Compact Difference Schemes on a Three-Point Stencil for Second-Order Hyperbolic Equations

Differential Equations - We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable...     

Novel numerical techniques for the finite moment log stable computational model for European call option

Option pricing models are often used to describe the dynamic characteristics of prices in financial markets. Unlike the classical Black–Scholes (BS) model, the finite moment log stable (FMLS) model can explain large movements of prices during small time steps. In the FMLS, the second-order spatial derivative of the BS model is replaced by a fractional operator of order α which generates an α-stable Lévy process. In this paper, we consider the finite difference method to approximate the FMLS model. We present two numerical schemes for this approximation: the implicit numerical scheme and the Crank–Nicolson scheme. We carry out convergence and stability analyses for the proposed schemes. Since the fractional operator routinely generates dense matrices which often require high computational cost and storage memory, we explore three methods for solving the approximation schemes: the Gaussian elimination method, the bi-conjugate gradient stabilized method (Bi-CGSTAB) and the fast Bi-CGSTAB (FBi-CGSTAB) in order to compare the cost of calculations. Finally, two numerical examples with exact solutions are presented where we also use extrapolation techniques to achieve higher-order convergence. The results suggest that the proposed schemes are unconditionally stable and convergent, and the FMLS model is useful for pricing options.     

On Hölder calmness of solution mappings in parametric equilibrium problems

We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces.     

Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality...     

Ab initio simulations of liquid electrolytes for energy conversion and storage

Understanding physicochemical properties of liquid electrolytes is essential for predicting and optimizing device performance for a wide variety of emerging energy technologies, including photoelectrochemical water splitting, supercapacitors, and batteries. In this work, we review recent progress and open challenges in predicting structural, dynamical, and electronic properties of the liquids using first-principles approaches. We briefly summarize the basic concepts of first-principles molecular dynamics (FPMD), and we discuss how FPMD methods have enriched our understanding of a number of liquids, including aqueous solutions, organic electrolytes and ionic liquids. We also discuss technical challenges in extending FPMD simulations to the study of liquid electrolytes in more complex environments, including the interface between electrolytes and electrodes, which is a key component in many energy storage and conversion systems.     

Predicting 19F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase–Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor–protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable ¹⁹F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the ¹⁹F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein–inhibitor conformations as well as monomeric and dimeric inhibitor–protein complexes, thus rendering it the largest computational study on chemical shifts of ¹⁹F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.     

Glycosyl‐Substituted Dicarboxylates as Detergents for the Extraction,Overstabilization, and Crystallization of Membrane Proteins

To tackle the problems associated with membrane protein (MP) instability in detergent solutions, we designed a series of glycosyl‐substituted dicarboxylate detergents (DCODs) in which we optimized the polar head to clamp the membrane domain by including, on one side, two carboxyl groups that form salt bridges with basic residues abundant at the membrane–cytoplasm interface of MPs and, on the other side, a sugar to form hydrogen bonds. Upon extraction, the DCODs 8 b , 8 c , and 9 b preserved the ATPase function of BmrA, an ATP‐binding cassette pump, much more efficiently than reference or recently designed detergents. The DCODs 8 a , 8 b , 8 f , 9 a , and 9 b induced thermal shifts of 20 to 29 °C for BmrA and of 13 to 21 °C for the native version of the G‐protein‐coupled adenosine receptor A_2AR. Compounds 8 f and 8 g improved the diffraction resolution of BmrA crystals from 6 to 4 Å. DCODs are therefore considered to be promising and powerful tools for the structural biology of MPs.     

Synthesis and photophysical investigation of squaraine rotaxanes by "clicked capping"

Pseudorotaxane complexes of squaraine dyes and tetralactam macrocycles are converted into permanently interlocked rotaxane structures using copper-catalyzed and copper-free cycloaddition reactions with bulky stopper groups. The photophysical properties of the encapsulated squaraine depend on the structure of the macrocycle. In one case, squaraine rotaxanes are produced in near-quantitative yields and with intense near-IR fluorescence. In another case, squaraine fluorescence is greatly diminished upon macrocyclic encapsulation but the signal can be restored by dye displacement with anions.     

Effect of ionic surfactants on drainage and equilibrium thickness of emulsion films

This paper presents new theoretical and experimental results that quantify the role of surfactant adsorption and the related interfacial tension changes and interfacial forces in the emulsion film drainage and equilibrium. The experimental results were obtained with plane-parallel microscopic films from aqueous sodium dodecyl sulphate solutions formed between two toluene droplets using an improved micro-interferometric technique. The comparison between the theory and the experimental data show that the emulsion film drainage and equilibrium are controlled by the DLVO interfacial forces. The effect of interfacial viscosity and interfacial tension gradient (the Marangoni number) on the film drainage is also significant.