Entire Functions Sharing Small Functions With Their Difference Operators

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.Comment: 14 pages, accepted for publicatio

GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

This paper is devoted to studying the growth of solutions of the higher order nonhomogeneous linear differential equation f(k) + Ak−1f(k−1) + ... + A2f " + (D1 (z) + A1 (z) eP(z)) f ' + (D0 (z) + A0 (z)e Q(z)) f = F (k ≥ 2) , where P (z) , Q(z) are nonconstant polynomials such that deg P = degQ = n and Aj (z) (j = 0, 1, ..., k − 1) , F (z) are entire functions with max{p(Aj) (j = 0, 1, ..., k − 1) , p(Dj) (j = 0, 1)} < n. We also investigate the relationship between small functions and the solutions of the above equation

On The Iterated Exponent of Convergence of Solutions of Linear Differential Equations

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f^{(k)}+A_{k-1}f^{(k-1)}+...+A₀f=0 for k≥2 and small functions, where A_{j} (j=0,1,...,k-1) are meromorphic functions of finite iterated p-order

Differential polynomials generated by some complex linear differential equations with meromorphic coefficients

In this paper, we investigate the relationship between small functions and differential polynomials g(z) = d2f\u27\u27 + d1f\u27 + d0f, where d0(z), d1(z), d2(z) are meromorphic functions which are not all equal to zero with ρ(dj) < n (j = 0,1,2) generated by some second order linear differential equations with meromorphic coefficients

Removal of RR-23 dye from industrial textile wastewater by adsorption on cistus ladaniferus seeds and their biochar

The use of low-cost, easily obtained and eco-friendly adsorbents has been employed as an ideal alternative for the methods of removing dyes from wastewater. Cistus ladaniferus seeds (CLS) and their biochar (BCCLS) are the biomaterials used as a bio-adsorbent for removing of Reactive red 23 (RR-23). The bio-char of cistus seed is prepared by a thermo-chemical route known as pyrolysis under optimum conditions, temperature equal to 450 °C, heating rate 21 °C.min-1 and particle sizes of 0.3 to 0.6 mm after the BCCLS is grinded with a ceramic grinder until the particle size is between 0.1 and 0.2 mm. The kinetics adsorption of dye by CLS and BCCLS are correctly described by the pseudo-2nd-order model with a correlation factor (R2 = 0.997) and (R2 = 0.998) respectively. As for the modeling of the adsorption isotherm, among the four models tested, Lungmuir type II and type I is most appropriate with a correlation factor equal to 0.999 and 0.98 for the BCCLS and the CLS respectively. On the other hand, the ability to remove the dye by the BCCLS is advantageous and the elimination efficiency reaches a maximum value of 99.237% for the BCCLS and 82% for the CLS. Keywords: Biochar, Isotherm, Adsorption, Cistus Seed, pyrolysis, Technical analysis

On Relative Convex Sequences

In this paper, we introduce the concept of relative convex sequences and establish their fundamental properties, highlighting their similarities to those of convex sequences. Additionally, we prove new inequalities of the Lupas and Hermite-Hadamard-Fej\'er type for relative convex sequences. In certain cases, and as an application, we show how the concept of relative convexity can facilitate the derivation of new inequalities for convex sequences.Comment: 12 page

Modified Chitosan Immobilized on Modified Sand for Industrial Wastewater Treatment in Multicomponent Sorption: Shrimp Biowaste Processing

In this paper, modified chitosan immobilized on modified sand (MCs/MS) was synthesized and characterized by infrared spectroscopy (FT-IR), X-ray diffraction (XRD), scanning electron microscope (SEM) and energy dispersive X-ray analysis (EDXA). MCs/MS composite was used to remove Reactive Red 23 (RR23), Reactive Blue 19 (RB19) and Iron III (Fe3+) in three single-component and three binary, RR23+RB19, RR23+Fe3+ and RB19+Fe3+. Batch experiments were carried out for adsorption kinetics, isotherms and thermodynamics. Operational parameters studied were pH, contact time, temperature, adsorbate and adsorbent concentrations. Adsorption kinetics in single and binary systems of components followed pseudo- second-order kinetics model. The isotherm data in single and binary systems followed Freundlich isotherm model. Thermodynamic parameters have disclosed that the adsorption is exothermic and not spontaneous with a physical adsorption for both single and binary systems. The results showed that MCs/MS composite was an effective adsorbent to remove hazardous pollutants with a removal rate between 80% and 99.6%, the optimal contact time was between 120 and 180 min for all components in single and multicomponent system. Keywords : Modified chitosan immobilized on modified sand, Multicomponent system, Reactive Red 23, Reactive Blue 19, Iron III, Hydrothermo-Chemical method

On The Iterated Exponent of Convergence of Solutions of Linear Differential Equations

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f^{(k)}+A_{k-1}f^{(k-1)}+...+A₀f=0 for k≥2 and small functions, where A_{j} (j=0,1,...,k-1) are meromorphic functions of finite iterated p-order