[PDF] Top 20 Beyond sum free sets in the natural numbers

... a − 1], whereas in Proposition 23 the s-sets lie in [1, s + a] but not in [1, s + a − 1]. Proposition 24. For 2 6 a 6 s−1, Spec(s, s+a) contains [ (s−a)(s−a+1) 2 , (s−a+1)(s−a+2) 2 −1]. Proof. To establish that ... See full document

... complete sum-free sets. A complete sum-free set in a finite group G is a sum-free set S satisfying G = S ∪ SS ...Any sum-free set S with the property that S ... See full document

... odd numbers in [n] and the set {bn/2c + 1, . . . , n} are maximal sum-free ...(A sum-free subset of [n] is maximal if it is not properly contained in another sum-free ... See full document

... is already not true (for some n) for the simplest known APN exponent 3. In the present section, we show that every APN exponent (known or unknown), satisfies a property which deals with the numbers gcd(d − 2 j , 2 ... See full document

... ( x  2 x  x  3  , although identical in all respects, are treated as multiplicity ([1], [3]). So, it is convenient to accept a collection like { 1 , 1 , 1 , 2 , 3 , 3 } of roots rather than a set like { 1 , 2 , 3 } ... See full document

... Although the ratio of S cations: 2 anions did not measure the internal ionic balance of the plants, R values and their relationship with % N were useful for explaining ion interactions, [r] ... See full document

... Relative profit maximization in duopoly with differentiated goods is an example of zero- sum game with two alternative strategic variables 1 . Each firm chooses its output or price. The results of this paper imply ... See full document

... Abstract: There are two categories of objects spatial information science investigates: actual objects and their spatial properties, such as in geography, and abstract objects which are employed metaphorically, as for ... See full document

... of natural numbers, that we will be using. When adding numbers in base 10 (or base b > 2) we have to use sequences of digits to represent natural ...a natural number is determined by ... See full document

... When the rule for a relation is written and no domain is stipulated then it is understood that the domain taken is the largest for which the rule has meaning.. This concept is considered[r] ... See full document

... The reflexive graph model of parametricity we present in Section 4 is defined with respect to the specific formulation of dependent type theory that we set out in this section. The type theory we consider is a standard ... See full document

... inclusion in each direction, disjointness, covering the universe, and the general case, respectively, Each can be dened in terms of the emptiness or otherwise of Boolean combinations of the sets, and the set of ... See full document

... Carl and I are natives of Northeast Ohio. We met in graduate school at Kent State University in 1997. I finished my Ph.D in Pure Mathematics in August 1998 and started teaching at Lorain County Community College in ... See full document

... The possibility to describe the properties of the cold dark matter in the universe using a candidate in various particle physics scenarios has been studied for a long time. For a re- view of different candidates see Ref. ... See full document

... According to this theory, all the male bees have a single parent whereas there are two parents of a female bee. On tracing the pedigree of the male bee, it is observed that it has 1 parent, 2 grandparents, 3 ... See full document

... maximal sum-free subsets S of [n] with the property that (i) the smallest element of S is n/4 ±o(n) and (ii) the second smallest element of S is at least n/2 − ...such sets within the containers.) We ... See full document

... Due to the commutativity of multiplication, these powers of primes can be put in any order to arrive at the product m. In order to provide a unique factorisation of m, we choose a canonical order for the primes, the most ... See full document

... We claim that our model captures most of the known constructions that make natural language provably not context-free as string sets, and that it does so with a small addition to the con[r] ... See full document

... Relative profit maximization in a symmetric oligopoly with differentiated goods is an ex- ample of symmetric n-person zero-sum game with two alternative strategic variables. Each firm chooses its output or price. ... See full document

... large numbers, were obtained for independent random sets or fuzzy random sets in the past decades, and little is known of dependent random sets or fuzzy random sets except the ... See full document