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MATHEMATICAL MODELS
agriculture Sciences Models
biomathematical Models
climatic System
data Assimilation
ecosystem
energy Sciences Models
food Sciences Models
geophysical Hydrodynamics
global Processes Models
hydrodynamics
life support systems and mathematical modeling
mathematical modeling
mathematical models
mathematical Models of Atmosphere
uses of mathematical modeling
water Sciences Models
world ocean
BASIC PRINCIPLES OF MATHEMATICAL MODELING
chemostat
closed loop
controllability
delay equation
differential equation
differential inclusion
discrete system
feed back
filter
infinite dimensional system
input
manifold
observability
observer
open loop
optimal control
output
partial differential equation
population dynamics
stabilizability
state
stochastic differential equation
stochastic system
structural stability
system
vector field
viability.
Asymptotic stability
CLASSIFICATION OF MODELS
Chemostat
competition
difference equations
discrete time
dynamical systems
food chains
Leslie models
linear models
Lotka-Volterra equations
Malthus model
nonlinear models
recurrence
Verhulst model
Differential equations
BASIC METHODS OF THE DEVELOPMENT AND ANALYSIS OF MATHEMATICAL MODELS
classification
cycles
dynamical systems
Leslie models
Liapunov functions.
limit sets
linear equations
linear models
linearized system
nonlinear models
phase plane
phase space
Poincaré-Bendixon theory
positive systems
recurrence
stability
Differential equations
MEASUREMENTS IN MATHEMATICAL MODELING AND DATA PROCESSING
estimation theory
hypothesis testing
signal processing
detection theory
CONTROLLABILITY, OBSERVABILITY AND STABILITY OF MATHEMATICAL MODELS
asymptotic stability
attractivity
chemostat
closed-loop
control-lability
differential equation
finite dimensional systems
input
Lie algebra
Lotka-Volterra systems
Lyapunov functions
nonlinear systems
observability
observer
output
stabilization
state
accessibility
IDENTIFICATION, ESTIMATION AND RESOLUTION OF MATHEMATICAL MODELS
approximation
identifiability
identification
least-squares
maximum likelihood method
realization
stochastic realization
subspace identification algorithm.
Dynamic system
MATHEMATICAL THEORY OF DATA PROCESSING IN MODELS (DATA ASSIMILATION PROBLEMS)
adjoint method
data assimilation
Ensemble Kalman filter
Extended Kalman filtering
linear Kalman filtering
Reduced-Rank Square Root filter.
stochastic models
variational method
State space models
CHAOS AND CELLULAR AUTOMATA
bifurcation
cellular automata
computer simulations
dynamical system
infectious disease
Chaos
MATHEMATICAL MODELS IN HYDRODYNAMICS
Direct Numerical Simulation
eddy viscosity
Large-Eddy Simulation
Reynolds-averaged Navier-Stokes Simulation
Simulation Techniques
turbulence modeling
Turbulent flows
MATHEMATICAL MODELING OF FLOW IN WATERSHEDS AND RIVERS
groundwater
infiltration
mathematical modeling
overland flow
routing
saturated flow
unsaturated flow
watershed
Hydrology
MATHEMATICAL MODELS OF CIRCULATIONS IN OCEANS AND SEAS
Adjoint Model
Data Assimilation
Marine Dynamics
Numerical Modeling
Ocean General Circulation
Primitive Equations
Shallow-Water Equations
Solvability of Sea Dynamics Problems
Mathematical Model
WAVE MODELING AT THE SERVICE OF SECURITY IN MARINE ENVIRONMENT
data assimilation
energy spectrum
Hamiltons principle
Navier-Stokes equation
nonlinear interactions
potential theory
ray theory
remote sensing
wave action
wave breaking
wave climate.
wave generation
Wind-generated waves
MATHEMATICAL MODELING OF THE TRANSPORT OF POLLUTION IN WATER
diffusion
Eulerian modeling
Lagrangian modeling
numerical modeling
oil spill modeling
tracer simulation
turbulence
turbulent mixing
Advection
MATHEMATICAL MODELS IN ELECTRIC POWER SYSTEMS
Distribution
Energy
Excitation System
Generation
Load
Power System
Power System Controls
Power System Stability
Prime Movers
Transmission
Power
MATHEMATICAL MODELS OF NUCLEAR ENERGY
energy production.
multi-group approximation
neutron
nuclear reactor
optimization
transfer equation
transmutation
Nucleus
MATHEMATICAL MODELS IN CHEMICAL PHYSICS AND COMBUSTION THEORY
activation
chain
combustion
detonation.
dissipation
explosion
heat
radical
reaction
molecule
MATHEMATICAL MODELING AND SIMULATION METHODS IN ENERGY SYSTEMS
activity analysis
economic equilibrium
energy-environement modeling
environemental constraints
linear and nonlinear programming
market based instruments
top-down and bottom-up modeling
MATHEMATICAL MODELS OF CLIMATE
applications of climate models.
atmospheric general circulation models
oceanic general circulation models
Energy balance climate models
MATHEMATICAL MODELS IN METEOROLOGY AND WEATHER FORECASTING
data assimilation
ensemble forecasting and predictability
future.
numerical models
numerical weather prediction
MATHEMATICAL MODELS OF HUMAN-INDUCED GLOBAL CHANGE
climate feedbacks.
climate simulation
global warming
greenhouse effect
greenhouse gases
mathematical models
numerical modeling
climate change
MATHEMATICAL MODELS IN AIR QUALITY PROBLEMS
Advection
Air Pollution
Boundary Layer.
Depositions
Emissions
Finite Difference Scheme
Finite Volume Method
Ordinary Differential Equations (ODE)
Chemical mechanism
INFILTRATION AND PONDING
Gardner soil
ponding
Richards’ equation
sorptivity
time condensation approximation
Green-Ampt
MATHEMATICAL EQUATIONS OF THE SPREAD OF POLLUTION IN SOILS
Adsorption
Convective-Diffusive equation
Erosion
Infiltration
Macropores
Mathematical models
Precursor
Preferential flow.
Snow plow
Soil pollution
Vadose zone. Péclet number
Solute transport
MATHEMATICAL SOIL EROSION MODELLING
deposition
enrichment
entrainment
multiple size classes
sediment transport
stochastic erosion model
Soil erosion
MATHEMATICAL MODELS OF BIOLOGY
adaptive dynamics
branching processes
ecology
ESS
evolution
evolutionary ecology
evolutionary genetics
function of models
game theory
ideal free distribution
marginal value theorem
optimal foraging
population dynamics
population genetics
quantitative genetics
modeling philosophy
MATHEMATICAL MODELS OF MARINE ECOSYSTEMS
marine ecosystem
mathematical modeling differential equations
plankton
spatial structure
turbulence
POPULATION MODELS
Age-Structure
Competition
Continuous Population Models
Discrete population Models
Distributed Mathematical Models
Evolution Models
Harvesting
Interacting Populations
Mathematical Models
Population ecology
Prey - Predator Models
Renewable Resources
Selection
Stability
Theoretical Population Genetics
Population Models
MODELS OF BIODIVERSITY
community drift
complex systems
diversity
equilibrium
food web
model
niche
process
scale
species richness
species-area curve
tradeoff
Biogeography
MATHEMATICAL MODELS IN EPIDEMIOLOGY
basic reproduction number
deterministic models
epidemics
epidemiology
HIV
infections
infectious diseases
macroparasites
malaria
mathematical models
measles
microparasites
parasites
population dynamics
transmission of infection
MATHEMATICAL MODELS OF PUBLIC HEALTH POLICY
complexity
difference equations
differential equations
health policy
infectious diseases
loop analysis
models
oscillations
qualitative models
simulation
socio-economic segregation
strategy
cellular automata
MATHEMATICAL MODELING AND THE HUMAN GENOME
bioinformatics
DNA
evolution.
sequence analysis
Human genome
MATHEMATICAL MODELS OF SOCIETY AND DEVELOPMENT: DEALING WITH THE COMPLEXITY OF MULTIPLE-SCALES AND THE SEMIOTIC PROCESS ASSOCIATED WITH DEVELOPMENT
Hierarchy Theory
Holarchies
Holons
Jevons Paradox
Modeling Relation Theory
Models vs Similes
Rosen
Semiotic identity
Multi-Scale Analysis
MATHEMATICAL MODELS IN DEMOGRAPHY AND ACTUARIAL MATHEMATICS
life table
marriage squeeze
multistate population
population momentum
population projection
stable population
two-sex population model
MATHEMATICAL MODELS IN ECONOMICS
dynamics
economics
equilibrium
models
mathematics
ECOLOGICAL AND SOCIO-ECOLOGICAL ECONOMIC MODELS
carrying capacity
complexity
economic-ecological interaction
game theory
information structure
leader-follower problems
nonlinear dynamic systems
optimization
sustainability
MATHEMATICAL MODELING IN SOCIAL AND BEHAVIORAL SCIENCE
Altruism
Chaos
Comparative statics analysis
Differential equations
Downs model
Game theory
Human capital
Job amenity
Logistical form
Malthus’ population theory
Nash equilibrium
Neoclassical growth theory
Operations research
Optimization
Public good
Stochastic process
Utility function
Social and behavioral sciences
MATHEMATICAL MODELS OF MANAGEMENT OF THE ENVIRONMENT AND ITS NATURAL RESOURCES
economic efficiency
exhaustible resources
externalities.
pollution
renewable resources
Environmental economics
MATHEMATICAL MODELS OF GLOBAL TRENDS AND TECHNOLOGICAL CHANGE
climate change
global change
global trends
integrated assessment model
sustainable development
technological change
vintage capital model
world dynamics
mathematical modeling
COMPUTATIONAL METHODS AND ALGORITHMS
a posteriori adaptation
discretization
domain decomposition
estimators of discretization error
explicit and implicit schemes
finite differences
finite elements
galerkin method
hierachical structures
mathematical models
multigrid
parallelism
richardson extrapolation
time-dependent problems
BASIC METHODS FOR SOLVING EQUATIONS OF MATHEMATICAL PHYSICS
a priori estimates
approximate solutions
conservation laws
double layer potential
eigenfunctions
finite difference methods
finite element method
Fourier method
Fourier series
Fourier transform
Frechet derivative
fundamental solution
Galerkin method
Gateaux differential
Green’s formulae
Green’s function
grid method
Hankel transform
integral transforms
invariant
invariant and partially invariant solutions
Laplace transform
Lie group
Mellin transform
monotone operators.
Newton-Kantorovich method
parametrix
projection methods
Ritz method
simple layer potential
Sturm-Liouville problem
variational methods
potential
METHODS OF POTENTIAL THEORY
cylindrical coordinates
Dirichlet problem
double layer potential
Fredholm equation
Green’s function
heat conductivity equation
Helmholtz equation
logarithmic potential
Neumann problem
Newton’s potential
Poisson equation
retarded potential
Schwartz method
simple layer potential
spherical coordinates
sweeping-out method
telegraph equation
volume potential
Potential
EIGENVALUE PROBLEMS: METHODS OF EIGENFUNCTIONS
cylindrical functions
eigenfunctions
Fourier method
Fourier series
heat conductivity problems
method of eigenfunctions
orthogonal polynomials
orthonormal systems
problems of the oscillation theory
problems of the theory of electromagnetism
special functions
spherical functions
Sturm-Liouville problem
eigenvalues
METHODS OF INTEGRAL TRANSFORMS
Bochner transform
Boussinesq problem
chain transform
coagulation equation
convolution transform
Fourier transform
Hankel transform
heat conductivity problems
Hilbert transform
Kontorovich-Lebedev transform
Laguerre transform
Laplace transform
Legendre transform
Mehler-Foque transform
Mellin transform
Meyer transform
physical kinetics.
problems of hydrodynamics
problems of the elasticity theory
problems of the oscillation theory
problems of the theory of neutron slowing-down
wavelet
wavelet transform
Integral transform
DISCRETIZATION METHODS FOR PROBLEMS OF MATHEMATICAL PHYSICS
Bubnov-Galerkin method
finite element method
grid method
method of least squares
method of moments
projection grid methods
projection methods
projection methods in Hilbert spaces
Ritz method
variational methods
Finite-difference methods
VARIATIONAL FORMULATION OF PROBLEMS AND VARIATIONAL METHODS
dirichlet boundary conditions
elasticity
elliptic operators
energy minimization
fourier boundary conditions
galerkin method
lax-Milgram’s theorem
navier-Stokes system
neumann boundary conditions
projection theorem
riesz’s theorem
stokes system
variational equations
variational inequalities
METHODS OF TRANSFORMATION GROUPS
bäcklund transformation
conservation laws
contact and tangential transformations
invariant
invariant and partly invariant solutions
kdV equation
lax pairs
lie group
lie-Bäcklund algebra
method of Inverse Scattering Problem
penleve property
schrodinger equation
sine-Gordon equation
solution
spectrum
τ-function
NUMERICAL ANALYSIS AND METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
collocation
differential equations
grid refinement
interpolation
interval analysis
linear algebra
mean square approximation
nonlinear equations
numerical analysis
quadrature formulae
spectrum of a matrix
spline
stability of a numerical method
stiff problems
SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
conjugate gradient methods
direct methods
domain decomposition methods
iterative methods
NUMERICAL INTEGRATION
cubature formula
quadrature formula
Approximate integration
NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMIC SYSTEMS
adams formulae
analytical methods
delay differential equations
error estimation
euler method
newton-Kantorovich method
perturbation method
runge-Kutta method
stiff systems
successive approximations
taylor series
trapezoid method
FINITE ELEMENT METHOD
energy minimization
error analysis.
finite element meshes
galerkin method
isoparametric elements
lagrangian interpolation
laxMilgram’s theorem
quadrature formulas
triangular and quadrangular finite elements
variational equations
AN INTRODUCTION TO FINITE VOLUME METHODS
advection equation
finite volume methods
gas dynamics
linear hyperbolic systems
roe method
two space dimensions
NUMERICAL METHODS FOR INTEGRAL EQUATIONS
collocation method
degenerate kernel
fredholm integral equations
integral equation
integral equation of the first kind
integral equation of the second kind
iterative method
kernel
linear integral equation
newton’s method
nonlinear integral equation
numerical solution of integral equation
projection method
quadrature formula
regular kernel
singular integral equation
singular kernel
successive approximation method
system of linear algebraic equations
volterra integral equation
NUMERICAL ALGORITHMS FOR INVERSE AND ILL-POSED PROBLEMS
direct problem
ill-posed problem
inverse problem
regularizing operator
well-posed problem
SOLUTION OF ELECTROMAGNETISM THEORY PROBLEMS
capacity
conductor
dielectric
electric conductivity
electrostatics
elliptical equation
energy
finite element method.
hyperbolic system of equations
inductance
magnet
magnetic field
magnetostatics
mathematical modelling
Maxwell equations
potential
variational principle
vector potential
Electric field
COMPUTATIONAL METHODS IN ELASTICITY
Energy minimization
Finite element method
Kirchhoff-Love model
Linear elasticity
Mindlin-Naghdi-Reissner model
Modal analysis
Step-by-step methods
Thin plates
Elastodynamics
COMPUTATIONAL METHODS FOR COMPRESSIBLE FLOW PROBLEMS
1- D problems
multidimensional problems
numerical examples
numerical schemes
computational methods
METHODS OF NONLINEAR KINETICS
Bhatnagar-Gross-Krook model
Chapman-Enskog method
direct simulation
discrete velocity models
Grad moment method
H theorem
Hilbert method
kinetic models
method of invariant manifold
quasi-equilibrium approximation
Boltzmann equation
METHODS FOR MAGNETOSPHERE AND NEAR-SPACE PROBLEMS
alfvèn-Mach number
bow shock
geomagnetic field
interplanetary magnetic field
magnetic barrier
magnetic field connection.
magnetohydrodynamics
magnetopause
magnetosheath
magnetosphere
solar wind
space plasma
NUMERICAL SIMULATION OF CLIMATE PROBLEMS
carbone acid
climate theory
computational models
global climate
greenhouse effect
numerical modeling
regional climate
NUMERICAL SIMULATION OF BIOSPHERE DYNAMICS
biosphere dynamics
biosphere's model
closed ecological systems
global change
global feedbacks
numerical simulation
NUMERICAL METHODS FOR WEATHER FORECASTING PROBLEMS
filtered Models
full Hydrothermodynamic Equations
global Models
numerical Methods
parameterization Schemes.
regional and Mesoscale Models
weather Forecast
OPTIMIZATION AND OPERATIONS RESEARCH
decision analysis
decision models
game theory
mathematical programming
modeling process
optimization models
scientific decision making
stochastic processes
FUNDAMENTALS OF OPERATIONS RESEARCH
combinatorial optimization
computational efficiency
constraints
discrete optimization
integer programming
linear programming
mathematical programming
modeling process
nonlinear programming
objective function
optimization algorithm
optimization model
THE ROLE OF MODELING
cave (parable of the)
decision making
explicit knowledge
external (explicit) model
greek roots
image
implicit (tacit) model
interdisciplinarity
internal model
internal stage
linear programming
management science
model
model design
model management
modeling
models for practice
models for theory
morphology
operations research
planet laws
plato
pythagoras
relational database
simulation
standard software for optimization
tacit knowledge
zwicky
LINEAR PROGRAMMING
average-case complexity
duality
ellipsoid method
interior point methods
linear inequalities
linear programming
optimization
polyhedra
simplex method
worst-case complexity
NONLINEAR PROGRAMMING
barrier method
convergence
interior point method
karush-Kuhn-Tucker condition
large scale optimization
nonlinear programming
optimality
optimization
penalty method
reduced gradient method
sequential convex programming
sequential linear programming
sequential quadratic programming
DYNAMIC PROGRAMMING
bellman
curse of dimensionality
decomposition
dynamic programming
functional equation
invariant embedding
markovian condition
monotonicity condition
objective function
optimization
policy
policy iteration
principle of optimality
recovery procedure
sequential decision process
stage
state
stationary
stochastic processes
successive approximation
transition function
value iteration
DISCRETE OPTIMIZATION
branch and bound
greedy algorithm
heuristic method
integer linear program
linear optimization
relaxation
THE ROLE OF SOFTWARE IN OPTIMIZATION AND OPERATIONS RESEACH
computational economics
mathematical programming
mathematical programming systems
optimization
ADVANCED DETERMINISTIC OPTIMIZATION
approximation schemes
combinatorial optimization
computational complexity
cutting planes
discrete optimization
duality
heuristics
integer programming
job scheduling
linear programming
matchings
matroids
network flows
packing and covering
polyhedra
routing
shortest paths
spanning trees
linear systems
COMBINATORIAL OPTIMIZATION AND INTEGER PROGRAMMING
branch-and-bound
combinatorial optimization problem
cutting plane
linear program
mixed integer program
NP-hard
polyhedra
relaxation
GRAPH AND NETWORK OPTIMIZATION
applications of graphs and networks
augmenting path algorithm
cycle-canceling algorithm
dijkstra’s algorithm
graphs
kruskal’s algorithm
label-correcting algorithm
maximum flow problem
minimum cost flow problem
minimum cut problem
minimum spanning tree problem
networks
optimality conditions
preflow-push algorithm
shortest path problem
transportation
SCHEDULING
approximation algorithms.
branch-and-bound methods
classification scheme
complexity
dynamic programming
genetic algorithms
local search methods
lower bounds
machine scheduling
NP-hard
polynomially solvable
project scheduling
scheduling
timetabling
ROUTING PROBLEMS
arc routing
capacitated arc routing problem
chinese postman problem
node routing
traveling salesman problem
vehicle routing
LARGE SCALE OPTIMIZATION
aggregation
Benders’ decomposition
Dantzig-Wolfe decomposition
Lagrangian Relaxation
LP relaxation
mixed integer program
projection
modeling issues.
large-scale optimization
DUALITY THEORY
complementary slackness
duality
karush-Kuhn-Tucker conditions
perturbation function
saddle point
supporting functions
NONSMOOTH OPTIMIZATION
bundle method
convexity
duality
Lagrangian relaxation
large-scale systems
SDP optimization
optimization
GLOBAL OPTIMIZATION AND META-HEURISTICS
genetic algorithms
meta-heuristics
optimization
scatter search
tabu search
APPROXIMATION ALGORITHMS
approximation algorithm
approximation scheme
complexity class
gap technique
optimization
performance ratio
reducibility
OPTIMIZATION IN INFINITE DIMENSIONS
calculus of variations
convex optimization
duality
dynamic programming
finite element method
lagrange function
necessary optimality conditions
nonsmooth optimization
optimal control
optimal shape design
partial differential equations
shape optimization
variational method
THE PRINCIPLES OF THE CALCULUS OF VARIATIONS
(necessary, sufficient) legendre condition
(strict, sufficient) legendre-Hadamard condition
(uniformly) strongly elliptic
(uniformly) superelliptic
(weak) extremal
(weak) lower semicontinuity
(weak) minimizer
area integral
brachistochrone problem
coercivity
compactness
completeness
convexity
critical case
critical point
direct method
dirichlet’s integral
dirichlet’s principle
euler-Lagrange equations
existence
first variation
friedrichs mollifier
fundamental lemma
generalized function
harmonic function
hilbert’s problems
index theory
indirect method
lagrange function
ljusternik-Schnirelman theory
local minimum (maximum)
minimal surface equation
minimax principle
minimizing sequence
morse theory
mountain-Pass lemma
multiple integrals
non-convex problems
palais-Smale condition
partial regularity
positive (semi) definite
regularity
relaxation
singularity
unstable critical points
variational integral
weyl’s lemma
yamabe problem
Γ-convergence
THE MAXIMUM PRINCIPLE OF PONTRYAGIN
Adjoint function
Bang-bang control
Dynamic programming
Homotopy method
Maximum principle
Multiple shooting method
Numerical solution
Polyhedral constraints
Shooting method
Singular control
Optimal control
DYNAMIC PROGRAMMING AND BELLMAN'S PRINCIPLE
calculus of variations
Hamilton-Jacobi equation
linear quadratic regulator
optimal control
optimal feedback control
optimal feedback synthesis
Riccati equation
viscosity solutions
dynamic programming
OPTIMIZATION AND CONTROL OF DISTRIBUTED PROCESSES
adjoints
control
discretization
distributed processes
distributed systems
feasible set
Gauss-Newton method
gradient
Hessian
interior-point methods
Lagrange function
Lagrange multipliers
line-search method
Newton method
optimal control
optimal shape design
optimality conditions
parameter identification
quasi-Newton method
sensitivity equation
sequential quadratic programming
state
state equation
trust-region method
adjoint equation
NONCONVEX VARIATIONAL PROBLEMS
calculus of variations
compatibility
convex
direct method
envelope
minimizer
minimizing sequence
nonconvex
oscillations
polyconvex
probability
quasiconvex
rank one convex
relaxation
vector valued
wells
young measure
GAME THEORY
allocation
apportionment
aumann economy
axiomatic approach
balanced games
bargaining solution
characters
coalitional form
convex games
cooperative game
coordination game
core
cost sharing
directed games
equivalence principle
evolutionary stability
exchange economy
extensive form
fictitious play
game form
homogeneous games
implementation
incentive compatible
kalai-Smorodinsky solution
knowledge
LP-game
maschler-Perles solution
mechanism
modiclus
nash equilibrium
nash solution
normal form
nucleolus
outcome function
payoff function
reduced games
repeated games
revelation principle
shapley value
simple games
social choice rule
TU-game
vNM-Stable Set
voting games
walrasian equilibrium.
FOUNDATIONS OF NON-COOPERATIVE GAMES
bayesian game
bayesian Nash equilibrium
chess-like game
consistency
determinacy
extensive form
information
nash equilibrium
non-cooperative game
non-zero-sum game
payoff function
rationality
strategic form
strategy
subgame perfect equilibrium
value
zero-sum game
NTU-GAMES
balancedness
bargaining sets
compromise solution
core
egalitarian bargaining solution
egalitarian NTU-solution
games with transferable utility
harsanyi solution
hart-Mas-Colell consistent solution
kalai-Samet solutions
kalai-Smorodinsky bargaining solution
market games
nash bargaining solution
non-cooperative procedure
nontransferable utility games
objections and counterobjections
pure bargaining games
reduced game
reduced game property
shapley NTU-solution
shapley TU-value
τ-value
TU-GAMES
bargaining set
characteristic function
coalition
competitive equilibrium
core
cost allocation
dominance relation
imputation
kernel
limit theorem
market game
nucleolus
revenue allocation
Shapley value
ShapleyShubik index
stable set
transferable utility
voting game
weighted majority game
cooperative game
THE EQUIVALENCE PRINCIPLE
approximately decentralization
atomless economy
core
equivalence
geanakoplos bargaining set
large finite economy
mas-Colell Bargaining set
nash equilibrium.
strongly fair net trades
value
walrasian allocation
walrasian equilibrium
MECHANISM THEORY
auction
balance
bargaining
bayesian equilibrium
bayesian incentive compatibility
direct mechanism
dominant strategy
efficiency
implementation.
individual rationality
mechanism
mechanism design
public goods
revelation principle
single-peaked preferences
social choice function
strategy-proof
STOCHASTIC AND REPEATED GAMES
bayesian game
cooperation
discounted game
finitely repeated game
infinitely repeated game
information
nash equilibrium
non-zero-sum game
stochastic game
strategic game
strategy
supergame
value
zero-sum game
EVOLUTION AND LEARNING IN GAMES
bounded rationality
coordination games
cournot equilibrium
efficiency
equilibrium selection
evolution
evolutionarily stable strategy
hawk-Dove game
learning
mutation
nash equilibrium
payoff monotonicity
random matching
replicator dynamics
risk dominance
walras equilibrium.
EXPERIMENTAL GAME THEORY
adaptation dynamics
characteristic function experiments
common knowledge
random price mechanism
repeated play
strategic bargaining
ultimatum game
STOCHASTIC OPERATIONS RESEARCH
adaptive dynamic programming
backward induction algorithm
black-Scholes model
economic order quantity
estimation and control.
limit distribution
little’s formula
markov chain
markov decision process
markowitz model
minimax theorem
multi-period inventory model
nash-equilibrium
optimal policy
queueing discipline
queueing system
recurrence
stochastic game
total and average reward criteria
two-fund separation
MARKOV MODELS
chapman-Kolmogorov equation
continuous-time Markov chains
discrete-time Markov chains
embedded Markov chain
intensity matrix
limit distribution
recurrence
solidarity property
stationary distribution
transience
MARKOV DECISION PROCESSES
average reward
backward induction algorithm
linear programming.
markov decision problem
optimal policy
optimality equation
policy improvement
policy iteration
stochastic dynamic program
total reward criteria
STOCHASTIC GAMES
discounted and average reward games
general-sum games
mathematical programming
minimax theorem
nash-equilibria
optimal strategies
zero-sum games
QUEUEING SYSTEMS
Erlangs loss system
Littles formula
multiclass queueing network
Pollaczek-Khintchine formula
product form distribution.
service facilities
virtual waiting time
waiting time
queueing discipline
INVENTORY MODELS
(s, S) policy
continuous review
economic order quantity
inventory control
markov decision processes
multi-level inventory systems
periodic review
INVESTMENT MODELS
black-Scholes model
HARA-utility
markowitz model
martingale method
mean-variance portfolio selection
minimum variance portfolio
stochastic control
stochastic dynamic programming
two-fund separation
ADAPTIVE DYNAMIC PROGRAMMING
adaptive
applications
average reward
decision process
discounted
dynamic programming
estimation and control
nonstationary value iteration
policy iteration
DECISION ANALYSIS
allais paradox
behavioral decision theories
decision making under uncertainty
decision rule
decision tree
dominance
efficiency
expected utility paradigm
influence diagram
multiple criteria decision making
rationality axioms
risk-value approach
EXPECTED UTILITY THEORY AND ALTERNATIVE APPROACHES
allais paradox
betweenness
common ratio effect
disappointment aversion
dual expected utility
expected utility
implicit expected utility
independence axiom
prospect theory
rank-dependent utility
weighted utility
RISK-DEFUSING BEHAVIOR
cognitive bias
control
cost of risk defusing operators
decision making
effect of risk defusing operators
lottery
outcome compensation
outcome prevention
probability
probability judgment
risk defusing operators
risky decisions
structuring the decision situation
worst-case plan
DECISION PROBLEMS AND DECISION MODELS
ambiguity
decision
decision criteria
decision tree
expected utility
influence diagram.
non-expected utility
rank-dependent expected utility
risk
uncertainty
voting theory
MULTIPLE-CRITERIA DECISION MAKING
decision theory
dominance
efficiency
interactive procedures
value functions
value theory
vector optimization
multiple-objective decision making (MODM)
DECISION TREES AND INFLUENCE DIAGRAMS
decision making under uncertainty
decision trees
influence diagrams
FRAMING EFFECTS IN THEORY AND IN PRACTICE
behavioral Decision Theory
behavioral Economics
bias
choice
framing
prospect theory
regulatory focus
risk
subjective Expected Utility
utility
FUZZY DECISION THEORY
decision theory
fuzzy intervals of the ε-λ-type
fuzzy probabilities
fuzzy utilities
information costs
multi-criteria decision making
MEASUREMENT OF RISK
decision making under risk
risk
risk judgement
risk measure
risk perception
risk-value models
value-at-risk
variance
volatility
FOUNDATIONS OF TARGET-BASED DECISION THEORY
customer satisfaction
reliability theory
targets
utilitarianism
utility theory
MATHEMATICS IN JAPAN
mathematics ; Japan ; China ; algebra ; analysis ; infinite series ; Tokugawa period ; abacus ; commercial arithmetic ;
THE MATHEMATIZATION OF THE PHYSICAL SCIENCES - DIFFERENTIAL EQUATIONS OF NATURE
applied mathematics
differential equations
mathematical physics
history of mathematics
A SHORT HISTORY OF DYNAMICAL SYSTEMS THEORY: 1885-2007
bifurcation
center manifold
deterministic chaos
dimension reduction
ergodic
homoclinic orbit
hyperbolic set
instability
invariant manifold
K system
Kolmogorov-Arnold Moser theorem
Melnikov function
mixing
nonlinear dynamics
nonlinear oscillators
normal form theory
Poincare map
quasiperiodic orbit
random
Smale horseshoe
stability
strange attractor
structural stability
symbolic dynamics
unfolding
van der Pol equation.
Arnold diffusion
MEASURE THEORIES AND ERGODICITY PROBLEMS
ergodic
invariance
measure
THE NUMBER CONCEPT AND NUMBER SYSTEMS
complex numbers
foundations of mathematics
geometry.
number theory
octonions
quaternions
History of mathematics
OPERATIONS RESEARCH AND MATHEMATICAL PROGRAMMING: FROM WAR TO ACADEMIA – A JOINT VENTURE
game theory
linear programming
logistic planning
Mathematical Programming
Taylorism
Operations Research OR
ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT
algebra
arithmetic
calculus
computation
geometry
History of mathematics
THE HISTORY AND CONCEPT OF MATHEMATICAL PROOF
axiom
computer proof
deduction
definition
intuitionism
postulate
rigor
Proof
BOURBAKI, AN EPIPHENOMENON IN THE HISTORY OF MATHEMATICS
abstract mathematics
algebra
sets
topology 10mm
Structure
MATHEMATICAL MODELS IN ECONOMICS
business cycle
core trade theorems
creative destruction
education
factor price equalization theorem
general equilibrium
Heckscher-Ohlin theorem
Keynesian economics
learning by doing
Malthus’ population theory
monetary economic growth
multi-sector growth model
neoclassical growth theory
OLG model
preference change
Ramsey growth model
Ricardo’s economic theory
Schumpeterian growth
Solow growth model
Tobin’s model
trade theory
von Thunen’s spatial economics.
chaos
INTRODUCTION TO MATHEMATICAL ECONOMICS
business cycle theory
calculus of variations
capital value
central place theory
duopoly and oligopoly
dynamical processes
expected utility doctrine
general economic equilibrium
imperfect markets
internal rate of return
investment decisions
land use theory
linear and nonlinear programming
location theory
migration
multiple coexistent attractors
optimization
portfolio selection
rank-size relations
uniqueness and optimality.
attraction basins
MATHEMATICAL MODELS IN INPUT-OUTPUT ECONOMICS
decomposition analysis
dynamic models
environmental models
Leontief inverse
multipliers
multiregional models
open and closed models
physical and price models
price-quantity duality
scenario analysis
world models
input-output economics
ECONOMIC DYNAMICS
Cobweb model
Cournot duopoly model
difference equation
differential equation
Hopf bifurcation
Kaldor model
logistical map
Lyapunov stability
oligopoly
periodic motion
quasi-periodic motion
Solow-Swan model
tâtonnement
chaotic dynamics
ECONOMETRIC METHODS
Generalized Method of Moments
limited dependent variables
Maximum Likelihood
panel
time series
Least Squares
GENERAL EQUILIBRIUM
Commodity space
Continuum economies
Core
Edgeworth equilibrium allocations
Equilibrium
Exchange economy
Feasible allocation
Incomplete markets
Non-convexities
Pareto optimum
Price space
Production economy
Public goods
Quasi-equilibrium
Time and uncertainty
LABOUR MARKET ANALYSIS: ISSUES AND FACTS
basic amenities
informal sector
low income households
non-farm
poverty
remittances
rural-urban migration
segmentation
slums
urbanization
agglomeration economies
HOUSEHOLD BEHAVIOR AND FAMILY ECONOMICS
Collective Approach
Consensus Model
Domestic Production
Good Demand
Household Behavior
Identifiability
Income Pooling
Intra-household Bargaining
Labor Supply
Rotten Kid Theorem
Slutsky Matrix
Strategic Approach
Testability
Unitary Approach
Family Economics
WELFARE THEORY: HISTORY AND MODERN RESULTS
Cost Benefit Analysis
First and Second Welfare Theorem
Microeconomics
Public Goods
Social Accounting
Welfare theory
SOCIAL CHOICE
Cycles
Nakamura Theorem
Voting.
Impossibility Theorem
MATHEMATICAL MODELING IN AGRICULTURAL ECONOMICS
Consumer theory
Econometrics
Game theory
Mathematical programming
Mechanism design
Microeconomics
Producer theory
Welfare economics.
Agriculture
MODELS OF ECONOMIC GROWTH
dynamics
endogenous growth
externalities
fiscal policy
human capital
indeterminacy.
infrastructure capital
investment
knowledge
marginal product of capital
Stylized facts
MATHEMATICAL MODELS OF ENVIRONMENTAL ECONOMICS
incentives
resources
strategic interactions
uncertainty.
externalities
MONEY IN ECONOMIC ANALYSIS
inflation and deflation
central bank
demand and supply of money
IS-LM analysis
Keynesian macroeconomics
liquidity preference
monetary policy
Tobin’s q
Walrasian general equilibrium
quantity theory of money
MODELS OF INTERNATIONAL ECONOMICS
balance of payments
comparative cost
factor endowments
flow approaches
Heckscher-Ohlin model
international finance
international monetary economics
international trade
intertemporal approach
non tariff barriers
open economy macroeconomics
optimum tariff
political economy of protectionism
Ricardo
stock approaches
tariffs
trade policy
Walras’ law.
Absorption
GROWTH, DEVELOPMENT AND TECHNOLOGICAL CHANGE
Economic growth
Horizontal Innovations
Scale effects
Vertical innovations.
Endogenous technical change
INNOVATION AND ECONOMIC DYNAMICS
and Non-proprietary Goods
Imitation
Market Power
Patent Rights
Research and Development (R&D)
Subsidies
Innovation
GROWTH AND DEVELOPMENT WITH INCOME AND WEALTH DISTRIBUTION
Balanced Growth
Income Inequality
Increasing Returns
Learning by Doing
Majority Voting
Median Voter
Optimal Paths
Cumulative Gross Investment
MATHEMATICAL MODELS OF TRANSPORTATION AND NETWORKS
Braess paradox
centralized versus decentralized decision-making
complex networks
dynamics of networks
electric power generation and distribution networks
financial networks
Internet
network equilibrium
network metrics and importance identification
supply chains
system-optimization
traffic assignment
transportation network vulnerability
user-optimization
variational inequalities
transportation
MATHEMATICAL MODELS IN REGIONAL ECONOMICS
computable general equilibrium model
endogenous growth
input-output model
neural network
new economic geography
spatial decision support system
spatial econometrics
spatial interaction
structural simultaneous equations model
MATHEMATICAL MODELS OF RESOURCE AND ENERGY ECONOMICS
Energy Efficiency
Faustmann’s Rule
Herfindahl’s Rule
Order of Exploitation
Tragedy of the Common
Hotelling’s Rule
MATHEMATICAL MODELS IN SPATIAL ECONOMICS
agglomeration
equilibrium and stability
equilibrium flows in two-dimensional space
gradient and divergence law
interaction costs
location
urban externalities
spatial competition
Last Update: 3 July 2008
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