Paying off the mortgage, once a widespread rite of passage for homeowners approaching retirement, has become less common in recent years. Concerns are mounting that the increased prevalence of housing debt among older homeowners could compromise financial security in retirement by expanding housing affordability problems, crimping essential nonhousing spending, increasing vulnerability to home ...

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and c...

Symplectic methods for Hamiltonian systems are known to have favourable properties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variables instead of quadratic growth, correct qualitative behaviour) if they are applied with constant step sizes, while all of these properties are lost in a standard variable step size impl...

We define pure intuitionistic differential nets, extending Ehrhard and Regnier’s differential interaction netswith the exponential box of Linear Logic.Normalization of the exponential reduction and confluence of the full one is proved. Though interesting and independent on their own, these results are directed and adjusted to give a translation of Boudol’s untyped λ-calculus with multiplicities...

The negation map can be used to speed up the computation of elliptic curve discrete logarithms using either the baby-step giant-step algorithm (BSGS) or Pollard rho. Montgomery’s simultaneous modular inversion can also be used to speed up Pollard rho when running many walks in parallel. We generalize these ideas and exploit the fact that for any two elliptic curve points X and Y , we can effici...

Elliptic curve cryptographic protocols often make use of the inherent hardness of the discrete logarithm problem, which is to solve kG = P for k. There is an abundance of evidence suggesting that elliptic curve cryptography is more secure than the classical case. One reason for this is the best known general-purpose algorithm to solve the elliptic curve discrete logarithm problem is Pollard’s R...