Interval Ostrowski-type methods with guaranteed convergence

In this paper, interval extensions of the classic Ostrowski and its modified method are introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the schemes. The results of proposed methods are compared with the results of the interval Newton method.     

Synthesis of MnAl2O4 nanocrystallites by Pechini and sequential homogenous precipitation methods: characterization, product comparison, photocatalytic effect, and Taguchi optimization

Nanocrystalline manganese aluminate (MnAl₂O₄) has been synthesized by Pechini and sequential homogenous precipitation methods and the results have been compared. The Taguchi L₄ statistical design was utilized to optimize the production of MnAl₂O₄ nanoparticles by Pechini method. The MnAl₂O₄ nanocrystallites obtained by Pechini and sequential homogenous precipitation methods had the average particle size of 26.5 and 49.5 nm, respectively. The products were characterized with X-ray diffraction, laser light scattering, thermogravimetry analysis, Fourier transform infrared, UV–visible, energy dispersive X-ray, scanning electron microscope and inductively coupled plasma analyses. The photocatalytic activities of MnAl₂O₄ nanoparticles synthesized by two methods were investigated using aqueous solution of methylene blue under irradiation of visible light.     

A Universal DNA Aptamer that Recognizes Spike Proteins of Diverse SARS-CoV-2 Variants of Concern

We report on a unique DNA aptamer, denoted MSA52, that displays universally high affinity for the spike proteins of wildtype SARS-CoV-2 as well as the Alpha, Beta, Gamma, Epsilon, Kappa, Delta and Omicron variants. Using an aptamer pool produced from round 13 of selection against the S1 domain of the wildtype spike protein, we carried out one-round SELEX experiments using five different trimeric spike proteins from variants, followed by high-throughput sequencing and sequence alignment analysis of aptamers that formed complexes with all proteins. A previously unidentified aptamer, MSA52, showed K_d values ranging from 2 to 10 nM for all variant spike proteins, and also bound similarly to variants not present in the reselection experiments. This aptamer also recognized pseudotyped lentiviruses (PL) expressing eight different spike proteins of SARS-CoV-2 with K_d values between 20 and 50 pM, and was integrated into a simple colorimetric assay for detection of multiple PL variants. This discovery provides evidence that aptamers can be generated with high affinity to multiple variants of a single protein, including emerging variants, making it well-suited for molecular recognition of rapidly evolving targets such as those found in SARS-CoV-2.     

Comparative investigations on nano and micro titania photocatalysts in degradation and mineralization: Use of turbidity in kinetic studies

An attempt was made to investigate the potential of two widely used commercial nano and micro TiO₂ photocatalysts in degradation and mineralization of a typical azo dye “ect blue 71” in water. A special circulating up-flow reactor with an UV-C-150 W lamp was employed and the influence of the operational parameters was investigated. The results showed that both the photolysis and photocatalysis cause decomposition simultaneously. Despite a half concentration, the nano TiO₂ particles provide a nearly twice efficiency, and for the vital case of mineralization 98% reduction in COD after 120 min irradiation. The influence of turbidity of catalyst particles was determined with a novel method and was taken into account in kinetic studies. It was found that the bulk degradation by the OH radicals has a major role in the photocatalysis process.     

Photo-oxidation of 5-acetyl-3,4-dihydropyrimidin-2(1H)-ones

A variety of Biginelli 5-acetyl-3,4-dihydropyrimidin-2(1H)-ones are efficiently oxidized to their corresponding pyrimidin-2(1H)-one derivatives upon UV irradiation under argon atmosphere in chloroform solution. The nature of the additional substituent on the phenyl ring located on C-4 of the heterocyclic ring influences the rate of reaction. An electron-transfer induced photoreaction is proposed based on the formation of HCl and CH₂Cl₂.     

A Legendre-based computational method for solving a class of Itô stochastic delay differential equations

Numerical Algorithms - This paper provides a numerical method for solving a class of Itô stochastic delay differential equations (SDDEs). The method’s novelty is its use of the spectral...     

Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes

We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.     

On a numerical technique for finding multiple zeros and its dynamic

An optimal method is developed for approximating the multiple zeros of a nonlinear function, when the multiplicity is known. Analysis of convergence for the proposed technique is studied to reveal the fourth-order convergence. We further investigate the dynamics of such multiple zero finders by using basins of attraction and their corresponding fractals in the complex plane. A fourth-order method will also be presented, when the multiplicity m is not known. Numerical comparisons will be made to support the underlying theory of this paper.