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Page "Abelian group" ¶ 7
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e and where
; Balanced design: An experimental design where all cells ( i. e. treatment combinations ) have the same number of observations.
Compound comparisons typically compare two sets of groups means where one set has two or more groups ( e. g., compare average group means of group A, B and C with group D ).
For example, where a person has committed harmful actions of body, speech and mind based on greed, hatred and delusion, rebirth in a lower realm, i. e. an animal, a ghost or a hell realm, is to be expected.
On the other hand, where a person has performed skillful actions based on generosity, loving-kindness ( metta ), compassion and wisdom, rebirth in a happy realm, i. e. human or one of the many heavenly realms, can be expected.
where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.
When a specific allophone ( from a set of allophones that correspond to a phoneme ) must be selected in a given context ( i. e. using a different allophone for a phoneme will cause confusion or make the speaker sound non-native ), the allophones are said to be complementary ( i. e. the allophones complement each other, and one is not used in a situation where the usage of another is standard ).
The first assumption is that in the case where the background is opaque ( i. e. ), the over operator represents the convex combination of and:
It is also interesting to note that the operator fulfills all the requirements of a non-commutative monoid, where the identity element is chosen such that ( i. e. the identity element can be any tuple with.
In Analytical Geometry a section of a line can be given by the formula where ( c, d )&( e, f ) are the endpoints of the line & m: n is the ratio of division
This case is also used for nouns in several other senses, e. g., where the action occurs " because of " or " without " a certain noun ; nouns indicating distance or direction.
* In a discharging battery or galvanic cell ( diagram at right ) the anode is the negative terminal since that is where the current flows into " the device " ( i. e. the battery cell ).
* In a cathode ray tube, it is the positive terminal where electrons flow out of the device, i. e., where positive electric current flows in.
The flow of electrons is always from anode to cathode outside of the cell or device, regardless of the cell or device type and operating mode, with the exception of diodes, where electrode naming always assumes current in the forward direction ( that of the arrow symbol ), i. e., electrons flow in the opposite direction, even when the diode reverse-conducts either by accident ( breakdown of a normal diode ) or by design ( breakdown of a Zener diode, photo-current of a photodiode or solar cell ).
where e is the elementary charge and I is the average current.
This view parted with the Jewish scriptures, where Israel offered praise with instruments by God's own command ( e. g.: 2 Chronicles 29: 25 ).
If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.
The AA compiler generated range-checking for array accesses, and allowed an array to have dimensions that were determined at run-time ( i. e. you could declare an array as < code >< u > integer </ u > < u > array </ u > Thing ( i: j )</ code >, where and were calculated values ).
There are, however, stronger ones that are simply pre-mixed spirits ( e. g. Bacardi Rum Island Iced Tea ), often containing about 12. 5 % alcohol by volume, that can be sold only where hard liquor is available.
Subsequently, the accelerative force on any given ion is controlled by the electrostatic equation, where n is the ionisation state of the ion, and e is the fundamental electric charge.
However, a common and well-accepted metric is the half power points ( i. e. frequency where the power goes down by half its peak value ) on the output vs. frequency curve.
In Denmark, recent archaeological excavations at Lejre, where Scandinavian tradition located the seat of the Scyldings, i. e., Heorot, have revealed that a hall was built in the mid-6th century, exactly the time period of Beowulf.

e and is
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.
Altruism is a motivation to provide something of value to a party who must be anyone but oneself, while duty focuses on a moral obligation towards a specific individual ( e. g., a god, a king ), or collective ( e. g., a government ).
* One-way ANOVA is used to test for differences among two or more independent groups ( means ), e. g. different levels of urea application in a crop.
* Repeated measures ANOVA is used when the same subjects are used for each treatment ( e. g., in a longitudinal study ).
The number of carbon atoms is used to define the size of the alkane ( e. g., C < sub > 2 </ sub >- alkane ).
The names were abandoned in Latin, which instead referred to the letters by adding a vowel ( usually e ) before or after the consonant ( the exception is zeta, which was retained from Greek ).
An argument of this form is invalid, i. e., the conclusion can be false even when statements 1 and 2 are true.
A relatively recent role for amateur astronomers is searching for overlooked phenomena ( e. g., Kreutz Sungrazers ) in the vast libraries of digital images and other data captured by Earth and space based observatories, much of which is available over the Internet.
He thought that certain uses of the verb " to be ", called the " is of identity " and the " is of predication ", were faulty in structure, e. g., a statement such as, " Elizabeth is a fool " ( said of a person named " Elizabeth " who has done something that we regard as foolish ).
Phytomelan is not unique to Asparagales ( i. e. it is not a synapomorphy ) but it is common within the order and rare outside it.
The flower is typically somewhat zygomorphic ( i. e. not radially symmetrical ) and has nectaries.
For example, " aloin " is derived from Aloe vera and Aloe ferox and has important medical uses ( e. g. as a laxative and in the treatment of burns ) as well as cosmetic uses ( e. g. in skin and hair products ).
Another theory by Yule and Burnell ( 1886 ) is based on an entry in the Catalogue of Indian Serpents from the Leyden Museum ( Ray, 1693 ) that reads: Anacondaia Zeylonensibus, id est Bubalorum aliorumque jumentorum membra conterens, meaning " the anacondaia of the Ceylonese, i. e. he that crushes the limbs of buffaloes and yoke beasts.
* 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.
According to Tillich, the last of these three types of existential anxiety, i. e. spiritual anxiety, is predominant in modern times while the others were predominant in earlier periods.

e and identity
* Bisexual characteristics, having an ambiguous sexual identity ( e. g. epicenity or androgyny )
The midrashic book of Jasher argues that prior to revealing his identity, Joseph asked Benjamin to find his missing brother ( i. e. Joseph ) via astrology, using an astrolabe-like tool ; it continues by stating that Benjamin divined that the man on the throne was Joseph, so Joseph identified himself to Benjamin ( but not the other brothers ), and revealed his scheme ( as in the Torah ) to test how fraternal the other brothers were.
It is equal to the group's identity if and only if g and h commute ( i. e., if and only if gh =
Then is a derivation and is linear, i. e., and, and a Lie algebra homomorphism, i. e.,, but it is not always an algebra homomorphism, i. e. the identity does not hold in general.
Religious affiliation is itself multi-layered and includes religious considerations other than being Muslim, such as sectarian identity ( e. g. Shia or Sunni, etc.
The commutator is equal to the identity element e if and only if gh
The identity element e = is always a commutator, and it is the only commutator if and only if G is abelian.
Language became increasingly linked to nation as opposed to culture, and was also used to promote religious and ethnic identity ( e. g. different Bible translations in the same language for Catholics and Protestants ).
In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components ( which may reflect individual physical processes of interest, for example ), or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity ( i. e., independence or non-interaction ).
From this property, one can deduce that h maps the identity element e < sub > G </ sub > of G to the identity element e < sub > H </ sub > of H, and it also maps inverses to inverses in the sense that
From the 6th century AD until 771, the area around modern-day Hastings, as the territory of the Haestingas tribe, considered itself to be a separate Kingdom from the surrounding Kingdoms of Suth Saxe (" South Saxons ", i. e. Sussex ) and Kent, and attempted to retain its separate cultural identity until the 11th century.
Whenever one makes an identity claim ( i. e. a claim which states that two things are the same ), one almost always uses two different descriptions.
Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.

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