Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

     

Luminescence kinetic and association equilibria of lanthanide ions in aqueous solutions. II. Determination of the formation constant of Tb acetato complex by means of luminescence lifetime measurement

The association constant K of mono-acetato complex of Tb³⁺ has been determined at normal p and T conditions by measurement of its luminescence lifetime in aqueous solution containing increasing concentrations of acetate. Two experimental arrangements used for the measurement are described.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

Trennung von Spurenelementaktivitäten aus Neutronenbestrahltem Selen mit Hilfe der Gegenstrom-Ionenwanderung

For the determination of trace elements in neutron irradiated, selenium by gamma-ray spectrometry the separation of the matrix activity is often necessary. In model experiments the decontamination of cation and anion impurities from the matrix solution was investigated by the counter current ion migration. After a processing of 3 hrs the trace activities of Co, Cr, Ga, Na and Zn were decontaminated from Se with a factor of >10³. For the trace elements As and Te representing the anionic constituents, a decontamination factor of 3·10² was obtained.     

Association of hydrofluoric acid in NaCl aqueous media under hydrothermal conditions

The apparent association constant of hydrofluoric acid Q _HF ^' in 1m NaCl aqueous media has been determined potentiometrically at pressures up to 1 kbar and temperatures up to 250°C. A concentration cell employing hydrogen electrodes was used. The association of HF increases with increasing temperature but decreases with increasing pressure.     

On Some Topological Indices Defined via the Modified Sombor Matrix

Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)−1/2 over all of the edges vivj of G. The modified Sombor matrix AMS(G) of G is the n by n matrix such that its (i,j)-entry is equal to (dvi2+dvj2)−1/2 when vi and vj are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of AMS(G). The sum of the absolute eigenvalues of AMS(G) is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is 2; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.     

Improved Mucoadhesion,Permeation and In Vitro Anticancer Potential of Synthesized Thiolated Acacia and Karaya Gum Combination: A Systematic Study

Thiolation of polymers is one of the most appropriate approaches to impart higher mechanical strength and mucoadhesion. Thiol modification of gum karaya and gum acacia was carried out by esterification with 80% thioglycolic acid. FTIR, DSC and XRD confirmed the completion of thiolation reaction. Anticancer potential of developed thiomer was studied on cervical cancer cell lines (HeLa) and more than 60% of human cervical cell lines (HeLa) were inhibited at concentration of 5 µg/100 µL. Immobilized thiol groups were found to be 0.8511 mmol/g as determined by Ellman’s method. Cytotoxicity studies on L929 fibroblast cell lines indicated thiomers were biocompatible. Bilayered tablets were prepared using Ivabradine hydrochloride as the model drug and synthesized thiolated gums as mucoadhesive polymer. Tablets prepared using thiolated polymers in combination showed more swelling, mucoadhesion and residence time as compared to unmodified gums. Thiol modification controlled the release of the drug for 24 h and enhanced permeation of the drug up to 3 fold through porcine buccal mucosa as compared to tablets with unmodified gums. Thiolated polymer showed increased mucoadhesion and permeation, anticancer potential, controlled release and thus can be utilized as a novel excipient in formulation development.     

Virtual Screening of Artemisia annua Phytochemicals as Potential Inhibitors of SARS-CoV-2 Main Protease Enzyme

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a human coronaviruses that emerged in China at Wuhan city, Hubei province during December 2019. Subsequently, SARS-CoV-2 has spread worldwide and caused millions of deaths around the globe. Several compounds and vaccines have been proposed to tackle this crisis. Novel recommended in silico approaches have been commonly used to screen for specific SARS-CoV-2 inhibitors of different types. Herein, the phytochemicals of Pakistani medicinal plants (especially Artemisia annua) were virtually screened to identify potential inhibitors of the SARS-CoV-2 main protease enzyme. The X-ray crystal structure of the main protease of SARS-CoV-2 with an N3 inhibitor was obtained from the protein data bank while A. annua phytochemicals were retrieved from different drug databases. The docking technique was carried out to assess the binding efficacy of the retrieved phytochemicals; the docking results revealed that several phytochemicals have potential to inhibit the SARS-CoV-2 main protease enzyme. Among the total docked compounds, the top-10 docked complexes were considered for further study and evaluated for their physiochemical and pharmacokinetic properties. The top-3 docked complexes with the best binding energies were as follows: the top-1 docked complex with a −7 kcal/mol binding energy score, the top-2 docked complex with a −6.9 kcal/mol binding energy score, and the top-3 docked complex with a −6.8 kcal/mol binding energy score. These complexes were subjected to a molecular dynamic simulation analysis for further validation to check the dynamic behavior of the selected top-complexes. During the whole simulation time, no major changes were observed in the docked complexes, which indicated complex stability. Additionally, the free binding energies for the selected docked complexes were also estimated via the MM-GB/PBSA approach, and the results revealed that the total delta energies of MMGBSA were −24.23 kcal/mol, −26.38 kcal/mol, and −25 kcal/mol for top-1, top-2, and top-3, respectively. MMPBSA calculated the delta total energy as −17.23 kcal/mol (top-1 complex), −24.75 kcal/mol (top-2 complex), and −24.86 kcal/mol (top-3 complex). This study explored in silico screened phytochemicals against the main protease of the SARS-CoV-2 virus; however, the findings require an experimentally based study to further validate the obtained results.     

Microwave Irradiation and Glutamic Acid-Assisted Phytotreatment of Tannery and Surgical Industrial Wastewater by Sorghum

We investigated how different doses of microwave irradiation (MR) affect seed germination in Sorghum, including the level of remediation against textile and surgical wastewater (WW) by modulating biochemical and morpho-physiological mechanisms under glutamic acid (GA) application. The experiment was conducted to determine the impact of foliar-applied GA on Sorghum under wastewater conditions. Plants were treated with or without microwave irradiation (30 s, 2.45 GHz), GA (5 and 10 mM), and wastewater (0, 25, 50, and 100). Growth and photosynthetic pigments were significantly decreased in plants only treated with various concentrations of WW. GA significantly improved the plant growth characteristics both in MR-treated and -untreated plants compared with respective controls. HMs stress increased electrolyte leakage (EL), hydrogen peroxide (H₂O₂), and malondialdehyde (MDA) content; however, the GA chelation significantly improved the antioxidant enzymes activities such as ascorbate oxidase (APX), superoxide dismutase (SOD), peroxidase (POD), and catalase (CAT) both in MR-treated and -untreated plants under WW stress compared with respective controls. The results suggested that the MR-treated plants accumulate higher levels of HMs under GA addition in comparison to the WW-only-treated and MR-untreated plants. The maximum increase in Cd accumulation was observed in the range of 14–629% in the roots, 15–2964% in the stems, and 26–4020% in the leaves; the accumulation of Cu was 18–2757% in the roots, 15–4506% in the stems, and 23–4605% in the leaves; and the accumulation of Pb was 13–4122% in the roots, 21–3588% in the stems, and 21–4990% in the leaves under 10 mM GA and MR-treated plants. These findings confirmed that MR-treated sorghum plants had a higher capacity for HMs uptake under GA and could be used as a potential candidate for wastewater treatment.     

How the Physicochemical Properties of the Bulk Material Affect the Ablation Crater Profile,Mass Balance,and Bubble Dynamics During Single-Pulse,Nanosecond Laser Ablation in Water

Understanding the key steps that drive the laser-based synthesis of colloids is a prerequisite for learning how to optimize the ablation process in terms of nanoparticle output and functional design of the nanomaterials. Even though many studies focus on cavitation bubble formation using single-pulse ablation conditions, the ablation efficiency and nanoparticle properties are typically investigated under prolonged ablation conditions with repetition rate lasers. Linking single-pulse and multiple-pulse ablation is difficult due to limitations induced by gas formation cross-effects, which occur on longer timescales and depend on the target materials’ oxidation-sensitivity. Therefore, this study investigates the ablation and cavitation bubble dynamics under nanosecond, single laser pulse conditions for six different bulk materials (Au, Ag, Cu, Fe, Ti, and Al). Also, the effective threshold fluences, ablation volumes, and penetration depths are quantified for these materials. The thermal and chemical properties of the corresponding bulk materials not only favor the formation of larger spot sizes but also lead to the highest molar ablation efficiencies for low melting materials such as aluminum. Furthermore, the concept of the cavitation bubble growth linked with the oxidation sensitivity of the ablated material is discussed. With this, evidence is provided that intensive chemical reactions occurring during the very early timescale of ablation are significantly enhanced by the bubble collapse.