For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;

For my seedbed I use good garden soil with a little sand added to encourage rooting.

For top and bottom pieces, use short end of mold as measurement guide.

For the reason just suggested, I shall assume the use of the first subtype of fully distributed cost apportionment in the following simplified example.

For the use of students and future restorers, a full, day-by-day record was kept of all three undertakings, complete technical reports on what we found and what we did.

For observational data, the derivation of confidence intervals must use subjective models, as emphasized by Ronald A. Fisher and his followers.

For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.

" For most Swahili speakers, the use of satire in writing is unfamiliar.

For his part Conan Doyle acknowledged basing his detective stories on the model of Edgar Allan Poe's C. Auguste Dupin, and his anonymous narrator, and basing his character Sherlock Holmes on Joseph Bell, who in his use of " ratiocination " prefigured Poirot's reliance on his " little grey cells ".

For a particularly robust two-pass algorithm for computing the variance, first compute and subtract an estimate of the mean, and then use this algorithm on the residuals.

For the algorithm above, one could use the following pseudocode:

For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples.

Like Jehovah's Witnesses, Adventists use key phrases from the Bible, such as " For the living know that they shall die: but the dead know not any thing, neither have they any more a reward ; for the memory of them is forgotten " ( Eccl.

For example, automobile wheels made of an aluminium alloy are commonly referred to as simply " alloy wheels ", although in point of fact steels and most other metals in practical use are also alloys.

For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation.

For a 256-bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively — this change only applies for the Rijndael cipher when used with a 256-bit block, as AES does not use 256-bit blocks.

For more details of this early work, see Alpha particle # History of discovery and use.

For example, psychologists use anagram-oriented tests, often called " anagram solution tasks ", to assess the implicit memory of young adults and adults alike.

For simplicity, we shall here use the shorthand notation for representing the over operator.

For that reason, the elements of an array data structure are required to have the same size and should use the same data representation.

For example, letters 1, 5, and 8 contain a discussion on the question, whether the use of a piece of metal with the figure of a lion, as a talisman, is permitted by Jewish law for medicinal purposes, or is prohibited as idolatrous.

For these reasons many CAD applications use the DWG format which can be licensed from AutoDesk or non-natively from the Open Design Alliance.

For example, for about a 15 % premium in building costs, the Passivhaus building codes in Europe use high performance insulating windows, R-30 insulation, HRV ventilation, and a small thermal mass.

For a return trip to Tahiti the navigators could use Sirius, the zenith star of that island.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

For example, if we can enumerate all such definable numbers by the Gödel numbers of their defining formulas then we can use Cantor's diagonal argument to find a particular real that is not first-order definable in the same language.

For waves traveling through three dimensions, such as light waves, sound waves, and matter waves, the formulas for phase and group velocity are generalized in a straightforward way:

For instance, the language of True quantified Boolean formulas is decidable in polynomial space, but not non-deterministic polynomial time ( unless NP = PSPACE ).

For two-and three-dimensional collisions the velocities in these formulas are the components perpendicular to the tangent line / plane at the point of contact.

For example, all of the following formulas are in DNF:

For example, in DNF, logical formulas of the following form have 2 < sup > n </ sup > terms:

For example, in what Foley called a " pivotal " contribution, Larry Benson introduced the concept of " written-formulaic " to describe the status of some Anglo-Saxon poetry which, while demonstrably written, contains evidence of oral influences, including heavy reliance on formulas and themes A number of individual scholars in many areas continue to have misgivings about the applicability of the theory or the aptness of the South Slavic comparison, and particularly what they regard as its implications for the creativity which may legitimately be attributed to the individual artist.

For instance in number theory, a partition of an integer n can be defined as a weakly decreasing sequence of positive integers whose sum is n. It is important that there is exactly one partition of the number 0 ( most formulas for counting partitions would break down if there were assumed to be no partitions of 0 ), and since terms must be positive, the empty sequence is the only possible candidate.

For more complex survey designs, different formulas for calculating the standard error of difference must be used.

For example, although the prominent scientist and statesman Shen Kuo ( 1031 – 1095 ) was one of Wang Anshi's most trusted associates and political allies, Shen nonetheless befriended Su Shi and even collaborated with him in compiling the pharmaceutical treatise of the Liang Fang ( 良方 ; Good medicinal formulas ).

For example, he coined the term " polymer " in 1833 to describe organic compounds which shared identical empirical formulas but which differed in overall molecular weight, the larger of the compounds being described as " polymers " of the smallest.

For each of the sorts of variable just defined, it is permissible to build up formulas by using universal and / or existential quantifiers.

For example, if,, and are quantifier-free formulas with the free variables shown then

For one-dimensional integration, quadrature methods such as the trapezoidal rule, Simpson's rule, or Newton – Cotes formulas are known to be efficient if the function is smooth.

For other statistics and other populations the formulas are more complicated, and often they don't exist in closed-form.

For example, there are formulas in the language of arithmetic defining the set of codes for arithmetic sentences, and for provable arithmetic sentences.

For example, the set of ( codes for ) formulas of first-order Peano arithmetic that are true in N is definable by a formula in second order arithmetic.

For each program there should be three groups of formulas: a formula or chart to compute ( daily ) target consumption, a formula for computing the cost of foods, and a formula for computing the value of activity under the program to earn extra consumption.

For 2010 PointsPlus, the formulas in Equations 16-19 of show the basic calculation of daily points targets for adults age 19 +:

For example, the ASME Boiler and Pressure Vessel Code ( BPVC ) ( UG-27 ) formulas are:

For computation of the inverse formulas ( e. g., using C / C ++, Fortran, or other programming language ), the use of the two-argument atan2 form of the inverse tangent function ( as opposed to atan ) is recommended.

For a normally distributed population, a z-score can be transformed into a " k factor " for a given via lookup tables or several approximation formulas.