Towards classification of the bifurcation structure of a spherical cavitation bubble

We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of (where R₀ is the bubble initial radius and λ is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of , share remarkable similarities in their bifurcating behavior and can be classified under a unit category.     

On fuzzy linear projection equation and applications

This paper introduces the concept of fuzzy projection of a fuzzy number on a set of fuzzy numbers based on r-cut approach. It is proved that the projection of a fuzzy number on the set of all fuzzy numbers is itself and under a special metric, the proposed fuzzy projection is a non-expansive mapping. By using this definition, the concept of fuzzy linear projection equation is defined and to solve it, a numerical method is applied. Based on the proposed algorithm and as an important application, two different types of system of fuzzy linear equations with fuzzy variables are solved. Numerical results illustrate the applicabilities of proposed approach.     

The C*-algebra of the N-dimensional harmonic oscillator

In this paper we study the Fredholm thoery of a C*-algebraOl of o-order pseudo-differential operators on L²(ⁿ). IfK denotes the ideal of all compact operators of L², the algebraOl will be generated by (i) the idealK, (ii) a function algebra CS(ⁿ) and (iii) by the bounded operators x_j, D_j, j=1,...,n, = H^–1/2, H=1+¦x¦²–. We show thatOl/K is a commutative C*-algebra with identity and obtain its Gelfany space M. This provides Fredholm criterion and index formula for a graded algebra of partial differential operators including all oeprators with polynomial coefficients. We also give Fredholm criterion and index formula for systems of such operators.     

A novel chemically modified carbon paste electrode based on a new mercury(II) complex for selective potentiometric determination of bromide ion

A new modified carbon paste electrode based on a recently synthesized mercury (II) complex of a pyridine containing proton transfer compound as a suitable carrier for Br⁻ ion is described. The electrode has a linear dynamic range between 3.00×10⁻² and 1.0×10⁻⁵ M with a near-Nernastian slope of 61.0±0.9 mV per decade and a detection limit of 4.0×10⁻⁶ M (0.32 ppm). The potentiometric response is independent of the pH of the solution in the pH range 4.0–8.3. The electrode possesses the advantages of low resistance, fast response and good over a variety of other anions. It was applied as an indicator electrode in potentiometric titration of bromide ions and for the recovery of Br⁻ from tap water.     

Preparation of Zinc (II) and cadmium (II) complexes of the tetradentate Schiff base ligand 2-((E)-(2-(2-(pyridine-2-yl)- ethylthio)ethylimino)methyl)-4-bromophenol (PytBrsalH)

We describe the synthesis and characterization of two new zinc (II) and cadmium (II) complexes of the tetradentate dissymmetric Schiff base ligand 2-((E)-(2-(2-(pyridine-2-yl)ethylthio)ethylimino)methyl)-4-bromophenol (PytBrsalH), prepared from 1-(2-pyridyl)-3-thia-5-aminopentane (pyta) and 5-bromosalicylaldehyde. The complexes were synthesized by treating an ethanolic solution of the ligand with equimolar amounts of appropriate metal salts in 1 M methanolic solution of NaOH or alternatively, by a more direct route in which the two reactants are added to a solution of the ligand immediately after formation of the latter and prior to any isolation. The complexes were characterized by elemental analysis, FTIR, (1)H-NMR, electronic spectra and molar conductivity. According to obtained data, the probable coordination geometries of zinc and cadmium in these complexes with mixed N, S and O donor atoms are tetrahedral- and octahedral-like,respectively. Both complexes were found to be 1:1 electrolyte systems in acetonitrile.     

Fischer–Tropsch synthesis over CNT-supported cobalt catalyst: effect of magnetic field

In the present work, the cobalt catalysts supported on carbon nanotubes (CNTs) were prepared by impregnation method in the presence and absence of magnetic field. The prepared catalysts were employed to yield higher hydrocarbons via Fischer–Tropsch synthesis. It is explored that using magnetized water can effectively change the catalyst geometry in impregnation catalyst preparation method. For the preparation of different sizes of cobalt particles on the CNTs support, the physical properties of solvent (water) in impregnation process were changed using the magnetizing process. The results showed that the average particle sizes of impregnated cobalt nanoparticles were decreased by using magnetized water in impregnation step. In addition, in the magnetized treated cobalt catalyst, the cobalt particles mostly dispersed outside the tubes because the capillary forces decreased by reducing water surface tension. Furthermore, the experimental results showed that the probability of chain growth (α) and selectivity to heavier hydrocarbons increased in magnetized water treatment catalysts.     

Optimal Control Formulation for Complementarity Dynamical Systems

In this paper, we show that the complementarity dynamical systems can be reformulated as optimal control problems. By using this reformulation, we present a pseudospectral scheme to discretize the complementarity dynamical systems. Applying this discretization, the complementarity dynamical system is reduced to a sequence of nonlinear programming problems. Numerical examples and comparison with two other methods are included to demonstrate the capability of the proposed method.     

Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model

In this paper, a bidirectional associative memory (BAM) neural network model, which consists of two neurons in the X-layer and three neurons in the Y-layer, with two time delays, will be considered. By analyzing the associated characteristic equation, we obtain that Hopf bifurcation occurs and a family of periodic solutions appears. Moreover, the stability and the period of the bifurcating periodic solutions are studied. To illustrate our theoretical results, numerical simulations are presented.     

Isolation and In Silico Prediction of Potential Drug-like Compounds with a New Dimeric Prenylated Quinolone Alkaloid from Zanthoxylum rhetsa (Roxb.) Root Extracts Targeted against SARS-CoV-2 (Mpro)

A new dimeric prenylated quinolone alkaloid, named 2,11-didemethoxy-vepridimerine A, was isolated from the root bark of Zanthoxylum rhetsa, together with twelve known compounds. The structure of the new compound was elucidated on the basis of spectroscopic investigations (NMR and Mass). The interaction of the isolated compounds with the main protease of SARS-CoV-2 (Mpro) was evaluated using molecular docking followed by MD simulations. The result suggests that 2,11-didemethoxy-vepridimerine A, the new compound, has the highest negative binding affinity against the Mpro with a free energy of binding of −8.5 Kcal/mol, indicating interaction with the Mpro. This interaction was further validated by 100 ns MD simulation. This implies that the isolated new compound, which can be employed as a lead compound for an Mpro-targeting drug discovery program, may be able to block the action of Mpro.