On the integro-differential equations with reflection

In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed-point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general-type reflection integro-differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe.     

Synthesis, thermal stability, electronic features, and antimicrobial activity of phenolic azo dyes and their Ni(II) and Cu(II) complexes

Four water soluble azo dyes, 4-(isopropyl)-2-[(E)-(4-chlorophenyl)diazenyl]phenol (L ¹), 4-(isopropyl)-2-[(E)-(2,4-dichlorophenyl)diazenyl]phenol (L²), 4-(sec-butyl)-2-[(E)-(4-chlorophenyl) diazenyl]phenol (L ³), 4-(sec-butyl)-2-[(E)-(2,4-dichlorophenyl)diazenyl]phenol (L ⁴), and their Cu(II) and Ni(II) complexes were synthesized and characterized using spectroscopic methods. Examination of their thermal stability revealed similar decomposition temperature of approximately 260–300°C and that they were more thermally stable than their metal complexes. Ni(II) complexes of ligands L² and L⁴ were more stable than the other coordination compounds. Among the synthesized ligands, L² and the complexes Cu(L³)₂ and Ni(L⁴)₂ showed both antimicrobial and antifungal activity. However, the other ligands and the complexes were poorly active against selected microorganisms.     

Thermal evaluation of cashew nutshell liquid as new bioadditives for poly(methyl methacrylate)

In this study, the thermal-oxidative stability of poly(methyl methacrylate), PMMA, 1 % additivated with replenishable phenolic lipids is evaluated by thermogravimetric (TG/DTG) analyses and differential scanning calorimetry (DSC) analyses. Since technical cashew nutshell liquid (CNSL), a byproduct from the cashew industry, is composed basically of two phenolic lipids, cardanol and cardol, the utilization of this industrial waste and its main components as a new source of bioadditives for use as antioxidants is evaluated. The TG analyses revealed that addition of the phenolic constituent of CNSL increased the thermal stability of PMMA films considerably. The results obtained were also confirmed by DSC analyses.     

On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions

The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that if a sequence of fuzzy numbers is strongly almost λ-convergent with respect to a sequence of Orlicz funtions then it is almost λ-statistical convergent.     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

Michael additions of primary and secondary amines to acrylonitrile catalyzed by lipases

The present Letter details our findings on the lipase-catalyzed Michael reactions between primary or secondary amines and acrylonitrile. Several lipases were evaluated, and good results were obtained leading to the formation of Michael adducts in shorter reaction times than the uncatalyzed reactions.     

On the classical Maki–Thompson rumour model in continuous time

In this paper, the Maki–Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge–Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research.     

Electronic structure and correlations of vitamin B<Subscript>12</Subscript> studied within the Haldane-Anderson impurity model

We study the electronic structure and correlations of vitamin B₁₂ (cyanocobalamine) by using theframework of the multi-orbital single-impurity Haldane-Anderson model of atransition-metal impurity in a semiconductor host. The parameters of the effectiveHaldane-Anderson model are obtained within the Hartree-Fock (HF) approximation. Thequantum Monte Carlo (QMC) technique is then used to calculate the one-electron andmagnetic correlation functions of this effective model. We observe that new states forminside the semiconductor gap found by HF due to the intra-orbital Coulomb interaction atthe impurity 3d orbitals. In particular, the lowest unoccupiedstates correspond to an impurity bound state, which consists of states from mainly the CNaxial ligand and the corrin ring as well as the Co e_g-like orbitals. We alsoobserve that the Co?(3d) orbitals can develop antiferromagneticcorrelations with the surrounding atoms depending on the filling of the impurity boundstates. In addition, we make comparisons of the HF+QMC data with the density functionaltheory calculations. We also discuss the photoabsorption spectrum of cyanocobalamine.