A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward–backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzero-sum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.     

Numerical modelling of optical trapping in hollow photonic crystal cavities

Photonic crystal (PhC) devices owing to their strong confinement of electromagnetic energy are considered to be excellent candidates for on chip optical trapping of dielectric or biological particles in the nanometer range. In this work, we study and present hollow PhC cavities and characterize them for their trapping stiffness, trapping stability and variation of resonance wavelength due to the presence of various sized single particles in the cavity.     

A Strategy Utilizing a Recyclable Macrocycle Transporter for the Efficient Synthesis of a Triazolium‐Based [2]Rotaxane

A general synthesis of triazolium‐containing [2]rotaxanes, which could not be accessed by other methods, is reported. It is based on a sequential strategy starting from a well‐designed macrocycle transporter which contains a template for dibenzo‐24‐crown‐8 and a N‐hydroxysuccinimide (NHS) moiety. The sequence is: 1) synthesis by slippage of a [2]rotaxane building‐block; 2) its elongation at its NHS end; 3) the delivery of the macrocycle to the elongated part of the axle by an induced translational motion; 4) the contraction process to yield the targeted [2]rotaxane and recycle the initial transporter.     

Five loop Konishi from AdS/CFT

We derive the perturbative five loop anomalous dimension of the Konishi operator in N=4$N=4$ SYM theory from the integrable string sigma model by evaluating finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2$L=2$ single impurity state in the β deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features — a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions — simple transcendentality structure and cancellation of μ-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.     

Rare-earth metal alkyl and hydride complexes stabilized by a cyclen-derived [NNNN] macrocyclic ancillary ligand

A trinuclear rare-earth metal hydride complex was synthesized from the dialkyl complex supported by a monoanionic [NNNN] macrocycle and shown to catalyze the hydrosilylation of olefins efficiently.     

All-cis cyclic peptides

Amide bonds -NH-CO- preferentially exist in trans conformations, the cis conformation being thermodynamically unfavored with respect to the trans by about 2 kcal/mol. Yet, the main reason most proteins or peptides cannot be made from cis-peptide plaques only lies in that connecting them into open chains appears to be sterically impracticable. It is possible, however, to build all-cis cyclic peptides in which all cis-plaques are efficiently locked. The present work examines, through quantum calculations, the structural and energetic issues associated with these peculiar arrangements. Systematic exploration at DFT-B3LYP level of the potential-energy surfaces for all-cis cyclopolyglycines cG(n)(c) (n = 2-10,15), and to a lesser extent, for all-cis cyclopolyalanines and all-cis cyclopolyphenylalanines confirms that all these structures are true minima. Optimal ring size occurs around eight peptide units, resulting in planar cG7(c), cG8(c), and cG9(c). In smaller systems, the ring strain is relieved through nonplanar cup-like distortions, particularly in cG6(c). From 10 peptide units and beyond, the ring framework distorts into a saddle-edge shape. These molecules disclose some molecular flexibility, as combinatorial tilting of the plaques may give sets of minima close in energy. Indexes based on isodesmic reactions are used to estimate the energy for joining all-cis or all-trans plaques into cyclic peptides. One of them, the mean plaque-junction energy (MPJE) suggests that within sensible sizes from six peptide units and beyond, all-cis plaque association is almost equally favorable as all-trans one. The frame of radiating cis-amide bonds can be considered as defining a new kind of peptidic material, endowed with specific self-assembling properties.     

High extraction efficiency,laterally injected,light emitting diodes combining microcavities and photonic crystals

The use of photonic crystals (PCs) for realistic light emitting diodes (LEDs) is discussed, given the constraints of planar semiconductor technology. A viable route for the fabrication of high-efficiency high-brightness electrically injected LEDs is presented. The starting point is a top-emitting microcavity using a single Alox Bragg mirror. The active area is surrounded by two-dimensional PCs, namely arrays of air rods etched through the top layers; injection of the electrons is achieved through the crystals. Design rules for PCs as efficient out-couplers are detailed. The building blocks are assessed experimentally, and we show that promising results are at hand.