A weak acid has a pK < sub > a </ sub > value in the approximate range − 2 to 12 in water.

Euripides sometimes ' resolved ' the two syllables of the iamb (˘¯) into three syllables (˘˘˘) and this tendency increased so steadily over time that the number of resolved feet in a play can be understood to indicate the approximate date of composition ( see Extant plays below for one scholar's list of resolutions per hundred trimeters ).

It has an approximate composition of SeS < sub > 2 </ sub >, with individual rings varying in composition, such as Se < sub > 4 </ sub > S < sub > 4 </ sub > and Se < sub > 2 </ sub > S < sub > 6 </ sub >.

From this information, the visual system attempts to determine the approximate composition of the illuminating light.

Usually this type of research involves reworking the components of the official measures of gross output and capital outlays to approximate Marxian categories, in order to estimate empirically the trends in the ratios thought important in the Marxian explanation of capital accumulation and economic growth: the rate of surplus-value, the organic composition of capital, the rate of profit, the rate of increase in the capital stock, and the rate of reinvestment of realised surplus-value in production.

Another technique adds modified whey to better approximate the composition of mare's milk.

This was number 35 in Thomas Wentworth Higginson's collection of Negro Spirituals that appeared in the Atlantic Monthly of June, 1867, with a comment by Higginson reflecting on how such songs were composed ( i. e., whether the work of a single author or through what used to be called " communal composition "): Even of this last composition, however, we have only the approximate date and know nothing of the mode of composition.

The main period for the composition of the shastras was between c. 100 CE, the approximate date of the Manu Dharma Shastra, and c. 300 CE, when it is likely that Vatsyayana Mallanaga composed the Kama Sutra.

However, the Harris-Benedict equations are only approximate and variation in BMR ( reflecting varying body composition ), in physical activity levels, and in energy expended in thermogenesis make it difficult to estimate the dietary consumption any particular individual needs in order to maintain body weight.

The approximate alloying composition of 531 tubing is 1. 5 % Mn, 0. 25 % Mo, 0. 35 % C, and is similar to the old British BS970 En 16 / 18 steel ( EN 16 is similar to grade BS970 605M36 ).

This way, if we have an optimization algorithm ( or approximation algorithm ) that finds near-optimal ( or optimal ) solutions to instances of problem B, and an efficient approximation-preserving reduction from problem A to problem B, by composition we obtain an optimization algorithm that yields near-optimal solutions to instances of problem A. Approximation-preserving reductions are often used to prove hardness of approximation results: if some optimization problem A is hard to approximate ( under some complexity assumption ) within a factor better than α for some α, and there is a β-approximation-preserving reduction from problem A to problem B, we can conclude that problem B is hard to approximate within factor α / β.

Close examination of the manuscript, including the different types of paper used, helped scholars construct an approximate timetable for its composition.

Here, in addition to schillerization, the original enstatite has been altered by hydration and the product has the approximate composition of serpentine.

The composition is in one movement, with an approximate duration of ten minutes.

A very approximate chronology of the composition of the four quintets runs as follows:

The apparent confusion between the numbering and approximate date of composition of the quintets arises from another long-held misconception, also corrected by the studies of Mr. Smith.

List of kings ' sagas, including works in Latin, in approximate order of composition ( many dates could be off by decades ):

The `` approximate '' is important, because even after the order of the work has been established by the chance method, the result is not inviolable.

Rhode Island's rate of $.07 per mile is considerably lower than reimburseable rates in the federal government and in industry nationally which approximate a $.09 per mile average.

The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.

He concluded that the anaconda's maximum length is 12 or 13 ( perhaps 14 ) meters, which would approximate from 39 to 42 feet ( 14 meters is slightly less than 46 feet ).

The restrained gyro-stabilized platform with reasonable response characteristics operates with an approximate equation of motion, neglecting transient effects, as follows: Af where U is a torque applied about the output axis of the controlling gyro.

To test the hypothesis that all treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced.

One Nepōhualtzintzin ( 91 ) represented the number of days that a season of the year lasts, two Nepōhualtzitzin ( 182 ) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin ( 273 ) is the number of days of a baby's gestation, and four Nepōhualtzintzin ( 364 ) completed a cycle and approximate a year ( 1 days short ).

This ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures and justifies the approximate empirical Principle of Thomsen and Berthelot, which states that the equilibrium state to which a system proceeds is the one which evolves the greatest amount of heat, i. e. an actual process is the most exothermic one.

Except for a few primitive types such as sponges ( which have no nervous system ) and jellyfish ( which have a nervous system consisting of a diffuse nerve net ), all living animals are bilaterians, meaning animals with a bilaterally symmetric body shape ( that is, left and right sides that are approximate mirror images of each other ).

* Some curves that seem simple, such as the circle, cannot be described exactly by a Bézier or piecewise Bézier curve ; though a four-piece cubic Bézier curve can approximate a circle ( see Bézier spline ), with a maximum radial error of less than one part in a thousand, when each inner control point ( or offline point ) is the distance horizontally or vertically from an outer control point on a unit circle.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

The approximate generation time for Danio rerio is three to four months.

where Fε < sup >- D </ sup > must be the number of units ε required to obtain L. The fractal dimension is the number of the dimensions of the figure being used to approximate the fractal: 0 for a dot, 1 for a line, 2 for a square.

The treatment of larger molecules that contain a few dozen electrons is computationally tractable by approximate methods such as density functional theory ( DFT ).

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.

This does not imply that the solution is an exact one ; they are all approximate quantum mechanical calculations.

In this type of calculation, there is an approximate Hamiltonian and an approximate expression for the total electron density.

From these figures for the size of a Biblical ell, that of the basic unit — the fingerbreadth ( Etzba ) — can be calculated to be either 22 or 21 mm ; Jewish rabbinical sources approximate at either 20 mm, or according to Talmudic scholar Chazon Ish, 25 mm.

With approximate dimensions, downtown is defined as anything upon the peninsula jutting into the Beaufort River that is located east of Ribaut Road ( US 21 ).

Applying the above formula to the 25-meter-diameter antennas often used in radio telescope arrays and satellite ground antennas at a wavelength of 21 cm ( 1. 42 GHz, a common radio astronomy frequency ), yields an approximate maximum gain of 140, 000 times or about 50 dBi ( decibels above the isotropic level ).

These problems are all hard: the clique decision problem is NP-complete ( one of Karp's 21 NP-complete problems ), the problem of finding the maximum clique is both fixed-parameter intractable and hard to approximate, and listing all maximal cliques may require exponential time as there exist graphs with exponentially many maximal cliques.

A historical marker at the corner of County Route 21 and Cole Road indicates the approximate former location of his boyhood home.

: " All that area consisting of that part of the Island of Newfoundland lying generally easterly and northerly of a line described as follows: commencing at a point midway between the towns of Triton and Leading Tickles in Notre Dame Bay ; thence southerly in said bay to Seal Bay ; thence southerly in a straight line to Frozen Ocean Lake at approximate latitude 49 ° 11 ' N and approximate longitude 55 ° 41 ' W ; thence westerly in a straight line to Hinds Lake ; thence southerly in a straight line to the mouth of Lloyds River at the westernmost extremity of Red Indian Lake ; thence southerly in a straight line to a point in Victoria Lake at latitude 48 ° 15 ' N and approximate longitude 57 ° 21 ' W ; thence easterly to the intersection of the Trans-Canada Highway ( Route No. 1 ) with Route No. 230 ; thence easterly along Route No. 230 to Route No. 230A ; thence easterly in a straight line to Ocean Pond ; thence southeasterly in a straight line to British Harbour at the entrance of Smith Sound on the north shoreline of Trinity Bay ; thence southeasterly to said bay.

: " All that area consisting of that part of the Island of Newfoundland lying southerly and westerly of a line described as follows: commencing at Bluff Head on the eastern shoreline of Port au Port Bay ; thence easterly in a straight line to Georges Lake ; thence easterly in a straight line to the mouth of Lloyds River at the westernmost extremity of Red Indian Lake ; thence southerly in a straight line to a point in Victoria Lake at latitude 48 ° 15 ' N and approximate longitude 57 ° 21 ' W ; thence generally easterly to the intersection of the Trans-Canada Highway ( Route No. 1 ) with Route No. 230 ; thence easterly along Route No. 230 to Route No. 230A ; thence easterly in a straight line to Ocean Pond ; thence southeasterly in a straight line to British Harbour at the entrance of Smith Sound on the north shoreline of Trinity Bay ; thence southeasterly to said bay ; thence southerly along Trinity Bay to the easterly production in Trinity Bay of the northerly limit of the Town of Sunnyside ; thence westerly along said production and said northerly limit to the Trans-Canada Highway ( Route No. 1 ); thence southerly along said highway to the northerly limit of the Town of Come By Chance ; thence westerly and southerly along the northerly and westerly limits of said town to the shoreline of Placentia Bay ; thence southerly along the Eastern Channel of Placentia Bay and Placentia Bay to a point approximately 20 km west of Cape St. Mary's.

The largest crowd ever for an Atlanta Hawks basketball game was in the 2010 NBA regular season ( against the Los Angeles Lakers ), where there was an approximate number of people of about 21, 000.

* Article 2 of Council Directive 89 / 104 / EEC ( of 21 December 1988 to approximate the laws of the Member States relating to trade marks ) must be interpreted as meaning that a trade mark may consist of a sign which is not in itself capable of being perceived visually, provided that it can be represented graphically, particularly by means of images, lines or characters, and that the representation is clear, precise, self-contained, easily accessible, intelligible, durable and objective.

Like all giant stars, Schedar rotates slowly with an approximate velocity of 21 km / s — a speed which takes the star approximately 102 days to make one complete revolution on its axis.

In 1941 Triggs and Armstrong reached an agreement whereby Armstrong would sell his approximate 25 % sales commission share in the Meadow Lea Margarine Company to Triggs ' son when he turned 21 in 1945.

However, David Zuckerman showed in 1996 that every one of these 21 problems has a constrained optimization version that is impossible to approximate within any constant factor unless P