Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Type S Non-Ribosomal Peptide Synthetases for the Rapid Generation of Tailormade Peptide Libraries**

Bacterial natural products in general, and non-ribosomally synthesized peptides in particular, are structurally diverse and provide us with a broad range of pharmaceutically relevant bioactivities. Yet, traditional natural product research suffers from rediscovering the same scaffolds and has been stigmatized as inefficient, time-, labour- and cost-intensive. Combinatorial chemistry, on the other hand, can produce new molecules in greater numbers, cheaper and in less time than traditional natural product discovery, but also fails to meet current medical needs due to the limited biologically relevant chemical space that can be addressed. Consequently, methods for the high throughput generation of new natural products would offer a new approach to identifying novel bioactive chemical entities for the hit to lead phase of drug discovery programs. As a follow-up to our previously published proof-of-principle study on generating bipartite type S non-ribosomal peptide synthetases (NRPSs), we now envisaged the de novo generation of non-ribosomal peptides (NRPs) on an unreached scale. Using synthetic zippers, we split NRPSs in up to three subunits and rapidly generated different bi- and tripartite NRPS libraries to produce 49 peptides, peptide derivatives, and de novo peptides at good titres up to 145 mg L⁻¹. A further advantage of type S NRPSs not only is the possibility to easily expand the created libraries by re-using previously created type S NRPS, but that functions of individual domains as well as domain-domain interactions can be studied and assigned rapidly.     

An Improved Model for Polyether Production from 1,3‐Propanediol

A dynamic mathematical model is developed for production of Cerenol polyether from 1,3‐propanediol in a batch reactor system. The model accounts for polycondensation reactions and side reactions in the liquid phase and for mass transfer of volatile species to the vapor. Parameters are estimated using measured liquid‐phase concentrations of monomer, oligomers, water, and end groups as well as the mass and composition of condensate collected from the overhead condenser system. The proposed model uses novel probability factors to keep the model equations relatively simple while accounting for the complex influence of superacid catalyst on reaction rates. The model is a significant advance over previous Cerenol models because it better accounts for mass‐transfer rates and for the dynamic behavior of the condenser. In addition, the proposed model accounts for the inhibitory influence of water on polycondensation kinetics due to hydration of hydroxyl ends. The model equations and parameter estimates provide a substantial improvement in fit to the data, especially for long reaction times and high catalyst levels, resulting in a 97% reduction in the value of the weighted least squared objective function compared to equations and parameters from a previous model.     

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.     

The electronic properties and electron transport of sawtooth penta-graphene nanoribbon under uniaxial strain: ab-initio study

ABSTRACT

The electronic properties and electron transport of a sawtooth penta-graphene nanoribbon (SSPGNR) under uniaxial strains are theoretically studied by density-functional theory (DFT) in combination with the non-equilibrium Green's function formalism. We investigated the electronic structures and the current–voltage (I–V) characteristics of the SSPGNRs under a sequence of uniaxial strains in range from 10% compression to 10% stretch. In this strained range, carbon atoms still keep a pentagon network, but with the changing bond lengths. The C–C bond lengths change almost linearly with the tolerable strain. The value of the band gap of SSPGNRs can be depicted as a parabola under uniaxial strain. Our calculations show that the current is monotonous increase with compressive strain at the same applied bias voltage. In case of tensile strain, the variable rule of the current is different that it increases at first and decrease later. The fundamental physical properties (band structure, I–V characteristic) of SSPGNRs seem to be more sensitive to compressive strain than the stretch strain. The current intensity of the compressive-SSPGNR is by 2 orders of magnitude compared to that of the tensile-SSPGNR at the same strain in range from 6% to 10%. The results obtained from our calculations are beneficial to practical applications of these strained structures in SSPGNRs-based electromechanical devices.     

General one-loop formulas for $$H\rightarrow f\bar{f}\gamma $$ H → f f ¯ γ and its applications

The European Physical Journal C - Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible...     

Mechanically Activated Solid-State Radical Polymerization and Cross-Linking via Piezocatalysis

Piezocatalysis offers a means to transduce mechanical energy into chemical potential, harnessing physical force to drive redox reactions. Working in the solid state, we show here that piezoelectric BaTiO₃ nanoparticles can transduce mechanical load into a flux of reactive radical species capable of initiating solid state free radical polymerization. Activation of a BaTiO₃ powder by ball milling, striking with a hammer, or repeated compressive loading generates highly reactive hydroxyl radicals (⋅OH), which readily initiate radical chain growth and crosslinking of solid acrylamide, acrylate, methacrylate and styrenic monomers. Control experiments indicate a critical role for chemisorbed water on the BaTiO₃ nanoparticle surface, which is oxidized to ⋅OH via mechanoredox catalysis. The force-induced production of radicals by compressing dry piezoelectric materials represents a promising new route to harness mechanical energy for solid state radical synthesis.     

Straightforward access to new vinca-alkaloids via selective reduction of a nitrile containing anhydrovinblastine derivative

A procedure to exclusively obtain 3′S-cyanoanhydrovinblastine 12 from two naturally occurring vinca-alkaloids (catharanthine and vindoline) in one step with good yield is described. Stereoselective reductions of 12, providing straightforward access to three new vinca-alkaloids, including two diastereomers 3′S-cyano-(4′R,5′-dihydro)-anhydrovinblastine and 3′S-cyano-(4′S,5′-dihydro)-anhydrovinblastine as well as (3′S-aminomethyl)-(4′S,5′-dihydro)-anhydrovinblastine in good yields is also reported.