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 ).

PLO leader Yasser Arafat | Yasir Arafat and Israel i prime minister Yitzhak Rabin, with US President, Bill Clinton.

Other supporters of the Bill, such as Thomas Jefferson, argued that a list of rights would not and should not be interpreted as exhaustive ; i. e., that these rights were examples of important rights that people had, but that people had other rights as well.

Succession is by male-preference primogeniture governed by both the Act of Settlement, 1701, and Bill of Rights, 1689, legislation that limits the succession to the natural ( i. e. non-adopted ), legitimate descendants of Sophia of Hanover and stipulates that the monarch cannot be a Roman Catholic, nor married to one, and must be in communion with the Church of England upon ascending the throne ; these particular clauses have prompted legal challenge.

The name " Ballistic Missile Defense Organization " ( BMDO ) came back into use in 1993 when SDIO was renamed BMDO by the administration of President Bill Clinton and this was accompanied by a shift in emphasis from national missile defense to theater missile defense, i. e. from global to regional coverage.

In Italy, the character is so familiar in popular culture that his name has been occasionnally used as a metaphor for " unlikeable and / or dishonest wealthy person ", " go-getter ", or " rival millionaire " ( i. e., a millionaire who is the rival of another millionaire, in this instance, Bill Koch, rival of Raul " Uncle Scrooge " Gardini ).

The advocates of repeal therefore promised, not only a Big Loaf ( which was to be doubled in size ) but also the passing of the Ten Hours Bill " ( i. e. to reduce working hours ).

The character was created when Bill Cosby wanted the show to express the accomplishment of successfully raising a child ( i. e., a college graduate ).

* Characters from the previous novels < i > Junkie </ i >, < i > Queer </ i > and Naked Lunch: Dr Benway, Clem Snide, Sailor, Bill Gains, and Kiki.

Bluegrass music is of particular regional importance ; Bill Monroe, " the father of bluegrass music ", was born in the Ohio County community of Rosine, and he named his band, the Blue Grass Boys, after the bluegrass state, i. e., Kentucky.

As an attempt to break the stalemate, U. S. President Bill Clinton proposed dividing sovereignty of the site vertically-the ground and area below coming under Israeli sovereignty, while that above the ground ( i. e. the Haram al-Sharif containing the Dome of the Rock and al-Aqsa Mosque ) would be under Palestinian sovereignty.

( However, Mr. Hands did most of the violence himself, because Sluggo would tell him to, i. e. " Sluggo says to ...") The violence would inevitably escalate, generally ending with Mr. Bill being crushed or dismembered while squealing in a high pitched voice, " Ohhhh noooooooooooooo ..."

In 2008 Congress enacted into law over President Bush ’ s veto an Omnibus Farm Bill that contained the “ Close the Enron Loophole Act .” This added to CEA Section 2 ( h )( 2 ) a new definition of “ electronic trading facility ” and imposed on such facilities requirements applicable to fully regulated exchanges ( i. e. “ designated contract markets ”) such as the NYMEX.

In 2008 Congress enacted into law over President Bush ’ s veto an Omnibus Farm Bill that contained the “ Close the Enron Loophole Act .” This added to CEA Section 2 ( h )( 2 ) a new definition of “ electronic trading facility ” and imposed on such facilities requirements applicable to fully regulated exchanges ( i. e. “ designated contract markets ”) such as the NYMEX.

In 1956, Bill Buchanan and Dickie Goodman released what they called a " break-in " song, ( i. e. material from one song would " break-in " to another ) called " The Flying Saucer ".

The album sold moderately well — including on-site sales at the Hungry i during the Kingston Trio's engagement there through the summer — but it was DJs Paul Colburn and Bill Terry at station KLUB in Salt Lake City whose enthusiasm for a single cut on the record spurred the next development in the group's history.

§ 1244, signed into law as part of the FY2010 Homeland Security Appropriations Bill on October 28, 2009 provides that the Act shall not apply to spring-assist or assisted-opening knives ( i. e. knives with closure-biased springs that require physical force applied to the blade to assist in opening the knife ).

* A new VIC-III graphics chip named CSG * 4567 R5 ( codenamed Bill ), capable of producing 256 colors from a palette of 4096 colors ; available modes include 320 × 200 × 256, 640 × 200 × 256, 640 × 400 × 16, 1280 × 200 × 16, and 1280 × 400 × 4 ( X × Y × colordepth i. e. number of colors / bit planes )

Succession is by male-preference primogeniture governed by both the Act of Settlement 1701, and Bill of Rights 1689, legislation that limits the succession to the natural ( i. e. non-adopted ), legitimate descendants of Sophia, Electress of Hanover, and stipulates that the monarch cannot be a Roman Catholic, nor have married one, and must be in communion with the Church of England upon ascending the throne.

The company is expecting to receive the casino licence for Savai ' i island in a new law legalising casinos proposed by the government, the Casino and Gambling Bill 2010 tabled to parliament by the prime minister Tuilaepa Aiono Sailele Malielegaoi in March 2010.

Bill McLaren says Greenwood was an advocate of fifteen man " total rugby ", i. e. the whole team playing as a unit, and capable of both back and forward play.

Following the defeat of the Shops Bill 1986, which would have enabled widespread Sunday trading, compromise legislation was introduced in July 1994 in England and Wales, coming into force on 28 August 1994, allowing shops to open, but restricting opening times of larger stores i. e. those over to a maximum of six hours, between 10am and 6pm only.