Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts.

Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

* The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.

Maroger published The Secret Formulas and Techniques of the Old Masters in 1948.

Redelius was assisting Maroger with a revision of The Secret Formulas and Techniques of the Old Masters before his death in 1962.

Formulas in Calligra Words are provided by the Formula plugin.

Formulas say how to mechanically compute new values from existing values.

*" Basic Concepts and Formulas in Microscopy: Numerical Aperture " by Michael W. Davidson, Nikon MicroscopyU ( website ).

For example, a 1901 medical book published for home health use gave the following two " Simple Remedy Formulas " for DYSENTERRY: ( 1 ) Thin boiled starch, 2 ounces ; Laudanum, 20 drops ; " Use as an injection every six to twelve hours "; ( 2 ) Tincture rhubarb, 1 ounce ; Laudanum 4 drachms ; " Dose: One teaspoonful every three hours.

This engine and its legacy drive the SD Trans Ams and Formulas as one of the more, if not the most, desirable Pontiacs ever produced.

Formulas, macros and other objects existed " outside " of the cells, which was intended to make editing much simpler and less error-prone.

Formulas were typed into a separate section, and referred to data through their range, not their physical position in the sheets.

Stirling Numbers of the First Kind., § 24. 1. 3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.

* Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions ( with Formulas, Graphs and Mathematical Tables ), U. S. Dept.

During this period he started supervising Ph. D. students, such as James Halpern ( Contributions to the Study of the Independence of the Axiom of Choice ) and Edgar Lopez-Escobar ( Infinitely Long Formulas with Countable Quantifier Degrees ).

His most notable works were his ethnographic studies of the Ghost Dance after Sitting Bull's death in 1890, a widespread 19th-century religious movement among various Native American culture groups, and the Cherokee: The Sacred Formulas of the Cherokees ( 1891 ), and Myths of the Cherokee ( 1900 ), all published by the US Bureau of American Ethnology.

Sacred Formulas of the Cherokees.

Fender later released a 7 " EP, " Four Formulas ", under his own name on XNTRIX records.

* The Perfect Sausages ( previously The Perfect Sausage and other Fundamental Formulas ), ISBN 0-439-95901-2 ( areas and volumes, ellipsoids and toruses, number formulas ( e. g. triangle, hexagonal ), speed, acceleration, stopping time, distance, force, gravity, projectiles, Money: percentages ; simple and compound interest, permutations and combinations.

* M. Abramowitz and I. Stegun eds., Handbook of Mathematical functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards.

A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables ( Dover: New York, 1972 ), p. 78.

Mathieu Functions ", in Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables ( Dover: New York, 1972 )

* Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables ( Dover: New York, 1972 )

Formulas for expressing the roots of polynomials of degree 2 in terms of square roots have been known since ancient times ( see quadratic equation ), and for polynomials of degree 3 or 4 similar formulas ( using cube roots in addition to square roots ) were found in the 16th century ( see cubic function and quartic function for the formulas and Niccolo Fontana Tartaglia, Lodovico Ferrari, Gerolamo Cardano, and Vieta for historical details ).

Formulas with the form described above are known as 2-CNF formulas ; the " 2 " in this name stands for the number of terms per clause, and " CNF " stands for conjunctive normal form, a type of Boolean expression in the form of a conjunction of disjunctions.

Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of propositional formulas ( in the language consisting of and 0 ) into A. Formulas mapped to 1 ( or 0 ) for all A-valuations are called A-tautologies.

Formulas can then be represented within the theory by the numerals corresponding to their Gödel numbers.

Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of X can be present:

Formulas p and q are syntactically equivalent if and only if p ↔ q is a theorem, while p and q are semantically equivalent if and only if p ↔ q is true in every model ( that is, p ↔ q is logically valid ).

Formulas for the other coefficients are much harder to get ; Todd classes of toric varieties, the Riemann – Roch theorem as well as Fourier analysis have been used for this purpose.

Formulas are quite often interpreted as propositions ( as, for instance, in propositional logic ).

Formulas for different colors of glass are closely guarded.

Formulas for triose and TP are C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OH and C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OPO < sub > 3 </ sub >< sup > 2 -</ sup > + 2H < sup >+</ sup >.

Formulas are given in SI units and Gaussian-cgs units.

This edition consisted of the following titles ( the three titles marked with an asterix (*) are the volumes that had appeared together as The Arcane Teaching in the previous edition ): The One and the Many * ( hardback ), Cosmic Law * ( hardback ), The Psychic Planes * ( hardback ), The Arcane Formulas, or Mental Alchemy ( binding unknown ), The Mystery of Sex, or Sex Polarity ( binding unknown ), and Vril, or Vital Magnetism ( binding unknown ).

Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers.

Formulas are available to estimate the effective length of a whistle, but an accurate formula to predict sounding frequency would have to incorporate whistle length, scale, gas flow rate, mouth height, and mouth wall area ( see below ).

Formulas such as XLys, XTrp Analog, XLys, XTrp Maxamaid, XLys, XTrp Maxamum or Glutarex 1 are designed to provide amino acids other than lysine and tryptophan, in order to tentatively prevent protein malnutrition.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

In the case of neutral-neutral reactions ( i. e., not involving any charged species, ions ), these type of barrier-free reactions usually involve free radical species such as molecular oxygen ( O2 ), the cyanide radical ( CN ) or the hydroxyl radical ( OH ).

This fourth play in his tetralogy for 438 BC ( i. e. it occupied the position conventionally reserved for satyr-plays ) is a ' tragedy ' that features Heracles as a satyric hero in conventional satyr-play scenes, involving an arrival, a banquest, a victory over an ogre ( in this case Death ), a happy ending, a feast and a departure to new adventures.

Graphic design is a creative process — most often involving a client and a designer and usually completed in conjunction with producers of form ( i. e., printers, signmakers, etc.

The amount and type of carbohydrates consumed, along with some types of amino acid, can influence processes involving insulin, glucagon, and other hormones ; therefore the ratio of omega-3 versus omega-6 has wide effects on general health, and specific effects on immune function and inflammation, and mitosis ( i. e. cell division ).

* A crucial part of QoS in mobile communications is Grade of Service, involving outage probability ( the probability that the mobile station is outside the service coverage area, or affected by co-channel interference, i. e. crosstalk ) blocking probability ( the probability that the required level of QoS can not be offered ) and scheduling starvation.

In electrical power wiring ( i. e., house and building wiring by electricians ) names generally involving the suffixed word "- way " are used ; however, these terms differ between British and American English and the terms two way and three way are used in both with different meanings.

These secondary peaks, not to be confused with high energy satellites which are discussed later, arise from the presence of the same element in multiple different chemical states on a surface ( i. e. Adsorbate layers ) or from relaxation transitions involving valence band electrons of the substrate.

and hence Fourier sums of continuum functions are readily mapped to umbral Fourier sums faithfully, i. e., involving the same Fourier coefficients multiplying these umbral basis exponentials.

A famous marching band tradition involving a senior sousaphone player is dotting the " i " in Script Ohio, as performed by The Ohio State University Marching Band.

In addition to traditional ( i. e. molecular and cellular ) biophysical topics like structural biology or enzyme kinetics, modern biophysics encompasses an extraordinarily broad range of research, from bioelectronics to quantum biology involving both experimental and theoretical tools.

Insulin resistance is often found in people with visceral adiposity ( i. e., a high degree of fatty tissue within the abdomen – as distinct from subcutaneous adiposity or fat between the skin and the muscle wall, especially elsewhere on the body, such as hips or thighs ), hypertension, hyperglycemia and dyslipidemia involving elevated triglycerides, small dense low-density lipoprotein ( sdLDL ) particles, and decreased HDL cholesterol levels.

the term algebra is the collection of all possible terms involving m, i, e and the variables ; so for example, m ( i ( x ), m ( x, m ( y, e ))) would be an element of the term algebra.

Given two complexes M < sub >*</ sub > and N < sub >*</ sub >, a chain map between the two is a series of homomorphisms from M < sub > i </ sub > to N < sub > i </ sub > such that the entire diagram involving the boundary maps of M and N commutes.

In a typical case involving lateral motion, the canines and incisors of the opposing arches are moved against each other laterally, i. e., with a side-to-side action, by the medial pterygoid muscles that lie medial to the temporomandibular joints bilaterally.

Litigation attorneys specialize in offensive and defensive legal actions involving other parties ( i. e. responding to a lawsuit from another person, issuing preliminary demands or commencing a legal action when one believe someone is violating his legal or contractual rights, responding to governmental inquiries or when accused of violations of the law, etc .).

Some advanced techniques ( involving high harmonic generation with amplified femtosecond laser pulses ) can be used to produce optical features with durations as short as 100 attoseconds in the extreme ultraviolet spectral region ( i. e. < 30 nm ).

and solving for the c < sub > i </ sub > constants, by substitution, by equating the coefficients of terms involving the powers of x, or otherwise.

The binary logarithm of n is the power to which the number 2 must be raised to obtain the value n. This makes the binary logarithm useful for anything involving powers of 2, i. e. doubling.

* The individual is able to, on an either regular or semi-regular basis, enter in to voluntarily-agreed and consensual situations involving partnered sexual activity, i. e. an activity other than solo masturbation.

Psychologist Endel Tulving ( 1972 ; 1983 ) further defined these two declarative memory conceptions of explicit memory ( in which information is consciously registered and recalled ) into semantic memory wherein general world knowledge not tied to specific events is stored and episodic memory involving the storage of context-specific information about personal experiences ( i. e. time, location, and surroundings of personal knowledge ).

Theoretically, royal pardon can be granted for the general offense or the accessory offenses alone ; if it is granted for the general offense, the accessory ones it implies are also pardoned, with the exception of punishments involving political rights ( i. e., removal of the right to run for a public office as a result of a sentence ), which have to be explicitly mentioned in the pardon decree if they are going to be pardoned.

* ( i ) arising under the constitution or involving its interpretation