Search results for "Solutions"

Comparative study of pH for different saline and multi-purpose contact lens solutions.

1997

In this study, we determined the pH of different saline and multipurpose contact lens solutions available on the Spanish market. We examined 10 samples of 14 solutions, seven of which are saline solutions and seven multipurpose ones, from different manufacturers. Both types of solution were found to have significant variations in pH, with values ranging from 6.70 to 7.57 for the saline solutions and 6.84 to 7.63 for the multipurpose solutions. We concluded that the solutions should not affect the ocular physiological performance because their pH values are within the buffering capacity of the eye.

Three periodic solutions for perturbed second order Hamiltonian systems

2009

AbstractIn this paper we study the existence of three distinct solutions for the following problem−u¨+A(t)u=∇F(t,u)+λ∇G(t,u)a.e. in [0,T],u(T)−u(0)=u˙(T)−u˙(0)=0, where λ∈R, T is a real positive number, A:[0,T]→RN×N is a continuous map from the interval [0,T] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F. More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.

Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects

2017

In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.

Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…

2016

In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…

Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations

2021

We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…

Conformation of the galactose ring adopted in solution and in crystalline form as determined by experimental and DFT 1H NMR and single-crystal X-ray …

2003

The solution-state conformations of various galactose derivatives were determined by comparison of the experimental (1)H-(1)H vicinal coupling constants to those calculated using density functional theory (DFT) at the B3LYP/cc-pVTZ//B3LYP/6-31G(d,p) level of theory. The agreement between the experimental and calculated vicinal coupling constants for 1,2:3,4-di-O-isopropylidene-alpha-d-galactopyranose was good, thereby confirming an (O)S(2) skew conformation for it and its derivatives on the basis of their similar observed couplings. Single-crystal X-ray analysis of 1,2:3,4-di-O-isopropylidene-6-O-(3,4,6-tri-O-acetyl-2-deoxy-2-N-phthalimido-beta-d-glucopyranosyl)-alpha-d-galactopyranose and …

Non-Markovian master equation for the XX central spin model

2008

The non-Markovian correlated projection operator technique is applied to the model of a central spin coupled to a spin bath through non uniform XX Heisenberg coupling. The second order results of the Nakajima-Zwanzig and of the time-convolutionless methods are compared with the exact solution considering a fully polarized initial bath state.

Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter

2013

The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational. © Heldermann Verlag.

Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

2010

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

2013

Abstract We compute the solutions of Prandtl’s and Navier–Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl’s equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier–Stokes solution at different Reynolds numbers Re = 103–105, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers Re = 104–105. We also investi…