One-pot ligation strategy for atypical ubiquitin chains synthesis by using the trifluoroacetamidomethyl-protected isopeptide-linked Ub (Tfacm-isoUb) unit

Protein chemical synthesis can provide the homogeneous atypical ubiquitin chains that are usually difficult to obtain by other methods. Herein, we report a new one-pot ligation approach for the synthesis of atypical Ub chains based on the Tfacm-protected isoUb building block with operational simplicity and high efficiency. The key intermediate, the Tfacm-protected isoUb building block can be readily prepared by Fmoc SPPS. The practicality and efficiency of the new method is demonstrated by the successful preparation of K11-linked di-Ub.     

A numerical algorithm for pricing electricity derivatives for jump-diffusion processes based on continuous time lattices

We present a numerical algorithm for pricing derivatives on electricity prices. The algorithm is based on approximating the generator of the underlying price process on a lattice of prices, resulting in an approximation of the stochastic process by a continuous time Markov chain. We numerically study the rate of convergence of the algorithm for the case of the Merton jump-diffusion model and apply the algorithm to calculate prices and sensitivities of both European and Bermudan electricity derivatives when the underlying price follows a stochastic process which exhibits both fast mean-reversion and jumps of large magnitude.     

Exceptionally Plastic/Elastic Organic Crystals of a Naphthalidenimine-Boron Complex Show Flexible Optical Waveguide Properties

The design of molecular compounds that exhibit flexibility is an emerging area of research. Although a fair amount of success has been achieved in the design of plastic or elastic crystals, realizing multidimensional plastic and elastic bending remains challenging. We report herein a naphthalidenimine–boron complex that showed size-dependent dual mechanical bending behavior whereas its parent Schiff base was brittle. Detailed crystallographic and spectroscopic analysis revealed the importance of boron in imparting the interesting mechanical properties. Furthermore, the luminescence of the molecule was turned-on subsequent to boron complexation, thereby allowing it to be explored for multimode optical waveguide applications. Our in-depth study of the size-dependent plastic and elastic bending of the crystals thus provides important insights in molecular engineering and could act as a platform for the development of future smart flexible materials for optoelectronic applications.     

Interaction of modulated pulses in nonlinear oscillator chains

We formally derive and rigorously justify the modulation equations of lowest order for the interaction of two modulated pulses on a one-dimensional nonlinear oscillator chain. We show that solutions with the initial form of the assumed ansatz preserve this form over time intervals with positive macroscopic length, and we show a bound on the possible shift of the envelope caused by the interaction. Thus, we rigorously justify and quantify the statement that under the given conditions there is almost no interaction of the modulated pulses.     

Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms

After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.     

Synthesis and Characterization of Benzonitrile-Substituted Silyl Ethers

The silyl ethers (siloxanes) Me_{4? x}Si(OC₆H₅CN)_x (x = 1–4) (1–4), O(Si(OC₆H₄CN) (Me)₂)₂ (5), and Me₃Si–O–C₆F₄CN (6) have been synthesized by the reaction of the respective p-hydroxybenzonitriles and chlorosilanes in the presence of N,N,N′,N′-tetramethylethylenediamine (TMEDA) as hydrogen chloride acceptor. All compounds have been fully characterized by CHN-analysis, melting point, IR, Raman, mass spectroscopy, and ¹H, ¹³C, ²⁹Si NMR spectroscopy. Furthermore, the crystal structures of these compounds—with the exception of Me₂Si(OC₆H₅CN)₂, which is a liquid—were determined by X-ray diffractometry.