By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the ‘difficulty’ of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme combines an asymmetric public key protocol with symmetric private ones and is intrinsecally secure against quantum eavesdropper attacks. PACS2008: 89.70.-a (Inform...

We present an arbitrage-free, non-parametric yield curve prediction model which takes the full discretized yield curve data as input state variable. The absence of arbitrage is a particular important model feature for prediction models in case of highly correlated data as, e.g., for interest rates. Furthermore, the model structure allows to separate constructing the daily yield curve from estim...

We consider the oxygen diffusion equation. Oxygen diffusion in a sike cell with simultaneous absorption is an important problem. Oxygen diffusion has a wide range of medical applications. Numerical solutions of its partial differential equation are obtained by extrapolation method with the vector of values V approximating to C (diffusion) at the mesh points. And the results gave a good agreemen...

We present a Parrondo’s paradox for free energy in a classical flashing ratchet model and use it as an alternative way to interpret the working mechanism of molecular motors. We also study the efficiency of molecular motors measured by their free energies. Our example demonstrates that a molecular motor can gain up to 20% in its free energy during the process. In addition, we report a noise ind...

In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...

We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 exponentially (as time goes to infinity), and slow solutions decaying to 0 as negative powers of t. Here we provide a characterization of slow/f...

We consider the inviscid limit of the stochastic damped 2D NavierStokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The...

We consider Schrödinger operators on the real line with limitperiodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral measures are purely singular continuous. Moreover, we show that for a dense set of limit-periodic potentials, the spectrum of the associated Schrödinger operator has Hausdorff dimension zero. In both results one can i...

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technologies in general and the creation and exploration...

We obtain an asymptotic upper bound for the minimal number of generators for a finite direct sum of matrix algebras with entries in a finite field. This produces an upper bound for a similar quantity for integer matrix rings. We obtain an exact formula for the minimal number of generators for a finite direct sum of 2-by-2 matrix algebras with entries in a finite field. As a consequence, we show...