Translate the axes so that the vertex of the catenary lies on the y-axis and its height a is adjusted so the catenary satisfies the standard equation of the curve

Changes in the stoichiometric coefficients of a balanced cell equation will not change E °< sub > red </ sub > value because the standard electrode potential is an intensive property.

Hence, and so we may divide by and rearrange the equation into the standard form

: In the general ( or standard ) form the linear equation is written as:

The graph of the equation has x-intercept a and y-intercept b. The intercept form is in standard form with A =

For any generalized parabola, with its equation given in the standard form

The calibration yields a value for the standard electrode potential, E < sup > 0 </ sup >, and a slope factor, f, so that the Nernst equation in the form

One of the first standard results using the class equation is that the center of a non-trivial finite p-group cannot be the trivial subgroup ( proof ).

Other standard iterative methods for matrix equation solutions can also be used, for example the Gauss – Seidel method, where updated values for each patch are used in the calculation as soon as they are computed, rather than all being updated synchronously at the end of each sweep.

A PIN diode obeys the standard diode equation for low frequency signals.

Using standard trigonometric identities, this equation can be converted to the following form:

This is done by subtracting the sum of the standard enthalpies of formation of the reactants ( each being multiplied by its respective stoichiometric coefficient, ν ) from the sum of the standard enthalpies of formation of the products ( each also multiplied by its respective stoichiometric coefficient ), as shown in the equation below:

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

Here, is the standard complex-valued wavefunction known from quantum theory, which evolves according to Schrödinger's equation

For ideal gases, the molar volume is given by the ideal gas equation: this is a good approximation for many common gases at standard temperature and pressure.

The Legendre differential equation may be solved using the standard power series method.

To solve the PDE we transform the equation into a diffusion equation which may be solved using standard methods.

Using the standard method for solving a diffusion equation we have

The spectral theorem can again be used to obtain a standard equation akin to the one given above.

Then standard methods can be used to solve the linear difference equation in.

For instance, the standard fourth-order Runge – Kutta method applied to the differential equation yields Simpson's rule from above.

Under standard assumptions the orbital speed () of a body traveling along elliptic orbit can be computed from the Vis-viva equation as:

An invertible linear transformation applied to a sphere produces an ellipsoid, which can be brought into the above standard form by a suitable rotation, a consequence of the polar decomposition ( also, see spectral theorem ).

POV-Ray, in addition to standard geometric shapes like tori, spheres and heightfields, supports mathematically defined primitives such as the isosurface ( a finite approximation of an arbitrary function ), the polynomial primitive ( an infinite object defined by a 15th order or lower polynomial ), the julia fractal ( a 3-dimensional slice of a 4-dimensional fractal ), the superquadratic ellipsoid ( intermediate between a sphere and a cube ), and the parametric primitive ( using equations that represent its surface, rather than its interior ).

It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface ( the datum or reference ellipsoid ) for raw altitude data, and a gravitational equipotential surface ( the geoid ) that defines the nominal sea level.

When the ellipsoid / tensor is represented by a matrix, we can apply a useful technique from standard matrix mathematics and linear algebra — that is to " diagonalize " the matrix.

* Stockholm school ( economics ) – the school of economic thought whose antithesis is the gold standard centered Austrian School of Economics

PCA of a multivariate Gaussian distribution centered at ( 1, 3 ) with a standard deviation of 3 in roughly the ( 0. 878, 0. 478 ) direction and of 1 in the orthogonal direction.

El Pueblo de Sonoma was laid out in the standard form of a Mexican town, centered around the largest plaza in California, in size.

Although this contributed greatly to an increase in literacy and the educational standard, the curriculum was centered on Japanese language and history, with the intent of assimilation of the populace into loyal subjects of the Japanese Empire.

Min Dong is centered around the city of Fuzhou ( Fuzhou dialect is the standard dialect of Min Dong ), capital of Fujian province, while Min Nan is dominant in the south of Fujian and into eastern Guangdong.

When the Kinai region centered on the ancient Imperial capitals such as Nara and Kyoto were the center of Japan, an archaic form of Kansai dialect was the de facto standard Japanese.

The international standard for SI states that in a forming a compound unit symbol, " Multiplication must be indicated by a space or a half-high ( centered ) dot (·), since otherwise some prefixes could be misinterpreted as a unit symbol " ( i. e., kW h or kW · h ).

The Stockholm school, or Stockholmsskolan, is a school of economic thought whose antithesis is the gold standard centered Austrian School of Economics.

They were usually centered around some materialistic goals like improving the standard of living or, for example, the political autonomy of the working class.

Nota bene: standard international rankings don not really suit the ENS system, as these structures are very small and centered more on the education of students rather than on internal research.

Gompers ' philosophy of labor unions centered on economic ends for workers, such as higher wages, shorter hours, and safe working conditions so that they could enjoy an " American " standard of living — a decent home, decent food and clothing, and money enough to educate their children.

It refers to the imaginary inverted equilateral triangle centered on the chest and the points being the standard leads on the arms and leg.

In determining Maleficent's design, standard depictions of witches and hags were dismissed as Mattinson's opted for an elegant, sinister, green-skinned beauty centered around the appearance of flames, ultimately crowning the villain with a black two pointed headdress, often called an atora.

361 = 19 < sup > 2 </ sup >, centered triangular number, centered octagonal number, centered decagonal number, member of the Mian – Chowla sequence ; also the number of positions on a standard 19 x 19 Go board.

Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages.

The Java programming language has a specific function for creating splash screens, called java. awt. SplashScreen that handles standard splash screen functions, e. g. display an image centered on screen then disappears when the first program window opens.

Soon after the Sonoma mission was built, it was secularized by the Mexican government, and, under the orders of Lieutenant, later General Mariano Guadalupe Vallejo, el Pueblo de Sonoma ( the town of Sonoma ) was laid out in the standard form of a Mexican town, centered around the historic plaza, which is still the town's focal point.

The badges appeared as the standard USAAF Pilot Badge with one of three letters centered on the badges ’ shield, or escutcheon.

The Submarine Supply Corps Insignia appears as the standard Submarine Warfare Insignia with the Supply Corps emblem centered in the middle of the badge.

Known as the Naval Flight Officer Astronaut insignia, the decoration is a standard NFO insignia upon which is centered a golden astronaut " shooting star " logo.

The Gunner Badge appeared as a standard observer badge, upon which was centered a winged bullet.

The badge consisted of a standard observer badge, centered upon which was a downward facing bomb.