On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.     

Continuum model for low-frequency phonons of boron nitride nanotubes

A continuum model is employed to calculate the low-frequency phonons of boron nitride nanotubes. We find an excellent agreement of the optically active modes calculated within this approach and those from more elaborate calculations within an energy and wavelength window that can be established beforehand, from the choice of the bulk input parameters. We verify that this model describes correctly the dependence of radial breathing mode with the radius, the existence of parabolic modes at small wavevectors, and other general characteristics of the dispersion relations of these systems.     

A new method to determine viscosity of liquids using vibration principles

A new method for determining viscosity of liquids is examined. The method employs the principles of vibration and measures the viscous damping due to the motion of a liquid placed in a cylindrical tube. The apparatus and the test liquid are treated as a dynamic system and the measured mechanical impedances are used to calculate energy dissipation due to the viscous damping. The newly designed apparatus is able to generate shear deformations in the liquid without using moving solid surfaces. A harmonic varying force with a frequency close to the resonance frequency of the system is applied through a piston and the resulting velocities of the oscillations generated in the system are measured. Liquids with higher viscosities result in lower velocities due to the higher damping. Analytical equations are provided to relate the viscous damping of the dynamic system to the viscosity of the liquids. The viscosities obtained from the proposed method are in good agreement with the ones obtained from standard rotational viscometry using a cone and plate geometry.     

Forced nonlinear oscillator with nonsymmetric dry friction

In this paper we discuss an approximately steady motion of an oscillator as a single whole with a constant “on the average” velocity. For that purpose we analyze the position and stability of some special points of the phase portrait. In the presence of internal excitation and nonsymmetric Coulomb dry friction, a motion of the oscillator with a constant “on the average” velocity is possible. The algebraic equation for this constant velocity is found. For different parameters of the model there exist at most three regimes of motion with a constant velocity, but only one or two of them are stable. The theoretical results obtained can be used for the design of worm-like moving robots.     

Sur les Transformations Simultanées de Deux Équations Différentielles Linéaires du Deuxième Ordre dans Elles-mêmes

AMS (MOS) Classification 34C20     

On oscillatory third order difference equations

In this paper, sufficient conditions have been obtained for oscillation/nonoscillation of a class of homogeneous/nonhomogeneous linear difference equations of third order.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

中微子质量和中微子振荡实验

本文介绍中微子质量测量的历史和现状。介绍太阳中微子丢失实验的结果和大气 μ中微子丢失实验结果。这些结果表明存在中微子振荡 ,即中微子具有质量。它是超出标准模型的信号。本文还介绍了 2 1世纪初研究中微子振荡的若干重要实验 ,例如长基线中微子振荡实验以及建造 μ子贮存环来产生高能电子中微子束进行中微子振荡的实验以及测量中微子振荡时的CP破坏的设想。     

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory.     

Corrigendum to: “Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients” [J. Comput. Appl. Math. 217 (1) (2008) 28–37]

This communication gives the corrigendum to the paper “Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients” (JCAM (2007), doi:10.1016/j.cam.2007.06.016).