We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics, and Fourier analysis.

A non-empty subset A of X = X1 × · · · × Xd is a (proper) box if A = A1 × · · · × Ad and Ai ⊂ Xi for each i. Suppose that for each pair of boxes A, B and each i, one can only know which of the three states takes place: Ai = Bi, Ai = Xi \ Bi, Ai 6∈ {Bi, Xi \ Bi}. Let F and G be two systems of disjoint boxes. Can one decide whether ⋃ F = ⋃ G ? In general, the answer is ‘no’, but as is shown in th...

At first, we show the following matter. Theorem 1. Let H∗(y; s) be as above. Suppose that y ≥ 1 and p(s) has N many zeros counted with multiplicity in the right half-plane R(s) > 1/2. Then H∗(y; s) has at most N +1 many zeros in the right half-plane R(s) > 1/2 counting with multiplicity, and the same thing holds in the left half-plane R(s) < 1/2. The trivial functional equation H(y; s) = H(y; 1...

Abstract In this article, we have investigated the peristaltic transport of electro-osmotic flow Jeffrey fluid in an asymmetric channel, which walls are modulated by array patches. presence Electrical Debye Layer (EDL), Poisson Boltzmann equation for electrical potential within micro channel is considered. To evaluate potential, Debye-Huckel linearization employed governing equations modeled an...