Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function

We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. The linear dependence on the characteristic of the weight $[w]_{A_{p/2}}$ turns out to be sharp for $3\le p<\infty$, whereas the sharpness in the range $2<p<3$ remains as an open question. Weighted weak-type estimates in the endpoint $p=2$ are also provided. The results arise as a consequence of a sparse domination shown for these operators, obtained by suitably adapting the ideas coming from Benea (2015) and Culiuc et al. (2016).Comment: 18 pages. Revised versio

Diabolical points in the magnetic spectrum of Fe_8 molecules

The magnetic molecule Fe_8 has been predicted and observed to have a rich pattern of degeneracies in its spectrum as an external magnetic field is varied. These degeneracies have now been recognized to be diabolical points. This paper analyzes the diabolicity and all essential properties of this system using elementary perturbation theory. A variety of arguments is gievn to suggest that an earlier semiclassical result for a subset of these points may be exactly true for arbitrary spinComment: uses europhys.sty package; 3 embedded ps figure

Nickel-catalyzed transamidation of aliphatic amide derivatives.

Transamidation, or the conversion of one amide to another, is a long-standing challenge in organic synthesis. Although notable progress has been made in the transamidation of primary amides, the transamidation of secondary amides has remained underdeveloped, especially when considering aliphatic substrates. Herein, we report a two-step approach to achieve the transamidation of secondary aliphatic amides, which relies on non-precious metal catalysis. The method involves initial Boc-functionalization of secondary amide substrates to weaken the amide C-N bond. Subsequent treatment with a nickel catalyst, in the presence of an appropriate amine coupling partner, then delivers the net transamidated products. The transformation proceeds in synthetically useful yields across a range of substrates. A series of competition experiments delineate selectivity patterns that should influence future synthetic design. Moreover, the transamidation of Boc-activated secondary amide derivatives bearing epimerizable stereocenters underscores the mildness and synthetic utility of this methodology. This study provides the most general solution to the classic problem of secondary amide transamidation reported to date

Integrated flight/propulsion control system design based on a centralized approach

An integrated flight/propulsion control system design is presented for the piloted longitudinal landing task with a modern, statically unstable, fighter aircraft. A centralized compensator based on the Linear Quadratic Gaussian/Loop Transfer Recovery methodology is first obtained to satisfy the feedback loop performance and robustness specificiations. This high-order centralized compensator is then partitioned into airframe and engine sub-controllers based on modal controllability/observability for the compensator modes. The order of the sub-controllers is then reduced using internally-balanced realization techniques and the sub-controllers are simplified by neglecting the insignificant feedbacks. These sub-controllers have the advantage that they can be implemented as separate controllers on the airframe and the engine while still retaining the important performance and stability characteristics of the full-order centralized compensator. Command prefilters are then designed for the closed-loop system with the simplified sub-controllers to obtain the desired system response to airframe and engine command inputs, and the overall system performance evaluation results are presented

Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian

The spin Hamiltonian that describes the molecular magnet Fe$_8$ has biaxial symmetry with mutually perpendicular easy, medium, and hard magnetic axes. Previous calculations of the ground state tunnel splittings in the presence of a magnetic field along the hard axis are extended, and the meaning of the previously discovered oscillation of this splitting is further clarified

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

A two-step approach to achieve secondary amide transamidation enabled by nickel catalysis.

A long-standing challenge in synthetic chemistry is the development of the transamidation reaction. This process, which involves the conversion of one amide to another, is typically plagued by unfavourable kinetic and thermodynamic factors. Although some advances have been made with regard to the transamidation of primary amide substrates, secondary amide transamidation has remained elusive. Here we present a simple two-step approach that allows for the elusive overall transformation to take place using non-precious metal catalysis. The methodology proceeds under exceptionally mild reaction conditions and is tolerant of amino-acid-derived nucleophiles. In addition to overcoming the classic problem of secondary amide transamidation, our studies expand the growing repertoire of new transformations mediated by base metal catalysis