In terms of numbers of species, Asteraceae is rivaled only by Orchidaceae.

Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers.

Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called " elementary numbers ", and these include the algebraic numbers, plus some transcendental numbers.

Most narrowly, one may consider numbers explicitly defined in terms of polynomials, exponentials, and logarithms – this does not include algebraic numbers, but does include some simple transcendental numbers such as e or log ( 2 ).

Differences between the two include pronunciation, grammar, vocabulary ( lexis ), spelling, punctuation, idioms, formatting of dates and numbers, although the differences in written and most spoken grammar structure tend to be much less than those of other aspects of the language in terms of mutual intelligibility.

The equipment of the land forces is impressive in terms of numbers, but most of it is nonoperational and scheduled to be scrapped or refurbished and exported to other nations.

With 20, 000 men ( including a rate of feminization of nearly 10 %) the Army remains the most important component in terms of numbers.

The terms " light " and " heavy " are sometimes also used informally to indicate relative atomic numbers ( not densities!

Bogotá's El Dorado International Airport handles 350 million metric tons of cargo and 8 million passengers a year, making it the largest airport in Latin America in terms of cargo and the third largest in passenger numbers.

Although a " bijection " seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets.

The customary acceptance of the fact that any real number x has a decimal expansion is an implicit acknowledgment that a particular Cauchy sequence of rational numbers ( whose terms are the successive truncations of the decimal expansion of x ) has the real limit x.

His axioms, however, do not guarantee that the circles actually intersect, because they do not assert the geometrical property of continuity, which in Cartesian terms is equivalent to the completeness property of the real numbers.

Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.

Clemence's 1948 proposal did not adopt a correction of this kind in terms of mean solar time: instead, the same numbers were used as in Newcomb's original uncorrected formula ( 1 ), but now in a reverse sense, to define the time and time scale implicitly, based on the real position of the Sun:

In mathematical terms, the sequence F < sub > n </ sub > of Fibonacci numbers is defined by the recurrence relation

The row products of the terms discarding zeros in the matrix above, are the natural numbers, 1, 2, 3 ...

However, these numbers are not known to be expressible by themselves in terms of elementary functions.

This definition is more rigorous and expandable than a simpler one involving common divisors, and it is often necessary to use it to determine the rationality or reducibility of numbers that are expressed in terms of variables.

* Polynomial roots that cannot be expressed in terms of the basic arithmetic operations and extraction of nth roots ( such as the roots of ).

A model of computation may be defined in terms of an abstract computer, e. g., Turing machine, and / or by postulating that certain operations are executed in unit time.

Ulric Neisser coined the term " cognitive psychology " in his book Cognitive Psychology, published in 1967 wherein Neisser provides a definition of cognitive psychology characterizing people as dynamic information-processing systems whose mental operations might be described in computational terms.

The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

Evaluating this definition directly requires O ( N < sup > 2 </ sup >) operations: there are N outputs X < sub > k </ sub >, and each output requires a sum of N terms.

Mining operations can be grouped into five major categories in terms of their respective resources.

At age 19, he showed there is no general algebraic solution for the roots of a quintic equation, or any general polynomial equation of degree greater than four, in terms of explicit algebraic operations.

In 1824, Niels Henrik Abel proved the striking result that there can be no general ( finite ) formula, involving only arithmetic operations and radicals, that expresses the roots of a polynomial of degree 5 or greater in terms of its coefficients ( see Abel-Ruffini theorem ).

PostScript 3 was significant in terms of replacing the existing proprietary color electronic prepress systems, then widely used for magazine production, through the introduction of smooth shading operations with up to 4096 shades of grey ( rather than the 256 available in PostScript Level 2 ), as well as DeviceN, a color space that allowed the addition of additional ink colors ( called spot colors ) into composite color pages.

Commencing operations on 25 June 1946, it approved its first loan on 9 May 1947 ( US $ 250M to France for postwar reconstruction, in real terms the largest loan issued by the Bank to date ).

He argues against fear of such gods by demonstrating through observations and argument that the operations of the world can be accounted for in terms of natural phenomena — the regular but purposeless motions and interactions of tiny atoms in empty space.

In 1982, AT & T and the Justice Department agreed on tentative terms for settlement of anti-trust suit filed against AT & T in 1974, under which AT & T divested itself of its local telephone operations, which became known as the " Baby Bells.

After a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.

Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error.

Nicias indeed proposed, when the expedition first arrived in Sicily ( 415 BCE ); that they should proceed at once to Selinunte and compel that city to submit on moderate terms ; but this advice being overruled, the efforts of the armament were directed against Syracuse, and the Selinuntines in consequence bore but a secondary part in the subsequent operations.

It supports public order and territorial control in urban areas, and contributes to the operations of civil authorities in terms of public safety.

A lady, you made clear to me both by precept and example, never raised her voice or slumped in her chair, never failed in social tact ( in heaven, for instance, would not mention St. John the Baptist's head ), never pouted or withdrew or scandalized in company, never reminded others of her physical presence by unseemly sound or gesture, never indulged in public scenes or private confidences, never spoke of money save in terms of alleviating suffering, never gossiped or maligned, never stressed but always minimized the hopelessness of anything from sin to death itself.

Again among those jubilantly reunited bunkmates, I was shy with Jessie and acted as I had during those early Saturday mornings when we all seemed to be playing for effect, to be detached and unconcerned with the girls who were properly our dates but about whom, later, in the privacy of our bunks, we would think in terms of the most elaborate romance.

This help is offered to applicants who ordinarily would not undertake the exploration under present conditions or circumstances at their sole expense and who are unable to obtain funds from commercial sources on reasonable terms.

If we stop thinking in terms of tremendous multimegaton nuclear weapons and consider employing much smaller nuclear weapons which may be more appropriate for most important military targets, it would seem that the B-52 or B-70 could carry a great many small nuclear weapons.

State and local expenditures ( in real terms ) increased persistently from $26.5-billion in 1949 to $44.3-billion in 1959, and it would not be surprising if they showed a comparable increase in this decade, which would carry them to the neighborhood of $75-billion by 1970.

indeed, that it would be limited to a finding of the total annual operating and capital costs of the business, followed by a calculation of this total in terms of annual cost per kilowatt-hour of consumption.

In many cases that statement -- `` We break even on our downtown operation and make money on our branches '' -- would be turned around if the cost analysis were recalculated on terms less prejudicial to the old store.

It would hardly be an exaggeration to say that ninety per cent of the energy of most churches -- whether in terms of finance or spiritual concern -- is poured into the private and domestic interests of the members.

That would amount to calculating the means and justifying them wholly in terms of their effectiveness in reaching desired goals.

A completely amorphous institution would be a contradiction in terms ; ;

In terms of war strategy, Lincoln articulated two priorities: to ensure that Washington was well-defended, and to conduct an aggressive war effort that would satisfy the demand in the North for prompt, decisive victory ; major Northern newspaper editors expected victory within 90 days.

Determined to find a course that would reunite the nation and not alienate the South, Lincoln urged that speedy elections under generous terms be held throughout the war.

It was also intended so that Americans with disabilities would be kept in the mainstream in terms of scientific and medical research and developments, especially opening future opportunities in Space exploration to them, as well as public policy changes, healthcare law and policy changes, and civil rights protections and public law changes for Americans with physical, mental and cognitive disabilities.

Immense as his terms were, the Emperor would have been well advised to grant them.

The emancipation of slaves would give the South more voters and cause the end of the three-fifths compromise in the Constitution in terms of Congressional apportionment.

In English terms it would be similar to the Canadian or Australian commonwealth status of the 20th century.

Elena Lourie ( 1975 ) suggested instead that it was Alfonso's attempt to neutralize the papacy's interest in a disputed succession — Aragon had been a fief of the Papacy since 1068 — and to fend off Urraca's son from her first marriage, Alfonso VII of Castile, for the Papacy would be bound to press the terms of such a pious testament.

The terms of the Artistic License 1. 0 were at issue in a 2007 federal district court decision in the US which was criticized by some for suggesting that FOSS-like licenses could only be enforced through contract law rather than through copyright law, in contexts where contract damages would be difficult to establish.

Another way of making the point is that if the Platonic world were to disappear, it would make no difference to the ability of mathematicians to generate proofs, etc., which is already fully accountable in terms of physical processes in their brains.

One of these was the property, an essential universal true of the species, but not in the definition ( in modern terms, some examples would be grammatical language, a property of man, or a spectral pattern characteristic of an element, both of which are defined in other ways ).

Not until the 1860s would Derby and Disraeli be on easy terms, and the latter's succession of the former assured.

According to these, the SI prefixes would only be used in the decimal sense, even when referring to data storage capacities: kilobyte and megabyte would denote one thousand bytes and one million bytes respectively ( consistent with SI ), while new terms such as kibibyte, mebibyte and gibibyte,

At times, Charlton was not on speaking terms with United's other superstars George Best and Denis Law, and Best refused to play in Charlton's testimonial match against Celtic, saying that " to do so would be hypocritical ".