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

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.

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

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.

*" 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 ).

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

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

Using launch systems presently available, we are developing satellites to scout the world's weather ; ;

They enlisted the help of the New Jersey congressman, who has been able to trace the letters to the national archives, where they are available on microfilm.

There are many soft and light shoe leathers available.

The respective vocabularies `` essential for travel '' are available in separate albums.

The program was instituted in 1940, and releases are available only from the Recording Laboratory of the Library of Congress, Washington 25, D.C..

There are lots of jobs available for trained high school graduates, but not for the dropouts.

Production specialists in SBA regional offices are available to help individual small business concerns with technical production problems.

Guidance and advice are available on new product research and development ; ;

Production specialists are available in SBA regional offices to help individual small business concerns with technical production problems.

Small Business Administration, What It Is, What It Does, SBA Services For Community Economic Development, and various other useful publications on currently important management, technical production, and marketing topics are available, on request, from Small Business Administration, Washington 25, D.C..

U.S. Government Purchasing, Specifications, And Sales Directory, 60 cents, are available from the Superintendent of Documents, U.S. Government Printing Office, Washington 25, D.C..

SBA loans, which may be made to small manufacturers, small business pools, wholesalers, retailers, service establishments and other small businesses ( when financing is not otherwise available to them on reasonable terms ), are to finance business construction, conversion, or expansion ; ;

and Small Business Pooling are available, on request, from Small Business Administration, Washington 25, D.C., and its regional offices.

Three distinct classes of loans are made available to farmers' cooperatives by the Banks for Cooperatives: Commodity loans, operating capital loans, and facility loans.

or a skilled labor force is trained before there are plants available in which they can be employed.

Few records are available concerning the subject prior to 1940.

Those that are available shed little light.

The mapping of important physical features such as slopes and types of soil and the collection of all available information pertaining to public utility service areas are being conducted as staff projects and, like the other two inventory projects, are scheduled for completion July 1, 1961.

Its elimination would result in the saving of interest costs, heavy when short-term money rates are high, and in freedom from dependence on credit which is not always available when needed most.

Research and development activities undertaken by the Secretary shall be coordinated or conducted jointly with the Department of Defense to the end that developments under this Act which are primarily of a civil nature will contribute to the defense of the Nation and that developments which are primarily of a military nature will, to the greatest practicable extent compatible with military and security requirements, be available to advance the purposes of this Act and to strengthen the civil economy of the Nation.

There are authorized to be appropriated such sums, to remain available until expended, as may be necessary, but not more than $75,000,000 in all, ( A ) to carry out the provisions of this Act during the fiscal years 1962 to 1967, inclusive ; ;