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.

Melzak's and Lambek's primitive models reduced this notion to four elements: ( i ) discrete, distinguishable locations, ( ii ) discrete, indistinguishable counters ( iii ) an agent, and ( iv ) a list of instructions that are effective relative to the capability of the agent.

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

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.

These realities form a " composite faithfulness " and are ( i ) " perseverance in the apostolic doctrine "; ( ii ) " the will to proclaim God's word "; ( iii ) " communion in the fundamental continuity of the Church, the Body of Christ, the faithful celebration of Baptism and the Eucharist "; ( iv ) " succession in the laying on of hands, the sign of ministerial continuity ".

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

In general, the difference between a statistics program and a biostatistics program is twofold: ( i ) statistics departments will often host theoretical / methodological research which are less common in biostatistics programs and ( ii ) statistics departments have lines of research that may include biomedical applications but also other areas such as industry ( quality control ), business and economics and biological areas other than medicine.

:"( 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.

The most notable alteration is the shortening of most feasts from nine to three lessons at Matins, keeping only the Scripture readings ( the former lesson i, then lessons ii and iii together ), followed by either the first part of the patristic reading ( lesson vii ) or, for most feasts, a condensed version of the former second Nocturn, which was formerly used when a feast was reduced in rank and commemorated.

This was in effect a series of two conferences: ( i ) between James and the Bishops ; ( ii ) between James and the Puritans on the following day.

i. 4, ii.

Was the notion of " effective calculability " to be ( i ) an " axiom or axioms " in an axiomatic system, or ( ii ) merely a definition that " identified " two or more propositions, or ( iii ) an empirical hypothesis to be verified by observation of natural events, or ( iv ) or just a proposal for the sake of argument ( i. e. a " thesis ").

Other possibilities are ( i ) that residual instrumental errors in WMAP cause the effect ( ii ) that unexpected microwave emission from within the solar system is contaminating the maps.

Labeling series that may be used include ordinary Arabic numerals ( 1, 2, 3, ...), Roman numerals ( I, II, III, ... or i, ii, iii, ...), or letters ( A, B, C, ... or a, b, c, ...).

Carbides can be generally classified by chemical bonding type as follows: ( i ) salt-like, ( ii ) covalent compounds, ( iii ) interstitial compounds, and ( iv ) " intermediate " transition metal carbides.

It first appeared in the sequence ii ( as in ingeníí ) in Latin manuscripts of the 11th century, then spread to i adjacent to m, n, u, and later spread to all lower-case i. The j, which separated from the i later, inherited the " dot ".

In Materialism and Empiriocriticism ( 1908 ), Lenin explained dialectical materialism as three axes: ( i ) the materialist inversion of Hegelian dialectics, ( ii ) the historicity of ethical principles ordered to class struggle, and ( iii ) the convergence of " laws of evolution " in physics ( Helmholtz ), biology ( Darwin ), and in political economy ( Marx ).

However, this view neglects the fact that i ) both modern cyanobacteria and alpha-proteobacteria are Gram negative bacteria, which are surrounded by double membranes ; ii ) the outer membranes of the endosymbiotic organelles ( chloroplasts and mitochondria ) are very similar to those of these bacteria in their lipid and protein compositions.

Clathrin coats are involved in two crucial transport steps: ( i ) receptor-mediated and fluid-phase endocytosis from the plasma membrane to early endosome and ( ii ) transport from the TGN to endosomes.

An imperial political structure is established and maintained in two ways: ( i ) as a territorial empire of direct conquest and control with force ( direct, physical action to compel the emperor's goals ), and ( ii ) as a coercive, hegemonic empire of indirect conquest and control with power ( the perception that the emperor can physically enforce his desired goals ).

The different components of a PEMFC are ( i ) bipolar plates, ( ii ) electrodes, ( iii ) catalyst, ( iv ) membrane, and ( v ) the necessary hardwares.

During the war of 1918 there were two kinds of Red and White political violence: ( i ) a calculated part of the general warfare, and ( ii ) more local, personal murders and corresponding acts of revenge.

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.

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

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 ).