In this paper , certain subclass of harmonic multivalent function defined in the exterior of the unit disk by used generalize hypergeometric functions is introduced . In This study an attempting have been made to investigate several geometric properties such as coefficient property , growth bounds , extreme points , convolution property , and  convex linear combination .

In this paper, we presented new types of Mc-function by using 𝜔-open and 𝑁-open sets some of them are weaker than Mc-function and some are stronger, which are 𝜔Mc-function, M𝜔c-function, 𝜔M𝜔c-function, 𝑁Mc-function, M𝑁c-function and 𝑁M𝑁c-function, also we submitted new kinds of continuous functions and compact functions and we illustrated the relationships between these types. The purpose of this paper is to expand the study of Mcfunction and to get results that we need to find the relationship with the types that have been introduced.

The proposed method is sensitive, simple , fast for the determination of mebeverine hydrochloride in pure form or in pharmaceutical dosage . Using Homemade instrument fluorimeter continuous flow injection analyser with solid state laser (405 nm) as a source. Where it is based upon the fluorescence of fluorescein sodium salt and quenching effect of fluorescence by mebeverine in aqueous medium. The calibration graph was linear in the concentration range 0.05 to10 mMol.L-1 (r= 0.9629) with relative standard deviation (RSD%) for 1 mMol.L-1mebeverine solution was lower than 3% (n=6). Three pharmaceutical drugs were used as an application for the determination of mebeverine. A comparison was made between the newly developed method of analysis wit

Nine new compounds of 2-amino-5-chlorobenzothiazole derivatives were synthesized. These new compounds were formed through the reaction of 2-amino-5-chlorobenzothiazole 1 with ethyl chloroacetate and KOH, which gave an ester derivative 2, followed by refluxing compound 2 with hydrazine hydrate to afford hydrazide derivative 3. The reaction of compound 3 with CS₂ and KOH gave 1,3,4-oxadiazole-2-thiol derivative 4, and then the reaction of compound 2 with thiosemicarbazide to produce compound 5  then treated it with 4%NaOH led to ring closure to provide 1,2,4-triazole-3-thiol derivative

The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.   

Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studie

In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere  so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for

In this paper, we show many conclusions on the Quasi-Hadamard products of new Subclass of analytic functions of β-Uniformly univalent function  defined by Salagean q-differential operator.

The present study utilised date palm fibre (DPF) waste residues to adsorb Congo red (CR) dye from aqueous solutions. The features of the adsorbent, such as its surface shape, pore size, and chemical properties, were assessed with X-ray diffraction (XRD), BET, Fourier-transform infrared (FTIR), X-ray fluorescence (XRF), and field emission scanning electron microscope (FESEM). The current study employed the batch system to investigate the ideal pH to adsorb the CR dye and found that acidic pH decolourised the dye best. Extending the dye-DPF waste mixing period at 25°C reportedly removed more dye. Consequently, the influence of the starting dye and DPF waste quantity on dye removal was explored in this study. At 5 g/L dye concentration, 48% d