The relative densities of rational primes q, such that a given rational prime p is a square of either a principal or a non-principal ideal in the quadratic number field Q( √ pq), essentially depend on the residue classes of both p and q modulo 4. The computation of these densities is complete when at least one residue of p or q is not equal to 1 modulo 4. When both residues are equal to 1 modul...

Human services, such as social supports and health care, have low contractibility; services are difficult to specify measure, manage when delivered by a third party. Services can do fail, resulting in the inefficient use of public resources potential harm clients. This article develops conceptual framing using transaction cost economics (TCE) theory understand why human contract, management con...

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic cross-correlations. These sequences are decimations of the 2-adic expansions of rational numbers p/q such that 2 is a primitive root modulo q.

Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling and relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (resp. contractible open 3-manifold) M if and only if M is homeomorphic to S 3 (resp. R 3). A...

To achieve high resource utilization for multi-issue Digital Signal Processors (DSPs), production compilers commonly include variants of the iterative modulo scheduling algorithm. However, excessive cyclic data dependences, which exist in communication and media processing loops, often prevent the modulo scheduler from achieving ideal loop initiation intervals. As a result, replicated functiona...

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of decidingwhether a given input graph is contractible to H. We continue a line of research that wasstarted in 1987 by Brouwer & Veldman, and we determine the computational complexity ofH-CONTRACTIBILITY for certain classes of pattern graphs. In particular, we pin-pointthe complexity for all graphs H with five...

We prove the existence of a subset, with positive natural density, squarefree integers n>0 such that 4–rank ideal class group ℚ(-n,n) is ω 3 (n)-1, where (n) number prime divisors n are modulo 4. Recall for groups associated to ℚ(n) or ℚ(-n) an analogous subset does not exist.

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic crosscorrelations. These sequences are decimations of the 2adic expansions of rational numbers p=q such that 2 is a primitive root modulo q.

We show that a ring $R$ has stable range one if and only every left unit lifts modulo principal ideal. also quasi-morphic it is uniquely generated. Thus we answer in the affirmative two questions raised by W. K. Nicholson.