In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, excluding hydrogen ( H ), which is nominally a group 1 element but not normally considered to be an alkali metal as it rarely exhibits behaviour comparable to that of the alkali metals.

In the modern IUPAC nomenclature, the alkaline earth metals comprise the group 2 elements.

In modern IUPAC notation, it is called Group 15.

In the modern IUPAC nomenclature, Group 4 of the periodic table contains titanium ( Ti ), zirconium ( Zr ), hafnium ( Hf ) and rutherfordium ( Rf ).

In the modern IUPAC nomenclature, Group 5 of the periodic table contains vanadium ( V ), niobium ( Nb ), tantalum ( Ta ) and dubnium ( Db ).

In modern IUPAC nomenclature, Group 9 of the periodic table contains the elements cobalt ( Co ), rhodium ( Rh ), iridium ( Ir ), and meitnerium ( Mt ).

Bra-ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics — including a large portion of modern physics — is usually explained with the help of bra-ket notation.

A modern classification for libraries, with simple notation, mnemonics, and alternatives.

The first use of an equals sign, equivalent to 14x + 15 = 71 in modern notation.

In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example

According to Margaret Bent, " Renaissance notation is under-prescriptive by our standards ; when translated into modern form it acquires a prescriptive weight that overspecifies and distorts its original openness.

Accidentals … may or may not have been notated, but what modern notation requires would then have been perfectly apparent without notation to a singer versed in counterpoint ".

The solution to one particular case of the cubic equation ( in modern notation ), was communicated to him by Niccolò Fontana Tartaglia ( who later claimed that Cardano had sworn not to reveal it, and engaged Cardano in a decade-long fight ), and the quartic was solved by Cardano's student Lodovico Ferrari.

* Otto Müller Verlag Salzburg 1969: Hildegard von Bingen: Lieder ( modern edition in adapted square notation )

This framework eventually became modern calculus, whose notation for integrals is drawn directly from the work of Leibniz.

He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.

He also introduced the modern notation for the trigonometric functions, the letter for the base of the natural logarithm ( now also known as Euler's number ), the Greek letter Σ for summations and the letter to denote the imaginary unit.

In modern notation the first is CO ( carbon monoxide ) and the second is CO < sub > 2 </ sub > ( carbon dioxide ).

* Proposition ✸ 54. 43 in a more modern notation ( Metamath )

The system of logical notation he created to present the axioms did not prove to be popular, although it was the genesis of the modern notation for set membership (∈, which is from Peano's ε ) and implication (⊃, which is from Peano's reversed ' C '.

According to Margaret Bent ( 1998 ), " Renaissance notation is under-prescriptive by our standards ; when translated into modern form it acquires a prescriptive weight that overspecifies and distorts its original openness.

However, Renaissance musicians would have been highly trained in dyadic counterpoint and thus possessed this and other information necessary to read a score, " what modern notation requires would then have been perfectly apparent without notation to a singer versed in counterpoint.

Although Franciscus Vieta ( 1540 – 1603 ) gave the first notation of modern algebra, John Napier ( 1550 – 1617 ) invented logarithms, and Edmund Gunter ( 1581 – 1626 ) created the logarithmic scales ( lines, or rules ) upon which slide rules are based.

In modern notation, the free Boolean algebra on basic propositions p and q arranged in a Hasse diagram.

In 1659 Huygens derived the now well-known formula for the centripetal force, exerted by an object describing a circular motion, for instance on the string to which it is attached, in modern notation:

Huygens was the first to derive the formula for the period of an ideal mathematical pendulum ( with massless rod or cord and length much longer than it's swing ), in modern notation:

* All modern integrated development environments display variable types on demand, and automatically flag operations which use incompatible types, making the notation largely obsolete.

This is the only case in modern history of a people of Britannic origin submitting without continued struggle to what they view as foreign domination.

While sovereignty has roots in antiquity, in its present usage it is essentially modern.

Neither is primary experience understood according to the attitude of modern empiricism in which nothing is thought to be received other than signals of sensory qualities producing their responses in the appropriate sense organs.

Shakespeare's Shylock, too, is of dubious value in the modern world.

But a modern Oedipus who is doomed because he cannot oppose his own childhood is only pathetic, and for renouncing the mystery in favor of psychological truth he gives up the claim on our sympathies.

A characteristic expression of such concern and inquiry is found in Joseph P. Lyford's Introduction To The Agreeable Autocracies, a recent paperback study of the institutions of modern democratic society.

The men who speculate on these institutions have, for the most part, come to at least one common conclusion: that many of the great enterprises and associations around which our democracy is formed are in themselves autocratic in nature, and possessed of power which can be used to frustrate the citizen who is trying to assert his individuality in the modern world ''.

As Sandburg said at the time: `` It is as ancient as the medieval European ballads brought to the Appalachian Mountains, it is as modern as skyscrapers, the Volstead Act, and the latest oil well gusher ''.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

The Chicago contingent of modern critics follow Aristotle so far in this direction that it is hard to see how they can compare one poem with another for the purpose of evaluation.

Diplomatic is another area for which the dawn of the twentieth century marks the beginning of modern standards of scholarship.

This is certainly an irrational dogmatism, in which the modern mind attempts to understand the spirit of the sixteenth century on twentieth-century terms.

Rexroth is a longtime jazz buff, a name-dropper of jazz heroes, and a student of traditional as well as modern jazz.

In addition to his experiments in reading poetry to jazz, Patchen is beginning to use the figure of the modern jazz musician as a myth hero in the same way he used the figure of the private detective a decade ago.

This angry and exasperated stance which Patchen has maintained in his poetry for almost fifteen years has been successfully modulated into a kind of woe that is as effective as anger and still expresses his disapproval of the modern world.

But the firm has recognized the tight dollar and the tourist's desire to visit the `` smaller, less-traveled and relatively inexpensive countries '', and is now prepared to teach modern Greek and Portuguese through recordings.

Perhaps there is more truth than we are wont to admit in the conviction of that ornament of Tarheelia, Robert Ruark's grandfather, who was persuaded that the great curse of the modern world is `` all this gallivantin' ''.

The possibility of recall into the Army is part of the price that a modern American has to pay for the enviable heritage of liberty which he enjoys.

Under modern conditions, this is especially true of the ready reserve.

However, its modern one-story layout is designed to increase our production capacity, permit more efficient manufacturing, and substantially reduce current repair and maintenance costs.