Lower bounds on the localisation length of balanced random quantum walks

Letters in Mathematical Physics - We consider the dynamical properties of Quantum Walks defined on the d-dimensional cubic lattice, or the homogeneous tree of coordination number 2d, with...     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Supratransmission in discrete one-dimensional lattices with the cubic–quintic nonlinearity

Nonlinear Dynamics - We numerically analyzed the supratransmission phenomenon in the discrete nonlinear Schrödinger equation with the cubic–quintic nonlinearity. It has been reported...     

Covalently Trapped Triarylamine-Based Supramolecular Polymers

C₃-Symmetric triarylamine trisamides (TATAs), decorated with three norbornene end groups, undergo supramolecular polymerization and further gelation by π–π stacking and hydrogen bonding of their TATA cores. By using subsequent ring-opening metathesis polymerization, these physical gels are permanently crosslinked into chemical gels. Detailed comparisons of the supramolecular stacks in solution, in the physical gel, and in the chemical gel states, are performed by optical spectroscopies, electronic spectroscopies, atomic force microscopy, electronic paramagnetic resonance spectroscopy, X-ray scattering, electronic transport measurements, and rheology. The results presented here clearly evidence that the core structure of the functional supramolecular polymers can be precisely retained during the covalent capture whereas the mechanical properties of the gels are concomitantly improved, with an increase of their storage modulus by two orders of magnitude.     

Blocking the Hype-Hypocrisy-Falsification-Fakery Pathway is Needed to Safeguard Science

In chemistry and other sciences, hype has become commonplace, compounded by the hypocrisy of those who tolerate or encourage it while disapproving of the consequences. This reduces the credibility and trust upon which all science depends for support. Hype and hypocrisy are but first steps down a slippery slope towards falsification of results and dissemination of fake science. Systemic drivers in the contemporary structure of the science establishment encourage exaggeration and may lure the individual into further steps along the hype-hypocrisy-falsification-fakery continuum. Collective, concerted intervention is required to effectively discourage entry to this dangerous pathway and to restore and protect the probity and reputation of the science system. Chemists must play and active role in this effort.     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.