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Whether or not there exists a set of values to satisfy a given system of equations
implies 5 = 6). Both types of equation system, inconsistent and consistent, can be any of overdetermined (having more equations than unknowns), underdetermined
Consistent and inconsistent equations
Consistent_and_inconsistent_equations
Statistical estimator
probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency as defined here is sometimes
Consistent_estimator
Several equations of degree 1 to be solved simultaneously
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example
System_of_linear_equations
Topics referred to by the same term
Consistency Theory, an album by 1200 Techniques Consistent and inconsistent equations, in mathematics Consistent life ethic, an ideology stating that life is
Consistency_(disambiguation)
Field-equations in general relativity
field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter-energy within it. The equations were
Einstein_field_equations
Description of the time-evolution of plasma
difference of this system of equations from equations for particles in an external electromagnetic field is that the self-consistent electromagnetic field depends
Vlasov_equation
More equations than unknowns (mathematics)
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[citation needed] An overdetermined system
Overdetermined_system
Family of macroeconomic models
continuous time as differential equations or differential-algebraic equations. Simple models can be solved analytically and investigated by means of concepts
Stock-flow_consistent_model
Interpretation of quantum mechanics
history obey the rules of classical probability while being consistent with the Schrödinger equation. In contrast to some interpretations of quantum mechanics
Consistent_histories
System of equations in mathematics
differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to
Differential-algebraic system of equations
Differential-algebraic_system_of_equations
independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept
Independent_equation
Mathematical concept
mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast
Underdetermined_system
Form of causal modeling that fit networks of constructs to data
indirect effects among his observed variables. The equations were estimated like ordinary regression equations but the substantive context for the measured
Structural_equation_modeling
Branch of mathematics
linear equations and combinations of them called systems of linear equations. It provides methods to find the values that solve all equations in the system
Algebra
Limitative results in mathematical logic
that both the statement and its negation are provable from the axioms, and inconsistent otherwise. That is to say, a consistent axiomatic system is one
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Equation in fluid dynamics
is equivalent to the Hagen–Poiseuille equation, which is analytically derived from the Navier–Stokes equations. The head loss Δh (or hf) expresses the
Darcy–Weisbach_equation
When a decision-maker's future preferences can contradict earlier preferences
In economics, dynamic inconsistency or time inconsistency is a situation in which a decision-maker's preferences change over time in such a way that a
Dynamic_inconsistency
Asymptotic variances under heteroskedasticity
heteroskedasticity-consistent (HC) standard errors arises in statistics and econometrics in the context of linear regression and time series analysis
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Hypothetical topological feature of spacetime
Wormholes are based on a special solution of the Einstein field equations, and are consistent with the general theory of relativity. In 1995, Matt Visser
Wormhole
Field equation for spin-3/2 fermions
such as γμψμ=0, must imply consistent secondary divergence constraints, and these constraints must be preserved by the equations of motion. Non-minimal electromagnetic
Rarita–Schwinger_equation
Expression which is not assigned an interpretation
particular calculation or property can produce mathematically inconsistent results, and therefore, it should be avoided. Caution must be taken to avoid
Undefined_(mathematics)
Group allowing solution of all algebraic equations
because the first two equations imply x = 1 {\displaystyle x=1\ } . In this case we say the set of conditions are inconsistent with G {\displaystyle
Algebraically_closed_group
Dynamical system
dynamics equation is recovered. The analysis differs in the continuous and discrete cases: in the former, methods from differential equations are utilized
Replicator_equation
Statistical hypothesis test in econometrics
efficiency, while under the alternative Fixed effects (FE) is at least as consistent and thus preferred. Regression model validation Statistical model specification
Durbin–Wu–Hausman_test
Technique in statistics
ordinary least squares produces biased and inconsistent estimates. However, if an instrument is available, consistent estimates may still be obtained. An
Instrumental_variables
Physical theory describing classical fields
Maxwell's equations, a set of differential equations which directly relate E and B to the electric charge density (charge per unit volume) ρ and current
Classical_field_theory
Quantization method for constrained Hamiltonian systems with second-class constraints
dependence on the momenta, which means that equations of motion (Hamilton's equations) are inconsistent. The Hamiltonian procedure has broken down. One
Dirac_bracket
Zero energy solution to the Schrödinger equation in loop quantum gravity
down the equations of the Kodama state, but as it described a positive (de Sitter universe) spacetime, which was believed to be inconsistent with observation
Kodama_state
Interpretation of quantum mechanics
internally consistent and actualized alternative history or timeline. The many-worlds interpretation uses decoherence to explain the measurement process and the
Many-worlds_interpretation
Theoretical paradox resulting from time travel
Thorne and two of his students at Caltech, Fernando Echeverria and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies, and found
Temporal_paradox
Physics phenomenon
the sum of its parts". In 1932, Erwin Schrödinger derived the defining equations of quantum entanglement but left them unpublished. In 1935, Grete Hermann
Quantum_entanglement
Cosmological model
and cosmological constant all equal zero and the spatial curvature is negative.[citation needed] From these assumptions and the Friedmann equations it
Milne_model
Concept in econometrics
equations: yi=β1xi+γ1zi+ui zi=β2xi+γ2yi+vi Estimating either equation by itself results in endogeneity. In the case of the first structural equation,
Endogeneity_(econometrics)
Principle suggesting that time travel paradoxes are inherently impossible
are those which are globally self-consistent. This principle allows one to build a local solution to the equations of physics only if that local solution
Novikov self-consistency principle
Novikov_self-consistency_principle
Concepts from linear algebra
stacking into matrix form a set of equations consisting of the above difference equation and the k – 1 equations xt–1 = xt–1, ..., xt–k+1 = xt–k+1, giving
Eigenvalues_and_eigenvectors
Conceptual conflict between general relativity and quantum mechanics
approach, if one discretizes the constraints and equations of motion, the resulting discrete equations are inconsistent: they cannot be solved simultaneously
Problem_of_time
Type of formal logic
with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion. Inconsistency-tolerant logics
Paraconsistent_logic
Russian professor of Applied Mathematics
the possibility of construction new time consistent optimality principles from the previously time inconsistent ones. Applications to environmental protection
Leon_Petrosyan
How psychological biases shape investor behaviour and financial markets
previous levels. This interpretation is inconsistent with EMH but is consistent with asset flow differential equations (AFDE) that incorporate behavioural
Behavioural_finance
Origins of Einstein's gravitation theory
arguing that it is inconsistent based on the "hole argument". In 1914 and much of 1915, Einstein was trying to create field equations based on another approach
History_of_general_relativity
Parameter estimation technique in statistics
sample moments. The number of such equations is the same as the number of parameters to be estimated. Those equations are then solved for the parameters
Method of moments (statistics)
Method_of_moments_(statistics)
Attraction of masses and energy
Newton's equations. The corrections introduced by general relativity on Earth are on the order of 1 part in a billion. The Einstein field equations are a
Gravity
Statistical mechanics framework
theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation. The technique justifies the otherwise
Chapman–Enskog_theory
Family of implicit and explicit iterative methods
Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-412-8
Runge–Kutta_methods
Quantum mechanics taking into account particles near or at the speed of light
units and natural units are common alternatives. All equations are in the position representation; for the momentum representation the equations have to
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Theory in particle physics
fundamentally inconsistent at high energies. Some believed that there is only one consistent theory which requires infinitely many particle species and whose
Bootstrap_model
Interpretation of quantum mechanics
interpretation are not. The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations was explored in the Wheeler–Feynman absorber
Transactional_interpretation
Mathematical framework
differential equation subject to a boundary value problem (BVP). Regardless of the differential equation, these constraints may be consistent or inconsistent. For
Theory of functional connections
Theory_of_functional_connections
such as joint and conditional maximum likelihood estimation. Joint maximum likelihood (JML) equations are efficient, but inconsistent for a finite number
Rasch_model_estimation
1960 article by Eugene Wigner
is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known in the mid-19th century. The equations also describe
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Interpretation of quantum mechanics
Madelung equations, being quantum analog of Euler equations of fluid dynamics, differ philosophically from the de Broglie–Bohm mechanics and are the basis
De_Broglie–Bohm_theory
Computational quantum mechanical modelling method to investigate electronic structure
studied as a set of n one-electron Schrödinger-like equations, which are also known as Kohn–Sham equations. Although density functional theory has its roots
Density_functional_theory
Interpretation of quantum mechanics
result in inconsistent probabilities being attributed to observed states of the system. This is done by means of ascribing values to "frameworks", and all values
Relational_quantum_mechanics
Least squares approximation of linear functions to data
0=∂S∂β2=20β1+60β2−154. These normal equations constitute a system of two linear equations in two unknowns. The solution is β1=3.5 and β2=1.4, and the best-fit line is
Linear_least_squares
Model compatible with special relativity
entropy and σ is entropy production. This mathematical model is inconsistent with special relativity: the Green function associated to the heat equation (also
Relativistic_heat_conduction
Hypothesized alternative to a black hole
entirely new, unique exotic matter. This solution to the Einstein equations is stable and has no singularities. Instead, a gravastar is filled either with
Gravastar
Extension of the Bohr model
fundamentally inconsistent and led to many paradoxes. The magnetic quantum number measured the tilt of the orbital plane relative to the xy plane, and it could
Bohr–Sommerfeld_model
each other. This leads to an inconsistency, which gives systematic errors for strong interacting molecules. This inconsistency is solved in the COSMOSPACE
COSMOSPACE
Background energy existing in space
time. The time required is dependent on the mass of the black hole (the equations indicate that the smaller the black hole, the more rapidly it evaporates)
Vacuum_energy
Quantum field that enables consistent quantization
quantize the electromagnetic field, ghost fields are strictly needed to consistently and rigorously quantize non-Abelian Yang–Mills theory, such as done with
Ghost_(physics)
Calculation rule in quantum mechanics
played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Several other researchers have also tried to derive
Born_rule
Theory of interwoven space and time by Albert Einstein
and measure the properties of particles moving at near the speed of light, where their behavior is consistent with relativity theory and inconsistent
Special_relativity
Mathematical functions
equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics
Inverse_hyperbolic_functions
Equations relating to massless particles in AdS space
The Vasiliev equations are classical equations and no Lagrangian is known that starts from canonical two-derivative Frønsdal Lagrangian and is completed
Vasiliev_equations
Hypothetical particle with one magnetic pole
zero, and the extended equations reduce to the conventional equations of electromagnetism such as ∇ ⋅ B = 0 (where ∇⋅ is the divergence operator and B is
Magnetic_monopole
Modelling evolution using differential equations
biology that developed from research using differential equations to model both genetic and phenotypic change. Thus it differs from population genetics
Evolutionary_dynamics
Study of matter-light interactions at small scales
energy levels was then consistent with observation. These results, based on a discrete set of specific standing waves, were inconsistent with the continuous
Atomic, molecular, and optical physics
Atomic,_molecular,_and_optical_physics
Description of physical properties at the atomic and subatomic scale
in quantum equations in position space, the momentum pi is replaced by −iℏ∂∂x, and in particular in the non-relativistic Schrödinger equation in position
Quantum_mechanics
Theory of gravity by Albert Einstein
theory: the equations describing how matter influences spacetime's curvature. Having formulated what are now known as Einstein's equations (or, more precisely
Introduction to general relativity
Introduction_to_general_relativity
Informal set theories
axiomatic set theories) cannot be proved consistent from within the theory itself – unless it is actually inconsistent. However, the common axiomatic systems
Naive_set_theory
Area of physical and philosophical debate
additive rules of classical probability. It is claimed to be consistent with the Schrödinger equation. According to this interpretation, the purpose of a quantum-mechanical
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Supergravity in eleven dimensions
that the resulting four dimensional theory is not consistent with the higher dimensional field equations. Physically this needs not be a problem in compactifications
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Analysis of the dimensions of different physical quantities
homogeneity, obtain a set of simultaneous equations involving the exponents a, b, c, ..., m. Solve these equations to obtain the values of the exponents a
Dimensional_analysis
Statistical property
normalized and centered, with a variance-covariance matrix that differs from the case of homoscedasticity. In 1980, White proposed a consistent estimator
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Form of statistical factor analysis
to be consistent with their theory. For example, if it is posited that there are two factors accounting for the covariance in the measures, and that these
Confirmatory_factor_analysis
Valuation separating financing effects
discounted cash flow valuation: consistent and inconsistent ways to value risky cash flows". "FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES" (PDF). Archived
Adjusted_present_value
International standard for the use and calculation of the thermodynamic properties
used for the calculation. Furthermore, EOS-80 was not consistent with meteorological equations while TEOS-10 is valid for humid air as well as for seawater
TEOS-10
Process in quantum mechanical theories
a wavefunction. The classical equations of motion of a field are typically identical in form to the (quantum) equations for the wave-function of one of
Canonical_quantization
Experiments to test Bell's theorem in quantum mechanics
decay and analyzed by Compton scattering. The experiment observed photon polarization correlations consistent with quantum predictions and inconsistent with
Bell_test
Proposed theories of gravity
Morduch, Kustaanheimo and Kustaanheimo and Nuotio are either incomplete or inconsistent. The incorporation of Maxwell's equations is incomplete unless
Alternatives to general relativity
Alternatives_to_general_relativity
T (1992) The inconsistency of consistent conjectures", Journal of Economic Behavior and Organization, volume 18, pp. 69–80 Dixon H and Somma E, (2003)
Conjectural_variation
Theory with particles of spin more than two
The Vasiliev equations are classical equations and no Lagrangian is known that starts from canonical two-derivative Fronsdal Lagrangian and is completed
Higher-spin_theory
inequalities, but Adian pointed out that these inequalities were inconsistent. Novikov and Adian had previously found a correct solution around 1968. Classification
List_of_incomplete_proofs
Predecessor to modern quantum mechanics (1900–1925)
mechanical wave-equation, which reproduced all the successes of the old quantum theory without ambiguities and inconsistencies. The Schrödinger equation developed
Old_quantum_theory
Concept in physical models
singular, exact solution of Einstein's equations with cosmological constant. In a subsequent article, Mbarek and Paranjape showed that it is in fact possible
Negative_mass
Economic model
subsequent equations are substituted into the first three equations above, one has a system of three equations in three unknowns, two of which are GDP and the
Mundell–Fleming_model
Cosmological theory
that the MUH is inconsistent with Gödel's incompleteness theorem. In a three-way debate between Tegmark and fellow physicists Piet Hut and Mark Alford, the
Mathematical universe hypothesis
Mathematical_universe_hypothesis
Regression models accounting for possible errors in independent variables
}}_{x}} is an inconsistent estimator for β {\displaystyle \beta } . However, β ^ x {\displaystyle {\hat {\beta }}_{x}} is a consistent estimator of the
Errors-in-variables_model
Belief that natural wholes are similar to machines
modern consensus in the scientific and mathematical community is that actual human reasoning is inconsistent: any consistent "idealized version" H of human
Mechanism_(philosophy)
Statistical estimation technique
estimator σ2∗(XTX)−1 (which is inconsistent in this framework) and instead use a HAC (Heteroskedasticity and Autocorrelation Consistent) estimator. In the context
Generalized_least_squares
Time travel using quantum mechanics
of general relativity. Quantum mechanics requires physicists to solve equations describing how probabilities behave along closed timelike curves (CTCs)
Quantum mechanics of time travel
Quantum_mechanics_of_time_travel
Hypothetical faster-than-light particle
they are inconsistent with the known laws of physics. If such particles did exist, they perhaps could be used to send signals faster than light and into the
Tachyon
Mathematician and philosopher (1906–1978)
value of all statements about the natural numbers, and cannot prove that it is itself consistent. To prove this, Gödel developed a technique now known
Kurt_Gödel
Theory in modern physics that describes gravity as an entropic force
equations from an entropic gravity perspective, Tower Wang shows that the inclusion of energy-momentum conservation and cosmological homogeneity and isotropy
Entropic_gravity
Obsolete physics theory
detector-target distances were consistent with there being no dependence of the speed of light on the velocity of the source, and were inconsistent with modeled behavior
Emission_theory_(relativity)
Claim that human mathematicians are not describable as formal proof systems
consistent. Referencing Benacerraf, he argues that humans cannot prove that they are consistent, and in all likelihood human brains are inconsistent algorithms
Penrose–Lucas_argument
Concept in computational chemistry
multi-configurational self-consistent field (MCSCF) method because the Hartree–Fock determinant is qualitatively wrong and so are the CI wave functions and energies. Coupled
Configuration_interaction
Turing machine with 748 states which halts if and only if there is an inconsistency in ZFC. If ZFC is consistent, it cannot prove this machine halts. It therefore
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Theory that the universe is the same in all directions
Georges Lemaître derived in 1927 the equations of an expanding universe from the General Relativity equations. Thus, a non-static universe is also implied
Cosmological_principle
from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
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CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
CONSISTENT AND-INCONSISTENT-EQUATIONS
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