Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity

This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives. This paper discusses the construction of Bäcklund transformations for nonlinear partial second-order derivatives of the soliton type with logarithmic nonlinearity and hyperbolic linear parts. The construction of transformations is based on the method proposed by Clairin for second-order equations of the Monge–Ampere type. For the equations studied in the article, using the Bäcklund transformations, new equations are found, which make it possible to find solutions to the original nonlinear equations and reveal the internal connections between various integrable equations.

On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity

We study the existence and multiplicity of positive solutions to the periodic problem u ′′ = p ⁢ ( t ) ⁢ u - q ⁢ ( t , u ) ⁢ u + f ⁢ ( t ) ; u ⁢ ( 0 ) = u ⁢ ( ω ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( ω ) , u^{\prime\prime}=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\quad u^{\prime}(0)=u^{\prime}(\omega), where p , f ∈ L ⁢ ( [ 0 , ω ] ) p,f\in L([0,\omega]) and q : [ 0 , ω ] × R → R q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R} is a Carathéodory function. By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.

Development of a virtual biomechanical manikin used in vibrations studies in occupied spaces

In this paper is developed and applied a virtual biomechanical manikin used in occupied spaces. This multi-nodal numerical model is applied in the vibrations of the different sections of the human body, under transient conditions. The integration of second order equations systems, based in Newton equation, after being converted in a first order equation system, is solved through the Runge-Kutta-Fehlberg method with error control. This multi-nodal numerical model will be used, in this work, in the study of the vibrations that a standing person is subjected when stimuli are applied to the feet. The influence of various types of stimuli is analyzed, with periodic irregularities, in the dynamic response of the vibrations in different sections of the human body. The signals of the stimuli, the displacement of some sections of the body and the power spectrum of the same signals will be presented. In the study the influence of the floor vibration in the human body sections is analyzed and presented.

Carboxin and Diuron Adsorption Mechanism on Sunflower Husks Biochar and Goethite in the Single/Mixed Pesticide Solutions

The study focused on the adsorption mechanism of two selected pesticides: carboxin and diuron, on goethite and biochar, which were treated as potential compounds of mixed adsorbent. The authors also prepared a simple mixture of goethite and biochar and performed adsorption measurements on this material. The adsorbents were characterized by several methods, inter alia, nitrogen adsorption/desorption, Boehm titration, Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy. The adsorption study included kinetics and equilibrium measurements, in the solution containing one or two pesticides simultaneously. The adsorption data were fitted to selected theoretical models (e.g., Langmuir, Freudlich, Redlich–Peterson, pseudo first-order and pseudo second-order equations). Based on the obtained results, it was stated that, among all tested adsorbents, biochar had the highest adsorption capacity relative to both carboxin and diuron. It equaled 0.64 and 0.52 mg/g, respectively. Experimental data were best fitted to the pseudo second-order and Redlich–Peterson models. In the mixed systems, the adsorption levels observed on biochar, goethite and their mixture were higher for diuron and lower for carboxin, compared to those noted in the single solutions. The presented results may enable the development of new mixed adsorbent for remediation of soils polluted with pesticides.

Wang-Ball Polynomials for the Numerical Solution of Singular Ordinary Differential Equations

This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

We investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.