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.

Formulas in Calligra Words are provided by the Formula plugin.

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

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 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.

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.

Formulas not involving st ( i. e., formulas of the usual language of set theory ) are called internal, other formulas are called external.

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 ).

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 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.

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 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 ).

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.

* The Animator's Survival Kit: A Manual of Methods, Principles and Formulas for Computer, Stop-motion, Games and Classical Animators, Faber and Faber, 2002 ( expanded edition 2009, adding ' Internet ' to the subtitle )

The Animator's Survival Kit: A Manual of Methods, Principles, and Formulas for Classical, Computer, Games, Stop Motion, and Internet Animators.

Including but not limited to A Moral Code of Ethics, The Sheet of Fives, Pyramid Formulas for Happiness, Harmony and Health, The Ten Stages of Growth and much more.

* Formulas for fast ( er ) matrix multiplication and inversion.

* Formulas for estimating the height of mountains, dated Bath, 13 February 1817 Annals of Philosophy, 9 ( March, 1817 ), 251 -- 252.

Formulas for Generating Pythagorean Triples

TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark ’ s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.

* Abramowitz and Stegun, the informal name for Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

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

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 ).

A Complete Collection of Thermodynamic Formulas ( abstract ).

The four titles in this edition were: The Arcane Teaching ( hardback ), The Arcane Formulas, or Mental Alchemy ( pamphlet ), The Mystery of Sex, or Sex Polarity ( pamphlet ), and Vril, or Vital Magnetism ( pamphlet ).

Willard Thorp, in his new book, American Writing In The Twentieth Century, observes, quite validly it seems: `` Certain subjects are conspicuously absent or have been only lightly touched.

I am certainly not adequately trained to describe or enlarge on human fears, but there are certain features of the fears dispelled by scientific explanations that stand out quite clearly.

Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.

There are many domains in which understanding has brought about widespread and quite appropriate reduction in ritual and fear.

In the field of the natural sciences, scientifically verified data are quite readily available and any discussion can be shortened with good results.

It has been a long time since he has seen any campaign money, and when the proposition is laid down to him as the friends of Mr. Hearst are laying it down these days he is quite likely to get aboard the Hearst bandwagon ''.

Stigmata quite sufficient for diagnosis are nevertheless there.

Some accounts are quite lengthy but Florida's is the shortest of all, requiring only four paragraphs.

It is quite evident that the people of Western Europe are overwhelmingly opposed to participation in a nuclear war.

But even he will not last indefinitely and the above-noted new arrangements are, quite simply, made to assure qualitative continuity in the Foundation's policies and practices.

In the industrial field, prospects for higher expenditures on electronic testing and measuring equipment are also quite bright.

The answers they give can often pave the way to performance increases and, quite often, are necessary for completing entry blanks for different events.

With the exception of the sports cars, even the quite tiny sedans will seat four passengers if you are willing to sacrifice comfort and luggage space for really economical transportation.

Rates in Greece and Finland are fairly high, actually the highest in Europe, and, surprisingly enough, they are also quite high in Ireland.

However, any oxygen nonequivalence would shorten either the already extremely short Af interlayer distance of 2.55 A or the non-hydrogen-bonded Af interlayer interactions which are already quite short at 2.58 Aj.

These examples are illustrative of the use of the words `` trial '' and `` experiment '' as they are used in this chapter, but they are quite flexible words and it is well not to restrict them too narrowly.

in working with these patients the therapist eventually gets to do some at least private mulling over of the possible meaning of a belch, or the passage of flatus, not only because he is reduced to this for lack of anything else to analyze, but also because he learns that even these animal-like sounds constitute forms of communication in which, from time to time, quite different things are being said, long before the patient can become sufficiently aware of these, as distinct feelings and concepts, to say them in words.

This can only be for one of two reasons: either the two are quite different and will require totally different theory ( and hence techniques ), or our existing theories are insufficiently general.

There may be certain items which are quite similar to a net operating loss carryover or operating deficit and whose right to survive a reorganization should perhaps be subject to the conditions applicable to those items.

Their experience is quite in contrast with that of children of upper- and upper-middle-class native-born parents, who are more likely to regard education as good for its own sake and to discount the vocational emphases in the curriculum.

and we are now so fatigued in body and mind that feeling is, as we say, quite dead.