Multiple existence results of solutions for quasilinear elliptic equations with a nonlinearity depending on a parameter

We provide existence results of multiple solutions for quasilinear elliptic equations depending on a parameter under the Neumann and Dirichlet boundary condition. Our main result shows the existence of two opposite constant sign solutions and a sign changing solution in the case where we do not impose the subcritical growth condition to the nonlinear term not including derivatives of the solution. The studied equations contain the \(p\) -Laplacian problems as a special case. Our approach is based on variational methods combining super- and sub-solution and the existence of critical points via descending flow.     

Thermal stability of piroxicam

The application of thermal method is of great importance regarding the pharmaceutical problems such as the control of raw materials, the determination of purity, the qualitative and quantitative analysis of drug formulation, tests of thermal stability and compatibility and the determination of kinetic parameters etc. The purpose of a kinetic investigation is to calculate the kinetic parameters and the determination of the kinetic model for the studied process. The results are further used to predict the system’s behaviour in various circumstances. A kinetic study regarding the piroxicam—active substance’s thermal decomposition was performed under isothermal conditions and nitrogen atmosphere, for the temperature steps: 200, 205, 210, 215 and 220 °C. The TG/DTG data were processed by three differential methods: isothermal—isoconversional, Friedman’s isothermal isoconversional and isothermal model-fitting. The obtained results are in good accord between them, as well as with those obtained under non-isothermal conditions from a previous work and confirm the necessity of the kinetic parameters determining in different thermal conditions, by the adequate calculation methods.     

Mixing Multilinear Operators with or Without a Linear Analogue

As a natural extension of mixing linear operators we introduce new notions of mixing multilinear operators with or without a linear analogue. We prove Pietsch’s composition theorems in this new context extending recent results from the case of dominated operators.     

Corrigendum to “Convexity and concavity constants in Lorentz and Marcinkiewicz spaces” [J. Math. Anal. Appl. 343 (2008) 337-351]

In this note we state the accurate formulas of convexity and concavity constants in Lorentz spaces, correcting the formulas from Kamińska and Parrish (2008) [2].     

Fractional Nambu Mechanics

The fractional generalization of Nambu mechanics is constructed by using the differential forms and exterior derivatives of fractional orders. The generalized Pfaffian equations are obtained and one example is investigated in details. On leave of absence from Institute of Space Sciences, P.O. Box, MG-23, 76900, Magurele-Bucharest, Romania.     

Morphology,structure, and photoactivity of two types of graphene oxide-TiO<Subscript>2</Subscript> composites

Two types of graphene oxide-TiO₂ composites were prepared: one by including graphene oxide flakes in the TiO₂ sol, followed by thermal treatment (GI composite) at 300°C, and the second by including graphene oxide flakes in the calcined (at 500°C) TiO₂ xerogel (GII composite). The composites were characterized by SEM, TEM-EDS, TEM-SADP, STEM-HAADF, HRTEM coupled with FT, XRD, and XPS. Photocatalysis results were fitted to different kinetic models (pseudo-first and pseudo-second kinetics, intraparticle Weber-Morris diffusion, film diffusion, and external mass transfer). The results showed that by introducing graphene oxide flakes in the TiO₂ sol, followed by thermal treatment at 300°C (GI composite), an efficient graphene oxide-TiO₂ catalyst with high specific surface area, heterogeneity, and many graphitized areas can be obtained. Complete crystallization of the composite is not the key issue for the best photoactivity achievement. The rate limiting step in the photocatalytic process is the photooxidation of SA molecules on the TiO₂ surface.     

Synthesis,characterization of nanosized CoAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and its electrocatalytic activity for enhanced sensing application

Nanosized cobalt aluminate (CoAl₂O₄) was prepared by thermolysis of heteronuclear coordination compound, namely [Al₂Co(C₂O₄)₄(OH₂)₆]. The synthesized precursor was characterized by chemical analysis, vibrational spectra and thermal analysis. The cobalt aluminate obtained after a heating treatment of the precursor at 700 °C was characterized by IR, XRD, TEM coupled with SAED measurements. Two types of carbon-based electrodes, glassy carbon and boron-doped diamond electrodes were decorated with the obtained cobalt aluminate in order to enhance the electroanalytical performance for the tetracycline (TC) detection in the aqueous solutions. Cyclic voltammetry technique was used to determine the effect of the nanosized CoAl₂O₄ on the electrochemical oxidation of TC and as consequence, for TC detection at both carbon-based electrodes. The obtained cobalt aluminate exhibited the electrocatalytic activity toward TC detection in direct relation with the type of the carbon substrate, which allowed enhancing the electroanalytical parameters of TC detection in the aqueous solution.