More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is

The coefficients c < sub > k </ sub > must be chosen so that every valid index tuple maps to the address of a distinct element.

In addition to the original 31. 25 kbit / s ( baud is the signalling rate and is the reciprocal of the shortest signalling element ; bits / sec is the data rate ) current-loop transported on 5-pin DIN, other connectors have been used for the same electrical data, and transmission of MIDI streams in different forms over USB, IEEE 1394 a. k. a. FireWire, and Ethernet is now common.

To give just a few examples: Some authors use face to refer to an ( n − 1 )- dimensional element while others use face to denote a 2-face specifically, and others use j-face or k-face to indicate an element of j or k dimensions.

A consequence of the theorem is that the order of any element a of a finite group ( i. e. the smallest positive integer number k with a < sup > k </ sup > = e, where e is the identity element of the group ) divides the order of that group, since the order of a is equal to the order of the cyclic subgroup generated by a.

Strong convergence of a sequence ψ < sub > k </ sup >∈ L < sup > 2 </ sup >( R < sup > n </ sup >) to an element ψ means that

A subset S of a partially ordered set P is called bounded above if there is an element k in P such that k ≥ s for all s in S. The element k is called an upper bound of S. The concepts of bounded below and lower bound are defined similarly.

where d < sup > 3 </ sup > k = dk < sub > x </ sub > dk < sub > y </ sub > dk < sub > z </ sub > is the differential volume element in k-space, and the integrals are taken over all k-space.

In particular, if K is a field then the units of KX < sup >− 1 </ sup > have the form aX < sup > k </ sup >, where a is a non-zero element of K.

Thus, every element of Dic < sub > n </ sub > can be uniquely written as a < sup > k </ sup > x < sup > j </ sup >, where 0 ≤ k < 2n and j = 0 or 1.

The notations,,, or, with or without hat / circumflex, are also used, particularly in contexts where i, j, k might lead to confusion with another quantity ( for instance with index symbols such as i, j, k, used to identify an element of a set or array or sequence of variables ).

Note that the result is a scalar ( an element of k ).

* Spec k, the spectrum of a field k is the topological space with one element.

The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.

In either case the observation element usually controls fire in detail against the target, such as adjusting it onto the target, moving it and co-ordinating it with the supported arm as necessary to achieve the required effects.

The advantage of this technique is that only a medium-resolution monochromator is necessary for measuring AAS ; however, it has the disadvantage that usually a separate lamp is required for each element that has to be determined.

When analyzing electrical circuits, the actual direction of current through a specific circuit element is usually unknown.

Although it is usually translated as " element ", the Chinese word xing literally means something like " changing states of being ", " permutations " or " metamorphoses of being ".

There are six clearly valid groups of languages which are usually included in the Cushitic family ( Beja, Agaw, Sidamic, Lowland East Cushitic, Dullay, and South Cushitic ), as well as a few poorly classified languages ( Yaaku, Dahalo, Aasax and Kw ' adza, Boon, and the Cushitic element of Mbugu ).

Direct examination is usually performed to elicit evidence in support of facts which will satisfy a required element of a party's claim or defense.

In statistics, data sets usually come from actual observations obtained by sampling a statistical population, and each row corresponds to the observations on one element of that population.

The common element of most house music is a 4 / 4 beat generated by a drum machine or other electronic means ( such as a sampler ), together with a solid ( usually also electronically generated ) synth bassline.

It is to be expected that the electronegativity of an element will vary with its chemical environment, but it is usually considered to be a transferable property, that is to say that similar values will be valid in a variety of situations.

The input circuit is biassed so that the active element ( e. g. transistor ) conducts for only a fraction of the rf cycle, usually one third ( 120 degrees ) or less.

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.

* Violent offenses usually contain some element of force or a threat of force against a person.

In these cases there is a design element ( usually text ) which is not symmetric and should be read in the same direction, regardless of whether the hoist is to the viewer's left or right.

A gymnast can perform up to four tumbling lines that usually includes at least one flight element without hand support.

The radiation sensing element is an inert gas-filled Geiger-Muller tube ( usually containing helium, neon or argon with halogens added ) which briefly conducts electrical charge when a particle or photon of radiation makes the gas conductive by ionisation.

It does not exist as a free element in nature, but is found combined in solid solution for zirconium in natural zirconium compounds such as zircon, ZrSiO < sub > 4 </ sub >, which usually has about 1 – 4 % of the Zr replaced by Hf.

Since in organic chemistry non-carbons usually are considered to replace carbon atoms, they are called heteroatoms, meaning ' different from carbon and hydrogen ' ( rings of heteroatoms of the same element are homocyclic ).

The common element of house is a prominent kick drum on every beat ( also known as a four-on-the-floor beat ), usually generated by a drum machine or sampler.

The formation of an ionic bond proceeds when the atom of an element ( usually metal ), whose ionization energy is low, releases some of its electron ( s ) to achieve a stable electron configuration and after releasing some of its electron ( s ) the atom becomes a cation.

The atom of another element ( usually non metal ), whose electron affinity is positive, then accepts the electron ( s ), again to attain a stable electron configuration and after accepting electron ( s ) the atom becomes an anion.

Lutetium usually occurs in association with the element yttrium and is sometimes used in metal alloys and as a catalyst in various chemical reactions.

A metallic radioactive transuranic element in the actinide series, mendelevium is usually synthesized by bombarding einsteinium with alpha particles.

In mass spectrometry, the molecular mass of a small molecule is usually reported as the monoisotopic mass, that is, the mass of the molecule containing only the most common isotope of each element.

While the second element is certainly from the Old Norse haugr usually meaning a mound, there have been several different theories postulated for the first element, maes.

Proponents of single elements tend to ensure predominance of that element without determining if it is justified, and the element with the most enthusiastic and vociferous proponents has assumed the greatest importance.

For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.

To reconcile the contradictory aspects of his character, as well as to explain how Minos governed Crete over a period spanning so many generations, two kings of the name of Minos were assumed by later poets and rationalizing mythologists, such as Diodorus Siculus and Plutarch — " putting aside the mythological element ", as he claims — in his life of Theseus.

It is assumed that there is a distinct element of which generates the observed data.

Klaproth assumed the yellow substance was the oxide of a yet-undiscovered element and heated it with charcoal to obtain a black powder, which he thought was the newly discovered metal itself ( in fact, that powder was an oxide of uranium ).

Another element that tends to be assumed is the environment, or type of warfare ( land, naval, air ) depicted, at least if the subject matter is land warfare ( a game on naval or air warfare will specify such if not immediately obvious ).

* August 18 – The element later named as helium is first detected in the spectrum of the Sun's chromosphere by French astronomer Jules Janssen during a total eclipse in Guntur, India, but assumed to be sodium.

Here, the mapping is assumed to be a homomorphism, that is, it preserves algebraic operations, and, in particular, maps neutral element to neutral element.

At element 118, the orbitals 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 6s, 6p, 6d, 7s and 7p are assumed to be filled, with the remaining orbitals unfilled.

Once Adolf Hitler assumed power in 1933, shortwave, under the Auslandsrundfunk ( Foreign Radio Section ), was regarded as a vital element of Nazi propaganda.

While the Verein assumed unlimited possibilities of development, according to Holdheim the Mosaic element, after the elimination of the national, is eternal.

The atomic weight takes into account the isotopic distribution of the element in a given sample ( usually assumed to be " normal ").

These ideal electrical elements represent real, physical electrical or electronic components but they do not exist physically and they are assumed to have ideal properties according to a lumped element model, while components are objects with less than ideal properties, a degree of uncertainty in their values and some degree of nonlinearity, each of which may require a combination of multiple electrical elements in order to approximate its function.

The first element, " dun " translated from Gaelic, has been accepted as a ( fortified ) hill, and is assumed to be referring to the rocky outcrop at the site of Malcolm Canmore's tower in Pittencrieff Glen ( now Pittencrieff Park ).

The element, called Task Force Olympia, deployed to Mosul, Iraq in January 2004, where it assumed its mission from the 101st Airborne Division to form a headquarters to exercise command and control of all coalition and Iraqi forces in northern Iraq.

Because the physical fields live at ghostnumber one, it is also assumed that the string field is a ghostnumber one element of the Fock space.

The strong wind also made matters difficult for the amphibious landings but also ensured the element of surprise as many of the defenders had assumed that no-one would attempt a landing in such poor conditions.

In the distributed element model, each circuit element is infinitesimally small, and the wires connecting elements are not assumed to be perfect conductors ; that is, they have impedance.

In geometric group theory, the set is usually assumed to be finite, symmetric ( i. e. ) and not containing the identity element of the group.

In the theory of radicals, rings are usually assumed to be associative, but need not be commutative and need not have an identity element.

With the division having only two brigades, it was assumed that in wartime, either a German or US brigade would be assigned to provide the necessary third manoeuvre element.