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 ).

Animism in the widest sense, i. e., thinking of objects as animate, and treating them as if they were animate, is near-universal.

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:

He and his peers were acutely aware that they were one step above the lowest on the socio-economic ladder, i. e. the black community.

When non-native speakers speak Hindi-Urdu, they might pronounce / व / in ' व ् रत ' as, i. e. as wrat instead of the correct vrat.

When they are realized without much allophonic variation, a simple ( i. e. ' broad ') transcription is used.

Their offices were compatible with other offices, i. e. they can hold two benefices or offices at one and the same time, some conferred by the Cardinal Vice-Chancellor, others by the Holy Father.

The Ames test uses several strains of the bacterium Salmonella typhimurium that carry mutations in genes involved in histidine synthesis i. e. it is an auxotrophic mutant, so that they require histidine for growth.

Managers aim to capture the inefficiencies arising from the heavy participation of non-economic investors ( i. e., high income " buy and hold " investors seeking tax-exempt income ) as well as the " crossover buying " arising from corporations ' or individuals ' changing income tax situations ( i. e., insurers switching their munis for corporates after a large loss as they can capture a higher after-tax yield by offsetting the taxable corporate income with underwriting losses ).

This chart shows that not all fish, shellfish, or the insects that they eat can tolerate the same amount of acid ; for example, frogs can tolerate water that is more acidic ( i. e., has a lower pH ) than trout.

The fact that in equivalent baseband models of communication systems, the signal spectrum consists of both negative and positive frequencies, can lead to confusion about bandwidth, since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as, where is the total bandwidth ( i. e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel ), and is the positive bandwidth ( the baseband bandwidth of the equivalent channel model ).

For instance, chapter 6 ( B '), which ought to follow chapter 7 ( A ') chronologically, is put in parallel with chapter 3 ( B ) because they both deal with the persecution of Daniel and his friends i. e. " God's people.

As such it draws to a conclusion the themes introduced in Genesis and played out in Exodus and Leviticus: God has promised the Israelites that they shall become a great ( i. e. numerous ) nation, that they will have a special relationship with Yahweh their god, and that they shall take possession of the land of Canaan.

The kings who follow Rehoboam in Jerusalem continue the royal line of David ( i. e., they inherit the promise to David ); in the north, however, dynasties follow each other in rapid succession, and the kings are uniformly bad ( meaning that they fail to follow Yahweh alone ).

Moreover ( and more embarrassingly, although this is essentially trivial ), mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they don't use the *- symbol, but an overline ( which the physicists reserve to averages ) to denote conjugate-complex numbers, i. e. for scalar products mathematicians usually write

:"( i ) that what the directors did was so related to the affairs of the company that it can properly be said to have been done in the course of their management and in the utilisation of their opportunities and special knowledge as directors ; and ( ii ) that what they did resulted in profit to themselves.

Male zebrafish are furthermore known to respond to more pronounced markings on females, i. e., " good stripes ", but in a group, males will mate with whichever females they can find.

No one has given a causal explanation, they argue, of why it would not be possible for a functionally equivalent non-conscious organism ( i. e., a philosophical zombie ) to achieve the very same survival advantages as a conscious organism.