The logarithm function obeys the following identity:

Maimonides describes the identity of the Messiah in the following terms:

In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one ( g / g = 1 ), with the resulting amount of moles ( the unit that was needed ), is shown in the following equation,

To promote and unify " Humanist " identity, prominent members of the IHEU have endorsed the following statements on Humanist identity:

In the following centuries Bulgaria established itself as a powerful empire, dominating the Balkans through its aggressive military traditions, which led to development of distinct ethnic identity.

These maps are " natural " in the following sense: the double dual operation is a functor, and the maps are the components of a natural transformation from the identity functor to the double dual functor.

( where 1 < sub > A </ sub > denotes the multiplicative identity of A ), there is a unique algebra homomorphism such that the following diagram commutes ( i. e. such that ):

The identity of the mother of some of Llywelyn's children before this union is uncertain, but the following are recorded in contemporary or near-contemporary records.

Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:

Contemporary transnational interactions between Hmong in the West and Miao groups in China, following the 1975 Hmong diaspora, have led to the development of a global Hmong identity that includes linguistically and culturally related minorities in China that previously had no ethnic affiliation.

This condition is necessary, for the following reason: if we suppose that A has an inverse then the constant term of is the constant term of the identity series, i. e., it is 1.

The following decades saw the rise of the political Catalanism still prevalent today: the first formulations of the modern Catalan national identity can be seen in Valentí Almirall.

In the following tournament, Adhemar and William are both assigned to tilt against Sir Thomas Colville but Adhemar withdraws having discovered his true identity is that of Edward, the Black Prince.

Many had also been particularly influential in intellectualising the FN's policies on immigration, identity and " national preference ", and, following the split, Le Pen denounced them as " extremist " and " racist ".

After Batman's disappearance following the events of Final Crisis and Battle For The Cowl and his son Damian becoming Grayson's Robin, Tim is now under the identity of Red Robin.

While the second half of the twentieth century saw the serious decline of Welsh heavy industry, along with serious unemployment and the hardship and suffering that came with it, it also saw significant cultural gains with regard to a separate Welsh identity within the British Isles, starting with the appointing of a Secretary of State for Wales in 1964, and the establishment of a Welsh Office in Cardiff the following year.

Hernán Godoy describes the psychological characteristics of the Chilean, and hence part of the Chilean national identity, with following words: roto, madness, sober, serious, prudent, sense of humor, great fear to the ridicule, servile, cruel, and lack of foresight, among other qualities.

According to Treynor ’ s original " identity shift effect " hypothesis, the peer pressure process works in the following way: One's state of harmony is disrupted when faced with the threat of external conflict ( social rejection ) for failing to conform to a group standard.

It was during the decades immediately following the reconstitution that the college began to establish its identity as one of the great public schools.

However after several incidents, the treaty was ignored and the New Zealand land wars broke out from 1845, with Māori suffering a loss of land and identity, while also increasingly becoming a minority group over the following century.

The following is a quote from one of his speeches: Since the great days of the magnificent German victories of the years 1870-71, we have become increasingly conscious of our German identity and now thumb more ardently through the books of German myth, legends and history.

The family of projection operators E < sub > T </ sub >( λ ) is called resolution of the identity for T. Moreover, the following Stieltjes integral representation for T can be proved:

The following four key brand requirements are critical for a successful corporate identity strategy.

It can be seen directly or indirectly in the work of Rubens, Jusepe de Ribera, Bernini, and Rembrandt, and artists in the following generation heavily under his influence were called the " Caravaggisti " or " Caravagesques ", as well as Tenebrists or " Tenebrosi " (" shadowists ").

A son of Cináed mac Ailpín (" Kenneth MacAlpin "), he succeeded his uncle Domnall mac Ailpín as Pictish king following the latter's death on 13 April 862.

In the following example of Ennius's early Latin hexameter composition, metrical weight (" ictus ") falls on the first and last syllables of certabant ; the ictus is therefore opposed to the natural stress on the second syllable when the word is pronouned.

# Council of Ephesus ( 431 ) repudiated Nestorianism, proclaimed the Virgin Mary as the Theotokos (" Birth-giver to God ", " God-bearer ", " Mother of God "), repudiated Pelagianism, and reaffirmed the Nicene Creed. This and all the following councils in this list are not recognized by the Assyrian Church of the East.

Although it had always included a euphemistic meaning for " poison " (" being given "), over the following centuries it gradually suffered a full semantic change to the sole present German meaning " poison ".

He passed his first bar exam (" Staatsexamen ") in Berlin in 1901, and the following year he received his doctorate with a dissertation on " The Theory of adequate causation.

Other aspects in ASL include the following: stative, inchoative (" to begin to ..."), predisposional (" to tend to ..."), susceptative (" to ... easily "), frequentative (" to ... often "), protractive (" to ... continuously "), incessant (" to ... incessantly "), durative (" to ... for a long time "), iterative (" to ... over and over again "), intensive (" to ... very much "), resultative (" to ... completely "), approximative (" to ... somewhat "), semblitive (" to appear to ..."), increasing (" to ... more and more ").

Over the following decades, Muslims faced the same fate and about 60 years after the Jews, they were also compelled to convert (" moriscos ") or be expelled.

They investigated the practices of a disaffected student of Mesmer, one Charles d ' Eslon ( 1750 – 1786 ), and despite the fact that they accepted that Mesmer's results were valid, their placebo-controlled experiments following d ' Eslon's practices convinced them that mesmerism was most likely due to belief and imagination rather than to any sort of invisible energy (" animal magnetism ") transmitted from the body of the mesmerist.

The following year he founded the clandestine newspaper Sardegna libera (" Free Sardinia ") which attracted him the hostility of the Fascist regime.

As an example of how the word natio was employed in classical Latin, the following quote from Cicero's Philippics Against Mark Antony in 44 BC contrasts the external, inferior nationes (" races of people ") with the Roman civitas (" community "):

The US philosopher Charles Sanders Peirce praised Cantor's set theory, and, following public lectures delivered by Cantor at the first International Congress of Mathematicians, held in Zurich in 1897, Hurwitz and Hadamard also both expressed their admiration.

The following year he took up a lectureship in the University of Bordeaux, where he proved his celebrated inequality on determinants, which led to the discovery of Hadamard matrices when equality holds.

Taking in above expression outside the integral sign and expanding the integrand with the help of the Hadamard lemma one can obtain the following useful expression for the derivative of matrix exponent:

All non-zero codewords of the Walsh – Hadamard code have a Hamming weight of exactly by the following argument.

Hadamard code could be constructed column by column: the column is the bits of the binary representation of integer, as shown in the following example.

Example: The linear block code with the following generator matrix is a Hadamard code:

However, this idea can be understood as a basis for the following proof of the Lemma.