Topotactical Route to Multiwalled Cerium Oxide Nanotubes from MWCNTs

The development of new strategies for synthesizing 1D cerium oxide (CeO₂) hollow nanostructures has attracted much attention in recent years due to the importance of their superior properties and highly anisotropic geometry. This study reports an unpublished route of fabricating novel multiwalled CeO_2-δ nanotubes (CeO_2-δ NTs) in which the entire volume of functionalized multiwalled carbon nanotubes (f-MWCNTs) is converted into the CeO_2-δ pseudomorph through oxidation and dehydration topotactic reactions. The stable CeO_2-δ (111) planes are topotactically grown on the curved C (002) planes, preferentially exposed along the nanotube axis. In their initial condition, the novel nanotubes consist of Ce oxyhydroxide (CeO_2-x(OH)_x) with residual carbon. When heating the air up to 500 °C, CeO_2-x(OH)_x transforms gradually by dehydration into CeO_2-δ, while the residual carbon is oxidized. Despite compositional changes, nanotubes maintain their multiwalled structural integrity up to ≈550 °C. The CeO_2-δ NTs exhibit an unusually high presence of Ce³⁺ ions and surface O vacancies, contributing to a low direct band gap ranging from 2.67 to 2.32 eV compared to their NPs counterparts (3.2 eV).     

Fractional square functions and potential spaces

Carlos Segovia and Richard Wheeden defined fractional square functions involving fractional derivatives. They obtained characterizations of potential spaces via square functions. Our aim in this paper is to reconsider the ideas of Segovia and Wheeden under the light of the semigroups of operators. We develop a quite general theory of fractional square functions associated to certain classes of operators. We present some examples of differential operators where our theory applies. We recover in a more compact way the results of Segovia and Wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and Ornstein–Uhlenbeck operators.     

Semigroups of partial transformations with kernel and image restricted by an equivalence

Semigroup Forum - For an arbitrary set X and an equivalence relation $$mu$$ on X, denote by $$P_mu (X)$$ the semigroup of partial transformations $$alpha$$ on X such that $$xmu subseteq x(ker...     

Heavy-tailed phase-type distributions: a unified approach

Extremes - A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being...     

Realisation functors in tilting theory

Mathematische Zeitschrift - Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived...     

Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries

In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov–Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.