One-sided invertibility of discrete operators with bounded coefficients

Aequationes mathematicae - For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either...     

Separation routine and extended formulations for the stable set problem in claw-free graphs

Mathematical Programming - The maximum weighted stable set problem in claw-free graphs is a well-known generalization of the maximum weighted matching problem, and a classical problem in...     

How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Kaurenoic acid extracted from Sphagneticola trilobata reduces acetaminophen-induced hepatotoxicity through inhibition of oxidative stress and pro-inflammatory cytokine production in mice

Acetaminophen (paracetamol) is a widely used analgesic and antipyretic drug that is safe at therapeutic doses. However, acetaminophen overdose can be fatal. Currently, the only treatment available is the N-acetyl cysteine. The diterpene kaurenoic acid (ent-kaur-16-en-19-oic acid, KA) is the major constituent of Sphagneticola trilobata (L.) Pruski. KA presents anti-inflammatory, anti-nociceptive and antioxidant properties. In this study, we evaluated the efficacy of KA in a model of acetaminophen-induced hepatotoxicity. KA increased, in a dose-dependent manner, the survival rate after acetaminophen overdose. KA reduced acetaminophen-induced hepatic necrosis and ALT and AST levels. KA decreased acetaminophen-induced neutrophil and macrophage recruitment, oxidative stress and the production of IL-33, TNF-α and IL-1β, alongside with normalisation of IL-10 levels in the liver. Therefore, KA showed preclinical efficacy in acetaminophen-induced hepatotoxicity and lethality.     

A semi-analytical solution for electric double layers near an elliptical cylinder

A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.     

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

On Lie symmetries and soliton solutions of $$$$-dimensional Bogoyavlenskii equations

The present article is devoted to find some invariant solutions of the \((2+1)\)-dimensional Bogoyavlenskii equations using similarity transformations method. The system describes \((2+1)\)-dimensional interaction of a Riemann wave propagating along y-axis with a long wave along x-axis. All possible vector fields, commutative relations and symmetry reductions are obtained by using invariance property of Lie group. Meanwhile, the method reduces the number of independent variables by one, which leads to the reduction of Bogoyavlenskii equations into a system of ordinary differential equations. The system so obtained is solved under some parametric restrictions and provides invariant solutions. The derived solutions are much efficient to explain the several physical properties depending upon various existing arbitrary constants and functions. Moreover, some of them are more general than previously established results (Peng and Shen in Pramana 67:449–456, 2006; Malik et al. in Comput Math Appl 64:2850–2859, 2012; Zahran and Khater in Appl Math Model 40:1769–1775, 2016; Zayed and Al-Nowehy in Opt Quant Electron 49(359):1–23, 2017). In order to provide rich physical structures, the solutions are supplemented by numerical simulation, which yield some positons, negatons, kinks, wavefront, multisoliton and asymptotic nature.     

Limit Cycles of Piecewise Smooth Differential Equations on Two Dimensional Torus

In this paper we study the limit cycles of some classes of piecewise smooth vector fields defined in the two dimensional torus. The piecewise smooth vector fields that we consider are composed by linear, Ricatti with constant coefficients and perturbations of these one, which are given in (3). Considering these piecewise smooth vector fields we characterize the global dynamics, studying the upper bound of number of limit cycles, the existence of non-trivial recurrence and a continuum of periodic orbits. We also present a family of piecewise smooth vector fields that posses a finite number of fold points and, for this family we prove that for any 2k number of limit cycles there exists a piecewise smooth vector fields in this family that presents k number of limit cycles and prove that some classes of piecewise smooth vector fields presents a non-trivial recurrence or a continuum of periodic orbits.     

Turbulent Flame Speeds of Premixed Supersonic Flame Kernels

It is unclear whether turbulent flame speed scalings established in low speed regimes are applicable to supersonic flames. To investigate this question, the canonical flame kernel is investigated in a scramjet-like channel having a one degree wall divergence. The growth, shape and internal kernel dynamics are investigated. Results are presented for three Mach numbers, four equivalence ratios, and three turbulence generators. Schlieren photography provides flame images for growth rate statistics and particle image velocimetry (PIV) provides turbulence statistics and investigation of internal kernel dynamics. Supersonic flame kernels are self-propagating and respond to the equivalence ratio in a fashion that is similar to low speed flames. However, supersonic flame kernels have features that are not present in subsonic flame kernels. Baroclinicity, resulting from pressure-density misalignment, creates a reacting vortex ring structure. Further, the mean kernel shape has a Mach number dependence and the vortex ring enhances the turbulent flame speed through entrainment of reactants and augmented flame surface growth. Hence, the previously established (low speed) flame speed scalings are inappropriate for supersonic flame kernels. Drawing motivation from vortex ring literature, the ring propagation velocity is used as the characteristic velocity and a new flame speed scaling is proposed.