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Longer titles found: Cubic equations of state (view)

searching for Cubic equation 40 found (109 total)

Tschirnhaus transformation (1,162 words) [view diff] exact match in snippet view article find links to article

y(x)=k1x2+k2x+k3{\displaystyle y(x)=k_{1}x^{2}+k_{2}x+k_{3}} for a cubic equation of degree n=3{\displaystyle n=3}, f(x)=x3+a2x2+a1x+a0{\displaystyle

Plummer model (1,037 words) [view diff] exact match in snippet view article find links to article

from single real root of the discriminant of the cubic equation, which is itself another cubic equation E_L_c3+(6E_2a_2+12)L_c2+(12E_3a_4+20E_a_2)L_c+(

Vyacheslav Lebedev (mathematician) (348 words) [view diff] exact match in snippet view article

to parallel computing. He even contributed to finding the roots of a cubic equation. He was a recipient of the Soviet State Award for developing mathematical

Redlich–Kwong equation of state (3,591 words) [view diff] exact match in snippet view article find links to article

and Joseph Neng Shun Kwong in 1949. It showed that a two-parameter, cubic equation of state could well reflect reality in many situations, standing alongside

Process simulation (1,079 words) [view diff] exact match in snippet view article find links to article

The modelling of chemical properties began much earlier, notably the cubic equation of states and the Antoine equation were precursory developments of the

Menaechmus (1,063 words) [view diff] exact match in snippet view article find links to article

at which two parabolas intersect, a solution equivalent to solving a cubic equation. There are few direct sources for Menaechmus's work; his work on conic

Hessian pair (334 words) [view diff] exact match in snippet view article find links to article

then transformed to 0 and ∞ by a fractional linear transformation, the cubic equation is transformed to one of the form x3 = D. Glossary of classical algebraic

Hasse principle (1,215 words) [view diff] exact match in snippet view article find links to article

Hasse–Minkowski theorem cannot be extended to forms of degree 3: The cubic equation 3x3 + 4y3 + 5z3 = 0 has a solution in real numbers, and in all p-adic

Snub disphenoid (1,856 words) [view diff] exact match in snippet view article find links to article

{2-2q}}\approx 1.28917.} Because this construction involves the solution to a cubic equation, the snub disphenoid cannot be constructed with a compass and straightedge

Sharaf al-Din al-Tusi (1,547 words) [view diff] exact match in snippet view article find links to article

the "Ruffini-Horner method" to numerically approximate the root of a cubic equation. He also developed a novel method for determining the conditions under

Philo line (2,343 words) [view diff] exact match in snippet view article find links to article

P_{x}-P_{y})x-(mP_{x}-P_{y})(P_{x}^{2}+P_{y}^{2}).} So solving that cubic equation finds the intersection of the Philo line on the horizontal axis. Plugging

Exercises in Style (951 words) [view diff] exact match in snippet view article find links to article

mathematician Philip Ording published his 99 Variations on a Proof (2019) of a cubic equation that offers solutions from various perspectives. The computer scientist

Quaternion Society (1,383 words) [view diff] exact match in snippet view article find links to article

1. Prof. A. Macfarlane read a communication on the solution of the cubic equation in which he explained how the two binomials in Cardano’s formula may

Doubling the cube (1,993 words) [view diff] case mismatch in snippet view article find links to article

& Sons. Guilbeau, Lucye (1930). "The History of the Solution of the Cubic Equation". Mathematics News Letter. 5 (4): 8–12. doi:10.2307/3027812. JSTOR 3027812

PH (6,066 words) [view diff] exact match in snippet view article find links to article

weak acids, a quadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set of non-linear simultaneous equations

Robert William Genese (357 words) [view diff] case mismatch in snippet view article find links to article

in space. "Suggestions for the Practical Treatment of the Standard Cubic Equation, and a Contribution to the Theory of Substitution." The Mathematical

Plato's number (1,138 words) [view diff] case mismatch in snippet view article find links to article

Weisstein, Eric W. "Plato's Numbers". MathWorld. Ramanujan And The Cubic Equation 33 + 43 + 53 = 63 Math world : Diophantine Equation--3rd Powers Sum

List of Runge–Kutta methods (4,255 words) [view diff] exact match in snippet view article find links to article

three roots of the cubic equation x3−3x2/2+x/2−1/24=0{\displaystyle x^{3}-3x^{2}/2+x/2-1/24=0}. The three roots of this cubic equation are approximately

Completing the square (3,102 words) [view diff] exact match in snippet view article find links to article

transformation is generally the first step of the mehods for solving the general cubic equation. More generally, a similar transformation can be used for removing terms

Thermistor (3,870 words) [view diff] exact match in snippet view article find links to article

the unit. To give resistance as a function of temperature, the above cubic equation in ln⁡R{\displaystyle \ln R} can be solved, the real root of which is

Parabola (12,576 words) [view diff] exact match in snippet view article find links to article

the circle around C{\displaystyle C} and the parabola leads to the cubic equation 4x3−3x−cos⁡(3α)=0{\displaystyle 4x^{3}-3x-\cos(3\alpha )=0}. The triple-angle

Diophantine equation (4,538 words) [view diff] exact match in snippet view article find links to article

encountered in practice, but no algorithm is known that works for every cubic equation. Homogeneous Diophantine equations of degree two are easier to solve

Timeline of scientific discoveries (10,188 words) [view diff] exact match in snippet view article find links to article

natural sciences. 16th century: Gerolamo Cardano solves the general cubic equation (by reducing them to the case with zero quadratic term). 16th century:

Nomogram (2,449 words) [view diff] exact match in snippet view article find links to article

missing term of the law of sines or the roots of the quadratic and cubic equation. Nomogram for the law of sines Nomogram for solving the quadratric x^2+px+q=0

List of numbers (3,861 words) [view diff] exact match in snippet view article find links to article

{23}{3}}}}}} 1.324717957244746025960908854478 The unique real root of the cubic equation x3 = x + 1.(OEIS: A060006) The limit ratio between subsequent numbers

VTPR (1,176 words) [view diff] case mismatch in snippet view article find links to article

Oldenburg, 2011 Twu C.H., Bluck D., Cunningham J.R., Coon J.E., "A Cubic Equation of State with a New Alpha Funktion and a New Mixing Rule", Fluid Phase

Science in the medieval Islamic world (5,288 words) [view diff] exact match in snippet view article find links to article

Omar Khayyam's "Cubic equation and intersection of conic sections"

Harmonic balance (1,786 words) [view diff] exact match in snippet view article find links to article

{1+y+2y^{2}}},\quad y=A_{3}/A_{1},\quad 51y^{3}+27y^{2}+21y-1=0.} The cubic equation for y{\displaystyle y} has only one real root y≈0.0448{\displaystyle

Field (mathematics) (10,249 words) [view diff] exact match in snippet view article

Scipione del Ferro and François Viète, which proceeds by reducing a cubic equation for an unknown x to a quadratic equation for x3. Together with a similar

Hypergeometric function (6,541 words) [view diff] exact match in snippet view article find links to article

hypergeometric function, connecting it to a different value of z related by a cubic equation. The first examples were given by Goursat (1881). A typical example

List of trigonometric identities (10,440 words) [view diff] exact match in snippet view article find links to article

construction of angle trisection to the algebraic problem of solving a cubic equation, which allows one to prove that trisection is in general impossible

Generalizations of Fibonacci numbers (4,337 words) [view diff] exact match in snippet view article find links to article

{-65+3{\sqrt {1689}}}{2}}}} and u{\displaystyle u} is the real root of the cubic equation u3−11u2+115u−169.{\displaystyle u^{3}-11u^{2}+115u-169.} Pentanacci

Edwards curve (3,137 words) [view diff] exact match in snippet view article find links to article

single point. When an elliptic curve is described by a non-singular cubic equation, then the sum of two points P and Q, denoted P + Q, is directly related

Meanings of minor planet names: 17001–18000 (539 words) [view diff] exact match in snippet view article find links to article

mystery from the so-called irreducible case of the solution of the cubic equation. JPL · 17696 17697 Evanchen 1997 EQ41 Evan Matthew Chen (born 1993)

Biological applications of bifurcation theory (2,477 words) [view diff] exact match in snippet view article find links to article

also be performed here, except using the generalized solution for a cubic equation instead of quadratic. The process is the same: 1) set the differential

List of Italian scientists (5,378 words) [view diff] exact match in snippet view article find links to article

mathematician, the first to discover a method to solve the depressed cubic equation Niccolò Fontana Tartaglia (1499–1557), mathematician who originated

Geometrical properties of polynomial roots (5,000 words) [view diff] exact match in snippet view article find links to article

\qquad a=\max\{|a_{i}|\}.} d2 is the positive root of the cubic equation Q(x)=x3+(2−|an−1|)x2+(1−|an−1|−|an−2|)x−a,a=max{|ai|}{\displaystyle

Virial expansion (3,828 words) [view diff] exact match in snippet view article find links to article

v^{\text{id}}={\frac {RT_{\text{sat}}}{P_{\text{sat}}}}} In the saturation region, the cubic equation has three roots, and can be written alternatively as:

Scanning helium microscopy (4,923 words) [view diff] exact match in snippet view article find links to article

with respect to the zone plate radius can be reduced the following cubic equation (once it has been set equal to zero): a3+2a2(RF−3ΓrZP)+aRF(RF−4rZP3

Viscosity models for mixtures (19,493 words) [view diff] exact match in snippet view article find links to article

_{0}\right]=\mu P\quad {\text{and}}\quad \left[P_{c}\right]=bar} The cubic equation of state (EOS) are very popular equations that are sufficiently accurate