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⟨ X | R ⟩ of a group H, one can recursively enumerate all homomorphisms h: H → G by first enumerating all mappings h < sup >†</ sup >: X → G. Not all of these mappings extend to homomorphisms, but, since h < sup >†</ sup >( R ), is finite, it is possible to distinguish between homomorphism and non-homomorphisms by using the solution to the word problem in G. " Weeding out " non-homomorphisms gives the required recursive enumeration: h < sub > 1 </ sub >, h < sub > 2 </ sub >, ..., h < sub > n </ sub >, ....
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⟨ and X
⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.
To prove this let ⟨ X | R ⟩ be a recursive presentation for S. Choose a ∈ S such that a ≠ 1 in S.
In regression analysis, ⟨ B ⟩ symbolizes non-standardized partial slope coefficients, whereas ⟨ β ⟩ represents standardized ( standard deviation-score form ) coefficients ; in both cases, the coefficients reflect the change in the criterion Y per one-unit change in the value of the associated predictor X.
⟨ and |
For a simple example, take the presentation ⟨ a | a < sup > 3 </ sup >⟩.
* Given a recursively enumerable set A of positive integers that has insoluble membership problem, ⟨ a, b, c, d | a < sup > n </ sup > ba < sup > n </ sup > = c < sup > n </ sup > dc < sup > n </ sup >: n ∈ A ⟩ is a finitely generated group with a recursively enumerable presentation whose word problem is insoluble
Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.
In Welsh, the Ll ( digraph ) | digraph ⟨ Ll ⟩, ⟨ ll ⟩ fused for a time into a typographic ligature | ligature.
The current connects the original vacuum with the Nambu – Goldstone state, ⟨ 0 | J < sub > 0 </ sub >( 0 )| θ ⟩ ≠ 0.
Its hallmark under the broken symmetry transformation is nonvanishing vacuum expectation ⟨ δφ < sub > g </ sub >⟩, an order parameter, for vanishing ⟨ φ < sub > g </ sub >⟩= 0, at some ground state | 0 ⟩ chosen at the minimum of the potential, ⟨∂ V /∂ φ < sub > i </ sub >⟩= 0.
⟨ and R
In phonetics, rhotic consonants, also called tremulants or " R-like " sounds, are liquid consonants that are traditionally represented orthographically by symbols derived from the Greek letter rho, including ⟨ R ⟩, ⟨ r ⟩ from the Latin script and ⟨ Р ⟩, ⟨ p ⟩ from the Cyrillic script.
They are transcribed in the International Phonetic Alphabet by upper-or lower-case variants of Roman ⟨ R ⟩, ⟨ r ⟩:,,,,,,, and.
Linking R and intrusive R are sandhi or linking phenomena involving the appearance of the rhotic consonant ( which normally corresponds to the letter ⟨ r ⟩) between two consecutive morphemes where it would not normally be pronounced.
⟨ and ⟩
An example is modern Greek which may write the phoneme in six different ways: ⟨ ι ⟩, ⟨ η ⟩, ⟨ υ ⟩, ⟨ ει ⟩, ⟨ οι ⟩, and ⟨ υι ⟩ ( although the last is rare ).
For example, the word cat consists of three letters ⟨ c ⟩, ⟨ a ⟩, and ⟨ t ⟩, in which ⟨ c ⟩ represents the sound, ⟨ a ⟩ the sound, and ⟨ t ⟩ the sound.
Thus, in the word ship ( pronounced ), the digraph ⟨ sh ⟩ ( two letters ) represents the sound.
⟨ and H
* Chemical nomenclature includes the infixes ⟨ pe ⟩, signifying complete hydrogenation ( from piperidine ), and ⟨ et ⟩ ( from ethyl ), signifying the ethyl radical C < sub > 2 </ sub > H < sub > 5 </ sub >.
This is why the earliest ( up to the 13th century ) shape of Cyrillic ⟨ И ⟩ was ⟨ H ⟩.
⟨ and one
Some researchers such as Brengelman ( 1970 ), have suggested that, in addition to this marking of word origin, these spellings indicate a more formal level of style or register in a given text, although Rollins ( 2004 ) finds this point to be exaggerated as there would be many exceptions where a word with one of these spellings, such as ⟨ ph ⟩ for ( like telephone ), could occur in an informal text.
For example, the sound of the English letter ⟨ t ⟩ may be transcribed in IPA with a single letter,, or with a letter plus diacritics,, depending on how precise one wishes to be.
Other modern orthographies for Slavic languages eliminated one of the two letters during alphabet reforms of the 19th or 20th centuries: Russian, Macedonian, Serbian and Bulgarian languages use only ⟨ И ⟩, whereas Belarusian uses only ⟨ І ⟩.
One possibility is that it was formed from two connecting Hebrew letters Shin ⟨ ש ⟩, the bottom one inverted.
The letter Sha ⟨ Ш ⟩, which represents the unvoiced counterpart of Zhe, is one of several Cyrillic letters which were derived directly from Hebrew letters.
For example, in such words as little and bottle one might view ⟨ le ⟩ as an " endocentric " digraph for, or view ⟨ e ⟩ as an empty letter ; similarly with ⟨ bu ⟩ or ⟨ u ⟩ in buy and build.
The letter combinations ⟨ aa ⟩ and ⟨ oe ⟩ were often written so that one of the letters stood above the other as a smaller letter, which led to the development of the modern letters ⟨ å ⟩, ⟨ ä ⟩, and ⟨ ö ⟩.
The difference between the two ⟨ ng ⟩ sounds,, found in singer and finger, is so unimportant that it makes no practical difference if one mixes them up, and some dialects pronounce the sounds the same in both words.
In English, the digraph ⟨ th ⟩ represents in most cases one of two different phonemes: the voiced dental fricative ( as in this ) and the voiceless dental fricative ( thing ).
However, the " belt " on the existing symbol for a voiceless lateral fricative,, forms the basis for occasional ad hoc symbols for the other lateral fricatives, the third one, ⟨ ⟩, representing the palatal lateral fricative:
⟨ and can
But because the substitution of any of these for any other cannot change the meaning of a word, they are considered to be allographs of the same grapheme, which can be written ⟨ a ⟩.
In addition, ⟨ ny ⟩ represents the palatal nasal, ⟨ ng ⟩ is used for the velar nasal ( which can occur word-initially ), ⟨ sy ⟩ for ( English ⟨ sh ⟩) and ⟨ kh ⟩ for the voiceless velar fricative.
** Palatalization of ⟨ ts ⟩ and ⟨ tz ⟩ ; e. g. pots ' cans, jars, you can ', dotze ' twelve '.
( To the extent that it can be defined, ⟨ p ⟩ = 0 for all times, despite the apparent acceleration of the front.
The vowel represented by ⟨ и ⟩, as well as almost any other Slavonic vowel, can be stressed or unstressed.
Serbian ⟨ и ⟩ with a circumflex can be unstressed as well ; in this case, it represent the genitive case of plural forms and is used to distinguish them from other similar forms.
* cluster ⟨ дз ⟩ can be pronounced ( mostly in Ukrainian and Belarusian ) as the voiced alveolar affricate ( Ukrainian дзеркало “ mirror ”) or its palatalized form ( Belarusian гадзіннік “ clock ”), but if ⟨ д ⟩ and ⟨ з ⟩ belong to different morphemes, then they are pronounced separately.
This can lead to some confusion, as the ⟨ ch ⟩ in the transcription may seem to indicate that Щ is a combination of Ш and a strong Ч, which is not true.
However, the inclusion of ⟨ Э ⟩ in its modern function in the Russian Academy ’ s Dictionary of 1789 – 94 marks the point from which it can be considered as an established part of the Russian orthographical standard.
For example, in fast speech, initial consonants go through lenition if they are in an unstressed syllable: pinyin ⟨⟩ become ⟨ r ⟩, so " don't know " can sound like ; ⟨ j q x ⟩ become ⟨ y ⟩, so " go quickly " can sound like ; pinyin ⟨ b d g ⟩ go through voicing to become ; similar changes also occur on other consonants.
⟨ and all
At this time ⟨ k ⟩ had fallen out of favor, and ⟨ c ⟩, which had formerly represented both and before open vowels, had come to express in all environments.
While the soft value of ⟨ g ⟩ varies in different Romance languages ( in French and Portuguese, in Catalan, in Italian and Romanian, and in Castilian Spanish, and in other dialects of Spanish ), in all except Romanian and Italian, soft ⟨ g ⟩ has the same pronunciation as the ⟨ j ⟩.
Apart of English, in all Brazilian Portuguese dialects the ⟨ rr ⟩ phoneme, or, may be actually realized as other, traditionally non-rhotic, fricatives ( and most often is so ), unless it occurs single between vowels, being so realized as a dental, alveolar, postalveolar or retroflex flap.
: j ( v ) j ( w ) + j ( w ) j ( v ) = 2 ⟨ v, w ⟩ for all
* Mirandese maintains distinct reflexes of all seven medieval Ibero-Romance sibilants: ⟨ ch ⟩, ⟨ x ⟩, ⟨ g / j ⟩, ⟨ c / ç ⟩, ⟨ z ⟩, ⟨ s /- ss -⟩, -⟨ s -⟩.
non-normalizable and has an undefined ( infinite ) ⟨ x ⟩ for all times.
The symbol in the International Phonetic Alphabet that represents this sound is ⟨ ⟩, and the equivalent X-SAMPA symbol is < tt > z `</ tt >. Like all the retroflex consonants, the IPA symbol is formed by adding a rightward-pointing hook extending from the bottom of a zee ( the letter used for the corresponding alveolar consonant ).
Irish orthography is similar in that its spelling system is both etymological and used to indicate whether preceding consonants are broad or slender so that such combinations as ⟨ aí ⟩, ⟨ ei ⟩, and ⟨ aío ⟩ all represent.
During the alphabet reforms of Peter I, all diacritic marks were removed from the Russian writing system, but shortly after Peter I's death in 1735, the distinction between ⟨ И ⟩ and ⟨ Й ⟩ was restored.
* spells all vowels and diphthongs using only vowel letters: ⟨ a ⟩, ⟨ e ⟩, ⟨ i ⟩, ⟨ o ⟩, ⟨ u ⟩
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