Two of the most studied functions in the theory of numbers are Euler’s totient function φ(n) and Carmichael’s function λ(n), the first giving the order of the group (Z/nZ) of reduced residues modulo n, and the latter giving the maximum order of any element of (Z/nZ). The distribution of φ(n) and λ(n) has been investigated from a variety of perspectives. In particular, many interesting propertie...

We study combinatorial group testing schemes for learning dsparse boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we give a general framework for construction...

We investigate the angular normal modes for small oscillations about an equilibrium of a single-component Coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an analytic solution for the eigenfrequencies of the angular normal modes. We also show the limiting d...

This paper describes a graph-spectral method for path estimation. Our aim is to find a maximum probability path through a lattice of pixel sites. We characterise the path recovery problem using a site transition matrix. A graph-spectral analysis of the transition matrix reveals how the maximum probability path can be located using an eigenvector of the associated normalised affinity matrix. We ...

lens is specified for tr-msitioning plane waves betwe " an media of specified is desired to have the plane wave in the second medium propagate .. .-.' " ~~ to the assumed plane boundary of that medium. The results for the case of normal. 'scide~ce are then gended to the c~ase of non-normal incidence. In particuk, the. ' '2@tions of tit the conservation and imptyhnce matching are related to the ...

We obtain an upper bound of the number of collisions of any billiard trajectory in a polyhedral angle in terms of the minimal eigenvalue of a positive definite matrix which characterizes the angle. Elements of the matrix are scalar products between the unit normal vectors of faces of the angle.

1. INTRODUCTION. In recent years, the term 'converb' has increasingly been used to describe constructions with cross-linguistically comparable forms and functions which include nonfinite verbal affixation, dependency on a finite verb, clause linking, and the sequencing of Asian converbs, differing primarily with respect to the potential for what Bickel refers to as 'narrative chaining': Asian c...

An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let φ = [φ1, · · · , φr] be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and ψ = [ψ1, · · · , ψr] an o.n. multiwavelet corresponding to φ, with two-scale symbols P and Q, respecti...

Let K⊂L be a finite Galois extension of fields, of degree n. Let G be the Galois group, and let (σα)σ∈G be a normal basis for L over K. An argument due to Mullin, Onyszchuk, Vanstone and Wilson (Discrete Appl. Math. 22 (1988/89), 149–161) shows that the matrix that describes the map x7→αx on this basis has at least 2n−1 non-zero entries. If it contains exactly 2n−1 non-zero entries, then the no...