Addition theorems on Zn

On linear versions of some addition theorems

Let K ⊂ L be a field extension. Given K-subspaces A,B of L, we study the subspace 〈AB〉 spanned by the product set AB = {ab | a ∈ A, b ∈ B}. We obtain some lower bounds on dimK〈AB〉 and dimK〈B 〉 in terms of dimK A, dimK B and n. This is achieved by establishing linear versions of constructions and results in additive number theory mainly due to Kemperman and Olson.

Addition Theorems via Continued Fractions

We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for Bessel functions and confluent hypergeometric functions. We also derive several addition theorems for basic hypergeometric functions. Applications to the evaluat...

Addition Theorems in Acyclic Semigroups

We give a necessary and sufficient condition on a given family A of finite subsets of integers for the Cauchy-Davenport inequality |A+ B| ≥ |A|+ |B| − 1, to hold for any family B of finite subsets of integers. We also describe the extremal families for this inequality. We prove this result in the general context of acyclic semigroups, which contain also the semigroup of sequences of elements in...

Two Addition Theorems on Polynomials of Prime Variables

The effect of Zn element addition on dissimilar Al6061/AZ31 friction stir welded joints

In this study, friction stir butt welding of Mg and Al alloys with applying Zn interlayer was performed. To obtain optimum condition, a combination of two travel and three rotation speeds were selected. Mg-Zn and Mg-Al-Zn IMCs, Al solid solution and residual Zn, were the most common phases in the stirred zone, which eliminated the formation of Al-Mg intermetallics. The maximum mechanical proper...