We construct a Kirby diagram of the rational homology ball used in “generalized rational blow-down” developed by Jongil Park. The diagram consists of a dotted circle and a torus knot. The link is simpler, but the parameters are a little complicate. Euclidean Algorithm is used three times in the construction and the proof. 1 Main theorem For a coprime pair (m,n) of positive integers, we take a s...

Coprime arrays represent a form of sparse sensing which can achieve narrow beams using relatively few elements, exceeding the spatial Nyquist sampling limit. The purpose of this paper is to expand on and experimentally validate coprime array theory in an acoustic implementation. Two nested sparse uniform linear subarrays with coprime number of elements ( M and N) each produce grating lobes that...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

In this note we determine weight distributions of minimal constacyclic codes of length p over the finite field Fl, where p is a prime which is coprime to l.

The function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to the first k primes. We give a new computational method for calculating strong upper bounds on h(k).

The function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to the first k primes. We give a new computational method for calculating strong upper bounds on h(k).

This note introduces a necessary condition for the model/data consistency problem with perturbed coprime factorizations and closed-loop noisy frequency-response measurements. The necessary condition involves the computation of structured singular values of complex linear fractional transformations.

For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers. Mathematics Subject Classification (2000). Primary 57M25; Secondary 57M12, 57M50.

Title of Thesis: Performance and Robustness Analysis of Co-Prime and Nested Sampling Ali Koochakzadeh, Master of Science, 2016 Thesis Directed By: Professor Piya Pal Department of Electrical and Computer Engineering Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of...