Aromatic Chemistry by D. Hepworth, D. R. Waring, M. J. Waring
نویسندگان
چکیده
منابع مشابه
From Fermat to Waring
The ring Zk(+, .) mod p k with prime power modulus (prime p > 2) is analysed. Its cyclic group Gk of units has order (p − 1)p, and all p-th power n residues form a subgroup Fk with |Fk| = |Gk|/p. The subgroup of order p − 1, the core Ak of Gk, extends Fermat’s Small Theorem (FST ) to mod p, consisting of p − 1 residues with n ≡ n mod p. The concept of carry, e.g. n in FST extension n ≡ np + 1 m...
متن کاملGeneralized Anti-Waring Numbers
The anti-Waring problem considers the smallest positive integer such that it and every subsequent integer can be expressed as the sum of the k powers of r or more distinct natural numbers. We give a generalization that allows elements from any nondecreasing sequence, rather than only the natural numbers. This generalization is an extension of the anti-Waring problem, as well as the idea of comp...
متن کاملWaring Decompositions of Monomials
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up t...
متن کاملWaring: Nephrogenic Systemic Fibrosis
In these patients, avoid use of gadolinium-based contrast agents unless the diagnostic information is essential and not available with non-contrast enhanced magnetic resonance imaging (MR). NSF may result in fatal or debilitating systemic fibrosis affecting the skin, muscle and internal organs. Screen all patients for renal dysfuction by obtaining a history and/or laboratory tests. When adminis...
متن کاملThe quadratic Waring–Goldbach problem
It is conjectured that Lagrange’s theorem of four squares is true for prime variables, i.e. all positive integers n with n 4 ðmod 24Þ are the sum of four squares of primes. In this paper, the size for the exceptional set in the above conjecture is reduced to OðN 3 8 þeÞ: r 2004 Elsevier Inc. All rights reserved. MSC: 11P32; 11P05; 11N36; 11P55
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Australian Journal of Chemistry
سال: 2003
ISSN: 0004-9425
DOI: 10.1071/ch00307_br