10.1016/j.apm.2015.04
Robust_fuzzy_programming
North Indian Ocean cyclone in 1975
G. S. (1 August 1985). "Numerical modelling of storm surges in the Arabian Sea". Applied Mathematical Modelling. 9 (4): 289–294. doi:10.1016/0307-904X(85)90067-8
1975_Porbandar_cyclone
Scientific field of study
[Journal of Mathematical Physics] purpose is the publication of papers in mathematical physics—that is, the application of mathematics to problems in
Physics
applied mathematics concerned with describing the progression of viral infections within a host organism. It employs a family of mathematical models that
Viral_dynamics
Art of Mathematics Mathematics and Art – AMS Mathematics and Art – Cut-the-Knot Mathematical Imagery – American Mathematical Society Mathematics in Art
Mathematics_and_art
British applied mathematician
materials through pioneering approaches like stochastic modelling of elasticity that bring mathematical rigour to real-world materials with complex behaviours
Angela_Mihai
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
Boy/Male
Biblical
Proud; quarrelsome (applied to Egypt).
Biblical
supplying; supplied
Surname or Lastname
English
English : patronymic from Abel, which was a popular Middle English personal name. Compare Aplin.
Boy/Male
Indian, Sanskrit
Dappled Leaves
Surname or Lastname
English
English : variant of Apley.
Girl/Female
Hindu
Mathematician
Boy/Male
Indian, Sanskrit
Shining; Dappled Horse
Surname or Lastname
English
English : variant of Appling.
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Girl/Female
Arabic
Spotted; Dappled
Boy/Male
Buddhist, Indian, Sanskrit
Term of Respect Applied to a Buddhist Mendicant
Biblical
proud; quarrelsome (applied to Egypt)
Boy/Male
Arabic, Muslim
Eternal; Everlasting; An Epithet Applied to Allah
Girl/Female
Gujarati, Hindu, Indian, Kannada, Telugu
Mathematician
Surname or Lastname
English
English : from Middle English appel ‘apple’ (Old English æppel), acquired as a surname in any of various senses: a topographic name for someone living by an apple orchard; an occupational name for a grower or seller of apples; or a nickname for someone supposed to resemble an apple in some way, e.g. in having bright red cheeks. The economic importance in medieval northern Europe of apples, as a fruit that could be grown in a cold climate and would keep for use throughout the winter, is hard to appreciate in these days of rapid transportation and year-round availability of fruits of all kind.Americanized form of Appel or Apfel.
Boy/Male
Biblical
Proud; quarrelsome (applied to Egypt).
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Telugu
An Astrologer; Mathematician
Girl/Female
Tamil
Mathematician
Girl/Female
Biblical
Supplying, supplied.
Boy/Male
Bengali, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
One who Calculates; Astrologer; Mathematician
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
Girl/Female
Indian
Inescapable, Not running away
Boy/Male
Arthurian Legend
A knight.
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Kashmiri, Malayalam, Marathi, Telugu
Earth; Light from a Jewel
Boy/Male
Biblical
Idols; masters; false gods.
Girl/Female
Hindu, Indian
Strong; Golden Eyes; Smoothing Flowers
Girl/Female
Hindu, Indian, Tamil, Traditional
Lord Ganesha's Vehicle
Surname or Lastname
English (Derbyshire)
English (Derbyshire) : variant of Foulks.
Boy/Male
German
Power of an Eagle
Boy/Male
Hindu, Indian, Mythological, Sanskrit
Teacher of Arjun in Hindu Epic Mahabharat
Surname or Lastname
English
English : metonymic occupational name for a carter or cartwright, from Middle English wain ‘cart’, ‘wagon’ (Old English wægen). Occasionally it may have been a habitational name for someone who lived at a house distinguished with this sign, probably from the constellation of the Plow, known in the Middle Ages as Charles’s Wain, the reference being to Charlemagne.Anthony Wayne and his son Isaac, of English ancestry, came from Ireland to Chester Co., PA, in about 1724. Gen. Anthony Wayne (1745–96), born in Waynesboro, PA, was a prominent military officer in the American Revolution and the Indian war of 1794–95.
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
APPLIED MATHEMATICAL-MODELLING
a.
Pertaining to, or having the nature of, an anathema.
a.
Of or pertaining to mathematical calculations; performing or able to perform mathematical calculations.
v. i.
To grow like an apple; to bear apples.
n.
He who, or that which, applies.
n.
Anything round like an apple; as, an apple of gold.
n.
That science, or branch of applied mathematics, which treats of the action of forces on bodies.
n.
One versed in mathematics.
a.
Alt. of Anathematical
a.
Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.
n.
The zorilla. The name is also applied to other allied species.
n.
See Otaheite apple.
a.
See Mathematical.
n.
Any fruit or other vegetable production resembling, or supposed to resemble, the apple; as, apple of love, or love apple (a tomato), balsam apple, egg apple, oak apple.
n.
That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.
n.
Any lineal or mathematical diagram; an outline.
n.
Learning; especially, mathematics.
imp. & p. p.
of Apply
v.
A mathematical point; -- regularly used in old English translations of Euclid.
n.
Mixed mathematics.
n.
Apple brandy.