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In the Latin-based orthographies of many European languages, including English, a distinction between hard and soft c occurs in which c represents two distinct phonemes. The sound of a hard c often precedes the non-front vowels a , o and u , and is that of the voiceless velar stop , /k/ (as in car ).
HSAB is an acronym for "hard and soft (Lewis) acids and bases".HSAB is widely used in chemistry for explaining the stability of compounds, reaction mechanisms and pathways. It assigns the terms 'hard' or 'soft', and 'acid' or 'base' to chemical species.
If the problem mandates that the constraints be satisfied, as in the above discussion, the constraints are sometimes referred to as hard constraints.However, in some problems, called flexible constraint satisfaction problems, it is preferred but not required that certain constraints be satisfied; such non-mandatory constraints are known as soft constraints.
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While c , which also has hard and soft pronunciations, exists alongside k (which always indicates a hard pronunciation), g has no analogous letter or letter combination which consistently indicates a hard g sound, even though English uses j consistently for the soft g sound (the rationale for the spelling change of "gaol" to "jail").
Formally, consider an n×n matrix A=(a i,j).If all matrix elements are zero outside a diagonally bordered band whose range is determined by constants k 1 and k 2: , = < > +;, then the quantities k 1 and k 2 are called the lower bandwidth and upper bandwidth, respectively. [1]
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