The diagonalizable operator is the special case of this in which Af for each i.

For each i, let Af.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

The family moved north across the Ohio River to free ( i. e., non-slave ) territory and made a new start in what was then Perry County but is now Spencer County, Indiana.

This religion preaches the view of Ahimsa – to live and let live, thereby not harming sentient beings, i. e. uncompromising reverence for all life.

The importance lies in sacrifice for the sake of the greater good ; Islam considers those practicing i ' thar as abiding by the highest degree of nobility.

This is similar to the notion of chivalry, but unlike that European concept, in i ' thar attention is focused on everything in existence.

A constant concern for Allah ( i. e. God ) results in a careful attitude towards people, animals, and other things in this world.

This concept was emphasized by Sufi mystics like Rabia al-Adawiyya who paid attention to the difference between dedication to Allah ( i. e. God ) and dedication to people.

For many Muslims, i ' thar must be practiced as a religious obligation during specific Islamic holidays.

However, i ' thar is also still an Islamic ideal to which all Muslims should strive to adhere at all times.

These two defunct phyla were the Myxomycota ( i. e., plasmodial slime molds, now classified in the taxon Myxogastria ), and Acrasiomycota ( i. e. cellular slime molds, now divided into the taxa Acrasida and Dictyosteliida ).

Compared to earlier telegraph codes, the proposed Bell code and ASCII were both ordered for more convenient sorting ( i. e., alphabetization ) of lists and added features for devices other than teleprinters.

Like other character encodings, ASCII specifies a correspondence between digital bit patterns and character symbols ( i. e. graphemes and control characters ).

; Balanced design: An experimental design where all cells ( i. e. treatment combinations ) have the same number of observations.

Alkanes ( also known as paraffins or saturated hydrocarbons ) are chemical compounds that consist only of hydrogen and carbon atoms and are bonded exclusively by single bonds ( i. e., they are saturated compounds ) without any cycles ( or loops ; i. e., cyclic structure ).

Saturated hydrocarbons can also combine any of the linear, cyclic ( e. g., polycyclic ) and branching structures, and they are still alkanes ( no general formula ) as long as they are acyclic ( i. e., having no loops ). They also have single covalent bonds between their carbons.

If the appellate court does find a legal defect in the decision " below " ( i. e., in the lower court ), it may " modify " the ruling to correct the defect, or it may nullify (" reverse " or " vacate ") the whole decision or any part of it.

In German, words starting with sch-( constituting the German phoneme ) would be intercalated between words with initial sca-and sci-( all incidentally loanwords ) instead of this graphic cluster appearing after the letter s, as though it were a single letter — a lexicographical policy which would be de rigueur in a dictionary of Albanian, i. e. dh -, ë -, gj -, ll -, rr -, th -, xh-and zh-( all representing phonemes and considered separate single letters ) would follow the letters d, e, g, l, n, r, t, x and z respectively.

This led to the conclusion ( Moseley's law ) that the atomic number does closely correspond ( with an offset of one unit for K-lines, in Moseley's work ) to the calculated electric charge of the nucleus, i. e. the proton number Z.

An argument of this form is invalid, i. e., the conclusion can be false even when statements 1 and 2 are true.

* In the year 1000, the Icelander Leif Ericson was the first European to set foot on North American soil, corresponding to today's Eastern coast of Canada, i. e. the province of Newfoundland and Labrador, including the area of land named " Vinland " by Ericson.

The practical definition may lead to confusion with the definition of a coulomb ( i. e., 1 amp-second ), but in practical terms this means that measures of a constant current ( e. g., the nominal flow of charge per second through a simple circuit ) will be defined in amperes ( e. g., " a 20 mA circuit ") and the flow of charge through a circuit over a period of time will be defined in coulombs ( e. g., " a variable-current circuit that flows a total of 10 coulombs over 5 seconds ").

* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence

The Aegean Sea (;, Aigaio Pelagos ; or historically ) is an elongated embayment of the Mediterranean Sea located between the southern Balkan and Anatolian peninsulas, i. e., between the mainlands of Greece and Turkey.

As researchers note, " a sense of ‘ responsibility ,’ or self agency, in a context of uncertainty ( probabilistic outcomes ) drives the neural system underlying appetitive motivation ( i. e., nucleus accumbens ) more strongly in temperamentally inhibited than noninhibited adolescents.

An analog or analogue signal is any continuous signal for which the time varying feature ( variable ) of the signal is a representation of some other time varying quantity, i. e., analogous to another time varying signal.

The primary disadvantage of analog signaling is that any system has noise – i. e., random unwanted variation.

For the incremental case ( i. e., ), this simplifies to:

Almonds are sold shelled ( i. e., after the shells are removed ), or unshelled ( i. e., with the shells still attached ).

It plays a role in repairing single-strand breaks in duplex DNA in living organisms, but some forms ( such as DNA ligase IV ) may specifically repair double-strand breaks ( i. e. a break in both complementary strands of DNA ).

During this interregnum, the heads of the dicasteries of the Roman Curia ( such as the prefects of congregations ) cease immediately to hold office, the only exceptions being the Major Penitentiary, who continues his important role regarding absolutions and dispensations, and the Camerlengo of the Holy Roman Church, who administers the temporalities ( i. e., properties and finances ) of the See of St. Peter during this period.

This role requires ordination by the congregation's preferred authority ( i. e. from a respected Orthodox rabbi or, if the congregation is Conservative or Reform, from academic seminaries ).

Some traditions ( i. e., the Vedanta ), believe that a supreme being plays some kind of role, for example, as the dispenser of the ' fruits ' of karma or as exercising the option to change one's karma in rare instances.

A Discovery Channel TV documentary titled, Undercover: Operation Harvest King, which documents Mark Whitacre's role in the ADM price fixing case aired several times during 2009 and 2010, where Discovery Channel interviewed the three FBI agents who handled the Mark Whitacre / ADM case ( i. e., Dean Paisley, Brian Shepard and Robert Herndon ), along with Mark and Ginger Whitacre.

Earlier ( I. i ), Boniface VIII is also mentioned for his role in sending Charles of Valois to Florence in 1300 to end the feud between the Black and White Guelphs.

In the 1980s it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order ( i. e., latent heat ) within the type I regime, and that the two regions are separated by a tricritical point.

Left communists like C. L. R. James and the Italian autonomists, as well as unorthodox Trotskyists like Tony Cliff, described Stalinism as " state capitalism " i. e., a form of capitalism where the state takes over the role of capital.

* May 15 – Charles Townshend, 2nd Viscount Townshend, retires from his role in the government of Great Britain, leaving Robert Walpole as sole and undisputed leader of the Cabinet ( i. e., prime minister ).

However in these same communities, an adjustment of norms ( i. e. deviant peers being replaced by positive role models ) can pose a positive effect.

the Bishopric of Liège, the Romance Flanders ( i. e. Cambrai, Lille, Tournai ), the French-speaking part of Brabant around Nivelles and, Namur, where Walloon is traditionally spoken ), the region is Germanic with Dutch and Luxembourgish being the dominant languages, although French has historically played an important role as it still does in Luxembourg.

In this, Canaris was successful, and the " Dutch War Scare " played a major role in causing Chamberlain to make the " continental commitment " ( i. e. sending a large British ground force to the defence of France ) in February 1939.

Actor Colin O ' Donoghue from < i > The Rite </ i > has been cast for this role.

Second, autoimmunity may have a role in allowing a rapid immune response in the early stages of an infection when the availability of foreign antigens limits the response ( i. e., when there are few pathogens present ).

Just as nous plays a critical role in salvation in orthodox Christianity, so too does buddhi play an important role in liberation ( i. e., enlightenment ) within Hinduism, Buddhism and Yoga.

On 20 August 1827, the British naval commander-in-chief in the Mediterranean ( i. e .. commander of " Blue " Squadron ), Vice-Admiral Sir Edward Codrington ( 1770 – 1851 ), veteran of 44 years at sea and a popular hero for his role in the Battle of Trafalgar, received his government's instructions regarding enforcement of the treaty.

In writing to George Devine, who directed the Old Vic production, Beckett suggests that “ the inquirer ( light ) begins to emerge as no less a victim of his inquiry than they and as needing to be free, within narrow limits, literally to act the part, i. e. to vary only slightly his speeds and intensities .” But the role of the light is even more ambiguous, for it has also been seen as “ a metaphor for our attention ( relentless, all-consuming, whimsical )” and a way of “ switching on and switching off speech exactly as a playwright does when he moves from one line of dialogue on his page to the next .” Neither of these analogies conflicts with the more popular views where the spotlight is believed by to represent God, or some other moral agent tasked with assessing, each character's case to be relieved from the binds of the urn by having them relive this relationship, which has ruined all their lives.

Since changing of gender role, i. e. living as a woman instead of living as a man, or living as a man instead of living as a woman, is much more important to almost all transgendered people than any medical procedures, this use is even more inaccurate.

Since changing of gender role, i. e. living as a woman instead of living as a man, or living as a man instead of living as a woman, is much more important to almost all transgender people than any medical procedures, this use is even more inaccurate.

The rite of the opening and closure of the Janus Quirinus would thus reflect the idea of the reintegretation of the miles into civil society, i. e. the community of the quirites, by playing a lustral role similar to the Tigillum Sororium and the porta triumphalis located at the south of the Campus Martius.

The political and decision-making authority of the cabinet has been gradually reduced over the last several decades, with some claiming its role has been usurped by a " Prime Ministerial " ( i. e. more " presidential ") government.

He engaged with them and played a leading role in a policy of obstructionism ( i. e., the use of technical procedures to disrupt the House of Commons ' ability to function ) to force the House to pay more attention to Irish issues, which had previously been ignored.