An interval branch and bound method for global Robust optimization

In this paper, we design a Branch and Bound algorithm based on interval arithmetic to address nonconvex robust optimization problems. This algorithm provides the exact global solution of such difficult problems arising in many real life applications. A code was developed in MatLab and was used to solve some robust nonconvex problems with few variables. This first numerical study shows the interest of this approach providing the global solution of such difficult robust nonconvex optimization problems.

     

k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

Analysis Mathematica - We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we...     

An effective method for the reduction of the device utilization amount in experimental realization of a fractional-order system

This study focuses on the experimental realization of the fractional-order FitzHugh–Nagumo (FHN) neuron model. Firstly, a second-order approximation function is included to the FHN neuron model to satisfy the fractional-order definition. Since these approximation functions can meet the response of the ideal system only in a limited frequency band, the identification of their center frequency is very critical. Thus, the center frequency ‘ω_c’ of this second-order approximation functions is swept until getting the spiking responses of this neuron model for the first time in this study. After the center frequency is determined, this approximation function is transferred into the ‘z’ domain by employing the Tustin discretization operator. This achieved discrete defined and fractional-order FHN neuron model becomes suitable for implementation on the digital platforms. To verify the proficiency of the proposed sweeping process experimentally, the fractional-order FHN model in ‘z’ domain is implemented on the FPGA platform. After these applications, the order of the approximation function is reduced to one. Once this followed frequency sweeping process is repeated for the first-order approximation, the fractional-order FHN neuron model, which is built by this least-order approximation function, is also implemented with the FPGA. Therefore, the reductions of the device utilization amounts by using this least-order approximation function and the importance of the specific frequency identification process are seen clearly.

     

Enhancing hydrogen evolution of MoS2 basal planes by combining single-boron catalyst and compressive strain

MoS₂ is a promising candidate for hydrogen evolution reaction (HER), while its active sites are mainly distributed on the edge sites rather than the basal plane sites. Herein, a strategy to overcome the inertness of the MoS₂ basal surface and achieve high HER activity by combining single-boron catalyst and compressive strain was reported through density functional theory (DFT) computations. The ab initio molecular dynamics (AIMD) simulation on B@MoS₂ suggests high thermodynamic and kinetic stability. We found that the rather strong adsorption of hydrogen by B@MoS₂ can be alleviated by stress engineering. The optimal stress of −7% can achieve a nearly zero value of ΔG_H (~ −0.084 eV), which is close to that of the ideal Pt–SACs for HER. The novel HER activity is attributed to (i) the B– doping brings the active site to the basal plane of MoS₂ and reduces the band-gap, thereby increasing the conductivity; (ii) the compressive stress regulates the number of charge transfer between (H)–(B)–(MoS₂), weakening the adsorption energy of hydrogen on B@MoS₂. Moreover, we constructed a SiN/B@MoS₂ heterojunction, which introduces an 8.6% compressive stress for B@MoS₂ and yields an ideal ΔGH. This work provides an effective means to achieve high intrinsic HER activity for MoS₂.     

Hydroxylation of Aromatics by H2O2 Catalyzed by Mononuclear Non-heme Iron Complexes: Role of Triazole Hemilability in Substrate-Induced Bifurcation of the H2O2 Activation Mechanism

Rieske dioxygenases are metalloenzymes capable of achieving cis-dihydroxylation of aromatics under mild conditions using O₂ and a source of electrons. The intermediate responsible for this reactivity is proposed to be a cis-Fe^V(O)(OH) moiety. Molecular models allow the generation of a Fe^III(OOH) species with H₂O₂, to yield a Fe^V(O)(OH) species with tetradentate ligands, or {Fe^IV(O); OH^.} pairs with pentadentate ones. We have designed a new pentadentate ligand, mtL₄², bearing a labile triazole, to generate an “in-between” situation. Two iron complexes, [(mtL₄²)FeCl](PF₆) and [(mtL₄²)Fe(OTf)₂]), were obtained and their reactivity towards aromatic substrates was studied in the presence of H₂O₂. Spectroscopic and kinetic studies reflect that triazole is bound at the Fe^II state, but decoordinates in the Fe^III(OOH). The resulting [(mtL₄²)Fe^III(OOH)(MeCN)]²⁺ then lies on a bifurcated decay pathway (end-on homolytic vs. side-on heterolytic) depending on the addition of aromatic substrate: in the absence of substrate, it is proposed to follow a side-on pathway leading to a putative (N₄)Fe^V(O)(OH), while in the presence of aromatics it switches to an end-on homolytic pathway yielding a {(N₅)Fe^IV(O); OH^.} reactive species, through recoordination of triazole. This switch significantly impacts the reaction regioselectivity.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Theoretical Study of Endohedral Fullerenes M@C60 (M = Li,Na, or K) in Periodic Boundary Conditions

Journal of Experimental and Theoretical Physics - Density functional calculations in periodic boundary conditions (PBCs) were performed to investigate the structural and electronic properties of...     

Naphthalimide‐phthalimide derivative based photoinitiating systems for polymerization reactions under blue lights

Naphthalimide‐phthalimide derivatives (NDPDs) have been synthesized and combined with an iodonium salt, N‐vinylcarbazole, amine or 2,4,6‐tris(trichloromethyl)‐1,3,5‐triazine to produce reactive species (i.e., radicals and cations). These generated reactive species are capable of initiating the cationic polymerization of epoxides and/or the radical polymerization of acrylates upon exposure to very soft polychromatic visible lights or blue lights. Compared with the well‐known camphorquinone based systems used as references, the novel NDPD based combinations employed here demonstrate clearly higher efficiencies for the cationic polymerization of epoxides under air as well as the radical polymerization of acrylates. Remarkably, one of the NDPDs (i.e., NDPD2) based systems is characterized by an outstanding reactivity. The structure/reactivity/efficiency relationships of the investigated NDPDs were studied by fluorescence, cyclic voltammetry, laser flash photolysis, electron spin resonance spin trapping, and steady state photolysis techniques. The key parameters for their reactivity are provided. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 665–674