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The case originally considered by Carl Friedrich Gauss was the quadratic Gauss sum, for R the field of residues modulo a prime number p, and χ the Legendre symbol.In this case Gauss proved that G(χ) = p 1 ⁄ 2 or ip 1 ⁄ 2 for p congruent to 1 or 3 modulo 4 respectively (the quadratic Gauss sum can also be evaluated by Fourier analysis as well as by contour integration).
Mometasone, also known as mometasone furoate, is a steroid (specifically, a glucocorticoid) medication used to treat certain skin conditions, hay fever, and asthma. [ 10 ] [ 11 ] [ 12 ] Specifically it is used to prevent rather than treat asthma attacks. [ 10 ]
2-Furoyl chloride is an acyl chloride of furan.It takes the form of a corrosive liquid, which is more irritating to the eyes than benzoyl chloride. [1] 2-Furoyl chloride is a useful pharmaceutical intermediate and is used in the synthesis of mometasone furoate, an antiinflammatory prodrug used in the treatment of skin disorders, hay fever and asthma.
For treating atopic dermatitis, newer (second generation) corticosteroids, such as fluticasone propionate and mometasone furoate, are more effective and safer than older ones. They are also generally safe and do not cause skin thinning when used intermittently to treat atopic dermatitis flare-ups.
In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum.
Let F be a finite field with q elements, and F s be the field such that [F s:F] = s, that is, s is the dimension of the vector space F s over F.. Let be an element of .. Let be a multiplicative character from F to the complex numbers.
The Gross–Koblitz formula states that the Gauss sum can be given in terms of the -adic gamma function by = < (())where is a power of a prime ,; is an integer with <, is the integer whose base-expansion is a cyclic permutation of the digits of by positions,
It is the first asthma triple-combination therapy; it consists of a fixed-dose combination of three active substances (indacaterol, glycopyrronium bromide and mometasone furoate) in capsules, to be administered using an inhaler. [11] An optional electronic sensor may also be co-packed with the product. [11]