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In this article, we examine the oscillation of a class of third-order damped nonlinear differential equations with multiple delays. Using the integral average and generalized Riccati techniques, new necessary criteria for the oscillation of equation solutions are established. The major effect is exemplified by an example.

Abstract Disorder induced phase slip (PS) events appearing in the current voltage characteristics (IVCs) are reported for two-dimensional TiN thin films produced by a robust substrate mediated nitridation technique. Here, high temperature annealing of Ti/Si3N4 based metal/substrate assembly is the key to produce majority phase TiN accompanied by TiSi2 & elemental Si as minority phases. The method itself introduces different level of disorder intrinsically by tuning the amount of the non-superconducting minority phases that are controlled by annealing temperature (T a ) and the film thickness. The superconducting critical temperature (T c ) strongly depends on T a and the maximum T c obtained from the demonstrated technique is about 4.8 K for the thickness range ~ 12 nm and above. Besides, the dynamics of IVCs get modulated by the appearance of intermediated resistive steps for decreased T a and the steps get more prominent for reduced thickness. Further, the deviation in the temperature dependent critical current (I c ) from the Ginzburg–Landau theoretical limit varies strongly with the thickness. Finally, the T c , intermediate resistive steps in the IVCs and the depairing current are observed to alter in a similar fashion with T a and the thickness indicating the robustness of the synthesis process to fabricate disordered nitride-based superconductor.

By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic behavior for a class of third-order neutral differential equations with discrete and distributed delay. These criteria dealing with some cases have not been covered by the existing results in the literature. We present many sufficient conditions and related examples in order to illustrate the main results.

Introduction Obsessive-compulsive disorder (OCD) patients with poor response to serotonin reuptake inhibitors (SRIs) may have dysfunction involving other neurotransmitters, including glutamate. Mismatch negativity (MMN), an event-related potential dependent on glutamatergic functioning, has not been studied in the adult OCD population and SRI non-responders. Objectives To compare the amplitude of MMN between OCD subjects who have responded(R) and not responded(NR) to SRIs, with healthy volunteers(HV). Methods MMN was measured in 15 OCD subjects fulfilling DSM-IV criteria (8 non-responders and 7 responders) and 22 healthy volunteers. Auditory MMN was measured using a multi-feature paradigm consisting of two variants each in frequency, duration, and intensity domains. EEG was recorded using 64 channel electrodes at 1000Hz. Epochs of 700 ms were extracted for each stimulus. MMN was evaluated as peak difference between the deviant and standard stimulus. MMN amplitudes at Fz were used for comparison between the groups using Kruskal-Wallis test followed by posthoc analysis, with significance set at p

The goal of this paper was to study the oscillations of a class of fourth-order nonlinear delay differential equations with a middle term. Novel oscillation theorems built on a proper Riccati-type transformation, the comparison approach, and integral-averaging conditions were developed, and several symmetric properties of the solutions are presented. For the validation of these theorems, several examples are given to highlight the core results.

The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

Distributed Bragg reflectors (DBRs) have received an intensive attention due to their increasing demand in optoelectronic and photonic devices. Such reflectors are capable to prohibit the light propagation within the specified wavelength range of interest. In this paper, we present the fabrication of TiO2/SiO2 stacks based Bragg reflectors by using a simple and in-expensive sol-gel spin coating technique. The prepared single-layer thin films of TiO2 and SiO2 onto glass substrates were characterized for their optical constants. By tuning the process parameters, one-seven DBR stacks of TiO2/SiO2 were prepared. The corresponding shift of the Bragg reflection peak was observed with the increased number of DBR stacks and as much as about 90% reflectance is observed from the 7DBR stacks. The experimentally measured reflectance was compared with the simulated one, which showed good in agreement. FESEM measurement has confirmed the formation of bright and dark strips of TiO2 and SiO2 films with their thicknesses 80 and 115 nm respectively. The simulation study was explored to a design of thin film silicon solar cell using 7DBR stacks. An enhancement in light absorption in the visible wavelength range is observed which coincides with the experimental result of the reflectance. The use of DBR at the bottom of the solar cell could felicitate the better light harvesting with the occurrence of Fabry-Perot resonances in the absorbing layer. Keywords: Bragg reflector, Photonic bandgap, Sol-gel coating, Reflection, Absorption

In this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the form $$ \Big(a_{1}(t)\big(a_{2}(t)Z^{\prime}(t)\big)^{\prime}\Big)^{\prime} + q(t) f\big(x(\sigma(t))\big) = 0, \quad t\geq t_0 > 0, $$ where \(Z(t) := x(t)+p(t)x^{\alpha}(\tau(t))\). Some new oscillation results are presented that extend those results given in the literature.

Silver incorporated zinc sulfide thin films are prepared by RF magnetron sputtering technique and the influence of silver incorporation on the structural, optical and luminescence properties is analyzed using techniques like grazing incidence X-Ray diffraction (GIXRD), atomic force microscopy (AFM), field emission scanning electron microscopy (FESEM), energy dispersive X-ray spectroscopy (EDS), micro-Raman spectroscopy, UV-Vis spectroscopy and laser photoluminescence spectroscopy. XRD analysis presents hexagonal wurtzite structure for the films. A reduction of crystallinity of the films is observed due to Ag incorporation. The Raman spectral analysis confirms the reduction of crystallinity and increase of strain due to the Ag incorporation. AFM analysis reveals a rough surface morphology for the undoped film and Ag incorporation makes the films uniform, dense and smooth. A blue shift of band gap energy with increase in Ag incorporation is observed due to quantum confinement effect. An absorption band (450-650 nm region) due to surface plasmon resonance of the Ag clusters present in the ZnS matrix is observed for the samples with higher Ag incorporation. The complex dielectric constant, loss factor and distribution of volume and surface energy loss of the ZnS thin films are calculated. Laser photoluminescence measurements gives an intense bluish green emission from the ZnS films and a quenching of the PL emission is observed which can be due to the metal plasmonic absorption and non-radiative energy transfer due to Ag incorporation.

The samples of Bi2Sr2Ca2Cu3-xMnxO10+δ (x = 0.0 to 0.30) were prepared by the standard solid-state reaction method. The phase identification characteristics of synthesized (HTSC) materials were explored through powder X-ray diffractometer reveals that all the samples crystallize in orthorhombic structure with lattice parameters a = 5.4053 Å, b = 5.4110 Å and c = 37.0642 Å up to Mn concentration of x = 0.30. The critical temperature (Tc) measured by standard four probe method has been found to depress from 108 K to 70 K as Mn content (x) increases from 0.00 to 0.30. The effects of sintering temperature on the surface morphology of Bi2Sr2Ca2Cu3-xMnxO10+δ have also been investigated. The surface morphology investigated through scanning electron microscope and atomic force microscopy (SEM & AFM) results that voids are decreasing but grains size increases as the Mn concentration increases besides, nanosphere like structures on the surface of the Mn doped Bi2Sr2Ca2Cu3-xMnxO10+δ (Bi-2223) samples.