Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator

In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.     

Organic polymer‐based monolithic capillary columns and their applications in food analysis

In recent years, the use of organic polymer monolithic capillary columns in separation science has gained popularity due to the fact that they are easy to fabricate and do not require retaining frits. These materials have been applied in different fields including foods, proteomics, and pharmaceuticals. The interest in food analysis still needs to develop in order to increase the sensitivity towards micro/nano‐scale food applications for food samples of < 5 μg (e.g., foodomics). In this regard, polymer monolithic capillary columns offer great separation capability in the food analytical separation science. We review the most important applications in food analysis using polymer monolithic capillary columns. In addition, several examples of the use of capillary separation methods combined with mass spectrometry detection in food analysis are summarized.     

A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

Journal of Mathematical Chemistry - A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear (2?+?1)-dimensional...     

Microwave-induced combustion synthesis and characterization of NixCo1−xFe2O4 nanocrystals (x = 0.0, 0.4, 0.6, 0.8, 1.0)

A series of Ni-doped cobalt ferrites Ni_xCo1_−xFe₂O₄ (x = 0.0, 0.4, 0.6, 0.8, and 1.0) were prepared using microwave-induced combustion. Nickel, cobalt, and ferric nitrates were used as starting materials and glycine as fuel. The influence of Ni content on the lattice parameter, stretching vibrations, and magnetization was studied. XRD, FTIR, and SEM were used for structure, composition, and morphology investigation. A porous network structure was observed with average particle size 60–67 nm. All samples had a cubic spinel structure. The unit cell parameter “a” decreases linearly with nickel concentration due to the smaller ionic radius of nickel. Magnetization measurements showed that coercivity decreased as Ni content increased; it increased with decreasing temperature.      

On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument

This paper investigates stability and boundedness of solutions to third order nonlinear differential equation with retarded argument: $$\begin{array}{l}x'''(t)+\varphi\bigl(x(t-r),x'(t-r),x''(t-r)\bigr)x''(t)\\\qquad{}+\psi\bigl(x'(t-r)\bigr)+h\bigl(x(t-r)\bigr)\\\quad=p\bigl(t,x(t),x(t-r),x'(t),x'(t-r),x''(t)\bigr).\end{array}$$ By the use of the Lyapunov functional, sufficient conditions for stability and boundedness of solutions to the considered equations are obtained. Examples are introduced throughout the paper for illustrations.     

一类四阶非自治微分方程解的有界和一致有界性

获得了一个四阶非线性微分方程的所有解是有界和一致有界的充分条件。     

Preparation,Characterization and Thermal Energy Storage Properties of Micro/Nano Encapsulated Phase Change Material with Acrylic-Based Polymer

The eutectic mixture of octacosane (C28)–heptadecane (C17) as core material was successfully encapsulated with an acrylic-based polymer (polymethylmethacrylate; PMMA) as shell material through emulsion polymerization. The polymeric reaction occurred around the core material was characterized by FTIR spectroscopy analysis. The polarized optical microscopy, scanning electron microscopy and particle size distribution investigations showed that the most of the prepared capsules had almost spherical shape with non-unimodal size distribution in micro-nano range. The differential scanning calorimetry analysis results exhibited that the capsules including highest amount of the eutectic PCM had a melting temperature of about 21°C and a latent heat capacity of about 98 J/g. The high thermal durability of the prepared capsules was confirmed by thermogravimetric analysis. The thermal cycling test designated that the synthesized capsules had good long-term usage latent heat thermal energy storage (LHTES) performance and chemical stability. Furthermore; the fabricated capsules with (1: 2) shell/core ratio had a reasonable thermal conductivity. It can be drawn a conclusion from all results that the prepared capsules especially PMMA/(C28–C17) (1: 2) product is a hopeful PCM that can be evaluated for low-temperature LHTES applications.     

The Novel N,S-Substituted Halonitrodienes from the Reactions of Thiosubstituted Nitrodiene with Piperazine and Morpholine

The substituted 1,2-dibromomethanethio nitrodiene 2 was obtained from the addition of bromine to S-substituted nitrodien 1 in carbon tetrachloride. N, S-substituted compounds 4a–h were synthesized from the reactions of compound 2 with several substituted piperazine derivatives 3a–h in dichloromethane. N, S-substituted compounds 6 and 8 were synthesized from the reaction of 2 with morpholine ( 5 ) and thiomorpholine ( 7 ) in dichloromethane, respectively. Dibutadienyl piperazines 10 , 12 , and 14 were synthesized from the reactions of 2 with homopiperazine ( 9 ), piperazine ( 11 ), and 2,5-dimethylpiperazine ( 13 ), respectively.     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.