On the Numerical Range of Operator Polynomials

An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.     

The solvent extraction of iron from steel solutions with 2-hexylpyridine prior to the determination of trace elements

The distribution of iron(III) between aqueous hydrochloric acid and 0.1M 2-hexylpyridine in benzene was examined as a function of acid concentration in the aqueous solution, the metal concentration being kept constant, and as a function of increasing ferric chloride concentration at a constant acidity of hydrochloric acid. The distribution coefficient of Fe(III) (tracer) is dependent on the square of the 2-hexylpyridine concentration in the benzene phase. Negatively charged complexes of the type FeCl(2-)(5) may be the species extracted. The formation of a mixture of 1:1 and 1:2 complexes with 2-hexylpyridine is indicated. Salting-out effects of a number of salts have been investigated. Separation factors of several metal ions relative to iron(III) in 7M hydrochloric acid are also reported. The results indicate that iron(III) can be selectively separated from a large number of elements, and the method has been utilized for the preconcentration of non-ferrous metal ions in mild steels by selective separation of iron, before their subsequent determination by emission spectrometry.     

Pharmacological Properties of 4′, 5, 7-Trihydroxyflavone (Apigenin) and Its Impact on Cell Signaling Pathways

Plant bioactive compounds, particularly apigenin, have therapeutic potential and functional activities that aid in the prevention of infectious diseases in many mammalian bodies and promote tumor growth inhibition. Apigenin is a flavonoid with low toxicities and numerous bioactive properties due to which it has been considered as a traditional medicine for decades. Apigenin shows synergistic effects in combined treatment with sorafenib in the HepG2 human cell line (HCC) in less time and statistically reduces the viability of tumor cells, migration, gene expression and apoptosis. The combination of anti-cancerous drugs with apigenin has shown health promoting potential against various cancers. It can prevent cell mobility, maintain the cell cycle and stimulate the immune system. Apigenin also suppresses mTOR activity and raises the UVB-induced phagocytosis and reduces the cancerous cell proliferation and growth. It also has a high safety threshold, and active (anti-cancer) doses can be gained by consuming a vegetable and apigenin rich diet. Apigenin also boosted autophagosome formation, decreased cell proliferation and activated autophagy by preventing the activity of the PI3K pathway, specifically in HepG2 cells. This paper provides an updated overview of apigenin’s beneficial anti-inflammatory, antibacterial, antiviral, and anticancer effects, making it a step in the right direction for therapeutics. This study also critically analyzed the effect of apigenin on cancer cell signaling pathways including the PI3K/AKT/MTOR, JAK/STAT, NF-κB and ERK/MAPK pathways.     

A novel method for non-destructive Compton scatter imaging based on the genetic algorithm

Compton scattering tomography is widely used in numerous applications such as biomedical imaging, nondestructive industrial testing and environmental survey, etc. This paper proposes the use of the genetic algorithm (GA), which utilizes bio-inspired mathematical models, to construct an image of the insides of a test object via the scattered photons, from a voxel within the object. A NaI(Tl) scintillation detector and a 185 MBq ¹³⁷Cs gamma ray source were used in the experimental measurements. The obtained results show that the proposed GA based method performs well in constructing images of objects.     

Spectrophotometric Studies of Entrapped Thymol Phtalein pH Indicator into Sol‐Gel Matrix

This research involves the behavior of thymol phtalein pH indicator entrapped into the sol‐gel derived inorganic matrix. The method is based on the physical entrapment of the reagent molecules in the sol‐gel matrix. The immobilized thymol phthalein pH indicator shows behavior similar to its solution counterpart. The UV/vis spectra indicate that the thymol phthalein retains its structure during the sol‐gel reactions in terms of response to pH. Thymol phthalein can be regarded as uniformly distributed in the sol‐gel matrix. This observation has been confirmed using polarized microscopy. This research shows that thymol phtalein can be immobilized in sol‐gel glasses and used as a solid pH sensor.     

1, 3-dipolar cycloaddition of C-phenyl carbamoyl-N-phenyl nitrone with some dialkyl-substituted 2-benzylidenecyclopropane-1,1-dicarboxylates: theoretical analysis of mechanism and regioselectivity

The regiochemistry of 1,3-dipolar cycloaddition reactions of C-phenyl carbamoyl-N-phenyl nitrone with some dialkyl-substituted 2-benzylidenecyclopropane-1,1-dicarboxylates as dipolarophile was investigated using density functional theory-based reactivity indexes and activation energy calculations at B3LYP/6-31G(d) level of theory. Analysis of the geometries and bond orders at the TS structures associated with the different reaction pathways shows that these 1,3-dipolar cycloaddition reactions occur via an asynchronous concerted mechanism. Analysis of the local electrophilicity and nucleophilicity indexes based on Parr functions only for reaction between 1 + 2a and based on Fukui functions only for 1 + 2b gives correct regioselectivity. The theoretical results obtained in the work clearly predict the regiochemistry of the isolated cycloadducts and agree to experimental results.     

The structure and thermodynamics of binary microclusters: A Monte Carlo simulation

The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microcluster's atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar₁₃, Ar₇Kr₆, Ar₃₆Kr₁₉ and Ar₁₉Kr₃₆, as well as to crudely model the bimetallic clusters of Cu₁₉Ni₃₆, Cu₁₉Ru₃₆ and Cu₁₉Os₃₆. A large variety of interesting features associated with these systems are described.     

Plastics as nuclear track detectors for thermal neutron dosimetry

An attempt is made to determine the response of CR-39 and cellulose nitrate plastic track detectors subjected to thermal neutrons. The α-particles are produced from (n, α) reactions in lithium tetraborate convertor placed in contact with different plastics and are recorded in the detectors. The corrected track density gives a fluence sensitivity and dose sensitivity of the order of 10^?4 tracks per neutron and 10² tracks/cm² mrem respectively. A linear relationship is observed between track density and neutron fluence.     

Green ultrasound-assisted extraction of carotenoids based on the bio-refinery concept using sunflower oil as an alternative solvent

A green, inexpensive and easy-to-use method for carotenoids extraction from fresh carrots assisted by ultrasound was designed in this work. Sunflower oil was applied as a substitute to organic solvents in this green ultrasound-assisted extraction (UAE): a process which is in line with green extraction and bio-refinery concepts. The processing procedure of this original UAE was first compared with conventional solvent extraction (CSE) using hexane as solvent. Moreover, the UAE optimal conditions for the subsequent comparison were optimized using response surface methodology (RSM) and ultra performance liquid chromatography – diode array detector – mass spectroscopy (UPLC–DAD–MS). The results showed that the UAE using sunflower as solvent has obtained its highest β-carotene yield (334.75 mg/l) in 20 min only, while CSE using hexane as solvent obtained a similar yield (321.35 mg/l) in 60 min. The green UAE performed under optimal extraction conditions (carrot to oil ratio of 2:10, ultrasonic intensity of 22.5 W cm^?2, temperature of 40 °C and sonication time of 20 min) gave the best yield of β-carotene.