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 ").

i. 1 § 27 ), while the other end being flat and circular served to render the surface of the tablets smooth again, and so to obliterate what had been written.

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.

In Attic, the shift did not take place after epsilon, iota, and rho ( ε, ι, ρ ; e, i, r ).

* In arithmetic, addition and multiplication of real numbers are associative ; i. e.,

After describing the manifestation of the Gospel in the Ogdoad and Hebdomad, he adds that the Basilidians have a long account of the innumerable creations and powers in the several ' stages ' of the upper world ( diastemata ), in which they speak of 365 heavens and say that " their great archon " is Abrasax, because his name contains the number 365, the number of the days in the year ; i. e. the sum of the numbers denoted by the Greek letters in ΑΒΡΑΣΑΞ according to the rules of isopsephy is 365:

v. 32 ; Diogenes Laertius i. 101-5 ; Athenaeus, iv.

It was at Anah that the emperor Julian met the first opposition on his disastrous expedition against Persia ( 363 ), when he got possession of the place and transported the people ; and there that Ziyad and Shureih with the advanced guard of Ali's army were refused passage across the Euphrates ( 36 / 657 ) to join Ali in Mesopotamia ( Tabari i. 3261 ).

He reasons that, i ) if we knew the nature of this power, then the mind-body divide would seem totally unmysterious to us ; ii ) if we had immediate knowledge of this mysterious power, then we would be able to intuitively explain why it is that we can control some parts of our bodies ( e. g., our hands or tongues ), and not others ( e. g., the liver or heart ); iii ) we have no immediate knowledge of the powers which allow an impulse of volition to create an action ( e. g., of the " muscles, and nerves, and animal spirits " which are the immediate cause of an action ).

* Velleius Paterculus i. 11 ; Florus ii.

The magazine's stated criteria for the Hall of Fame encompasses " games that have met or exceeded the highest standards of quality and play value and have been continuously in production for at least 10 years ; i. e., classics.

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

A value of 0 means that the pixel does not have any coverage information and is transparent ; i. e. there was no color contribution from any geometry because the geometry did not overlap this pixel.

* there were no " half-open " connections ; once one end initiated a tear-down of the connection, the whole connection would be closed ( i. e., ADSP is full-duplex, not dual simplex ).

i., Berlin, 1863 ; 1438-1454 ), small bronze cylinders inscribed, and used as oracles, were perhaps found here in the 16th century.

i. 18a ; compare Josephus, B. J. ii. 14, § 5 ; Jastrow, Dict.

Abbreviators are those who make an abridgment or abstract of a long writing or discourse by contracting the parts, i. e. the words and sentences ; an abbreviated form of writing common among the Romans.

They determined to reinvestigate the motion of γ Draconis ; the telescope, constructed by George Graham ( 1675 – 1751 ), a celebrated instrument-maker, was affixed to a vertical chimney stack, in such manner as to permit a small oscillation of the eyepiece, the amount of which ( i. e. the deviation from the vertical ) was regulated and measured by the introduction of a screw and a plumb line.

After March it began to pass northwards, a motion quite apparent by the middle of April ; in June it passed at the same distance from the zenith as it did in December ; and in September it passed through its most northerly position, the extreme range from north to south, i. e. the angle between the March and September positions, being 40 ″.

The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis ( the symmetrical axis of the system ) are infinitely small, i. e. with infinitesimal objects, images and lenses ; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits.