Positive solution of three-point boundary value problem for the one-dimensional p-Laplacian with singularities

In the paper, we deal with positive solutions of the following nonlinear three-point singular boundary value problem with a p-Laplacian operator:

     

Periodic solutions for a neutral nonlinear dynamical equation on a time scale

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel'ski? to show that the nonlinear neutral dynamic system with delay

     

On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order

For the nonlinear hyperbolic equation

u(2,1)=f(x,t,u,u(1,0),u(2,0),u(0,1),u(1,1))     

On a model of viscoelastic rod in unilateral contact with a rigid wall

^** Corresponding author. Email: atanackovic{at}uns.ns.ac.yu We study translatory motion of a body to which a viscoelasticrod with the constitutive equation with fractional derivativesis attached. The body with a rod impacts against a rigid wall.It is shown that the problem is described with a coupled systemof differential equations having integer and fractional derivativeshaving the form x⁽²⁾ = –f; f + af⁽⁾ = x + bx⁽⁾, x(0) =0, x⁽¹⁾(0) = 1. The unique solvability in S'₊ is proved andinterpretation of solutions is given. Also, some a priori estimatesof the solution are given. In particular, we showed that restrictionson coefficients that follow from the second law of thermodynamicsimply that the velocity after the impact is smaller than thevelocity before the impact.     

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3$N=3$ SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.     

Nonlinear Goos-Hänchen shifts due to surface polariton resonance in Kretschmann configuration with a Kerr-type substrate

As the surface polaritons are excited in Kretschmann configuration with a Kerr-type substrate, the nonlinear Goos-Hänchen (GH) shifts exhibit the optically hysteretic response to the intensity of incident light. For thicker metal films, the GH shifts become very sensitive to the intensity of incident light and the angle of incidence.     

Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism: Evidence from detrended fluctuation analysis of heart rate variability

Despite many previous studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent α1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves’ disease patients (32 females and 4 males; age 30 ± 1 years, means ± SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P<0.001) in α1 (hyperthyroid 1.28±0.04 versus control 0.91±0.02), long-term scaling exponent , overall scaling exponent , low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P<0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.     

Info-quantifiers’ map-characterization revisited

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.     

Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells

In this study, both the intersubband optical absorption coefficients and the refractive index changes as dependent on the magnetic field are calculated in square and graded quantum wells. Our results show that the position and the magnitude of the linear and total absorption coefficients and refractive index changes depend on the magnetic field strength and the shape of potential. The incident optical intensity has a great effect on the total absorption and refractive index changes.