And the standard deviation equations remain unchanged.

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.

These equations are called the " Biot – Savart law for a point charge " due to its closely analogous form to the " standard " Biot – Savart law given previously.

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i. e., sets of equations in which there are more equations than unknowns.

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 ).

The standard equations provide for electric charges, but they posit no magnetic charges.

Chemical equations make use of the standard molar entropy of reactants and products to find the standard entropy of reaction:

* Mathematically oriented derivation of standard vehicle dynamics equations, and definitions of standard terms.

in a ring R. Thus, they can be generated by the standard technique for Pell equations of taking powers of a fundamental solution:

In mathematical physics, Liouville made two fundamental contributions: the Sturm – Liouville theory, which was joint work with Charles François Sturm, and is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact ( also known as Liouville's theorem ) that time evolution is measure preserving for a Hamiltonian system.

Many standard methods require that the problem is formulated as a system of first-order ordinary differential equations.

Ephemeris time was consequently developed as a standard that was free from the irregularities of Earth rotation, by defining the time " as the independent variable of the equations of celestial mechanics ", and it was at first measured astronomically, relying on the existing gravitational theories of the motions of the Earth about the Sun and of the Moon about the Earth.

For example, given the four points the pencil of conics through them can be parameterized as yielding the following pencil ; in all cases the center is at the origin :< ref group =" note "> A simpler parametrization is given by which are the affine combinations of the equations and corresponding the parallel vertical lines and horizontal lines, and results in the degenerate conics falling at the standard points of

Coupled-cluster equations are equations whose solution is the set of coefficients t. There are several ways of writing such equations but the standard formalism results in a terminating set of equations which may be solved iteratively.

The ISO 31 and IEC 60027 Standards were revised by the two standardization organizations in collaboration (, ) to integrate both standards into a joint standard ISO / IEC 80000-Quantities and Units in which the quantities and equations used with SI are to be referred as the International System of Quantities ( ISQ ).

Despite the small difference in equations for the standard deviation and the standard error, this small difference changes the meaning of what is being reported from a description of the variation in measurements to a probabilistic statement about how the number of samples will provide a better bound on estimates of the population mean, in light of the central limit theorem.

Perelman introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way.

In industry and commerce, standard conditions for temperature and pressure are often necessary to define the standard reference conditions to express the volumes of gases and liquids and related quantities such as the rate of volumetric flow ( the volumes of gases vary significantly with temperature and pressure ).

This is because using for loops and functions are standard ways of providing flow control whereas the goto statement encourages arbitrary flow control.

While in standard Russian it represents, in many Ukrainian dialects it denotes ( following a vowel and preceding a consonant ( cluster ), either within a word or at a word boundary, it denotes the allophone, and like the off-glide of in the English words " flow " and " cow ", it forms a diphthong with the preceding vowel ).

) In the United States, compressed air flow is often measured in " standard cubic feet " per unit of time, where the " standard " means the equivalent quantity of air at standard temperature and pressure.

NPV is a central tool in discounted cash flow ( DCF ) analysis and is a standard method for using the time value of money to appraise long-term projects.

A standard for mimicking the old rate of outflow called the " agreed curve " was established, setting the maximum flow rate at 300 to 1, 700 cubic metres per second ( 392 – 2, 224 cu yd / sec ) depending on the lake's water level.

Depending on the physical technology ( FPGA, ASIC gate array, ASIC standard cell ), HDLs may or may not play a significant role in the back-end flow.

While a harness may safely rescue its user from a fall, the leg loops of a standard safety or climbing harness further restrict return blood flow from the legs to the heart, contributing to the decrease in blood pressure.

Another example of a data link layer which is split between LLC ( for flow and error control ) and MAC ( for multiple access ) is the ITU-T G. hn standard, which provides high-speed local area networking over existing home wiring ( power lines, phone lines and coaxial cables ).

The design steps ( or flow ) are also common to standard product design.

Because they project out above the surrounding sea floor, they disturb standard water flow, causing eddies and associated hydrological phenomena that ultimately result in water movement in an otherwise still ocean bottom.

A standard IV infusion set consists of a pre-filled, sterile container ( glass bottle, plastic bottle or plastic bag ) of fluids with an attachment that allows the fluid to flow one drop at a time, making it easy to see the flow rate ( and also reducing air bubbles ); a long sterile tube with a clamp to regulate or stop the flow ; a connector to attach to the access device ; and connectors ( called " s or Y-Set ( infusion ))" to allow "" of another infusion set onto the same line, e. g., adding a dose of antibiotics to a continuous fluid drip.

Kinematic viscosity is graded by measuring the time it takes for a standard amount of oil to flow through a standard orifice, at standard temperatures.

References will be made to " actual " flow rate through a meter and " standard " or " base " flow rate through a meter with units such as acm / h ( actual cubic meters per hour ), kscm / h ( kilo standard cubic meters per hour ), LFM ( linear feet per minute ), or MSCFD ( million standard cubic feet per day ).

after all, feelings of immortality and invulnerability are standard illusions of youth.

That means that, if we are to achieve a new standard of leadership, we must think in terms of the total context of our situation.

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

Shotgun-type rubber recoil pads are standard on all of the Magnums except the

Wall panels and structural timbers are standard as are windows and doors, making for a minimum of cutting.

The roof timbers are precut and the panels standard so that the house can be completely enclosed in a matter of three or four days.

The wall panels are constructed of a framework of standard Af and Af of a good grade, free from structural faults.

There are standard sliding glass windows in wood or aluminum frames for those panels requiring them.

The door panels are designed to accommodate standard doors which should be of exterior grade.

Harris has indicated that two devices, the Launder-Ometer and Terg-O-Tometer are most widely used for rapid detergent testing, and he has listed the commercially available standard soiled fabrics.

Although the standard deviation values on which spread of the lines is based are relatively larger for those centers which begin to ossify early ( Table 1 ), there are considerable differences in this value between centers having the closely timed Onsets.

The language and notation introduced are standard throughout the chapter.

On the whole they maintain much the same high standard, but they are much more difficult to discuss in detail because of their wider variety of subject matter.

Specimens are allowed to reach moisture equilibrium with a standard atmosphere of Af and Af and then laid out without tension on a flat, polished surface, care being taken that the fabric is free from wrinkles or creases.

There are many types of standard of review for appeals, such as de novo and abuse of discretion.

The alkali metals are a group of chemical elements in the periodic table with very similar properties: they are all shiny, soft, silvery, highly reactive metals at standard temperature and pressure and readily lose their outermost electron to form cations with charge + 1.

Alphabets are usually associated with a standard ordering of their letters.

The standard ampere is most accurately realized using a watt balance, but is in practice maintained via Ohm's Law from the units of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively.

On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.

Another example is about, which has three different ways of signing it ; these are the standard way and two regional variations ( Atlantic and Ontario ).

20 of the 22 proteinogenic amino acids are known as " standard " amino acids-those found in human beings and other eukaryotes, and which are encoded directly within the universal genetic code.