The main focus of this article is to introduce the notion of rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology by using rough pentapartitioned neutrosophic lower approximation, rough pentapartitioned neutrosophic upper approximation, and rough pentapartitioned neutrosophic boundary region. Then, we provide some basic properties, namely operations on rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology. By defining rough pentapartitioned neutrosophic set and topology, we formulate some results in the form of theorems, propositions, etc. Further, we give some examples to justify the definitions introduced in this article.

    The concepts of nonlinear mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type theorem is established. Furthermore, this work has presented plenty of composition and inclusion results between different classes of mappings in the abstract settings. Finally, a generalized notation of mixing maps and their characteristics are extended to a more general setting.

    In this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth

     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 .

    The attribute quality control charts are one of the main useful tools to use in control of quality product in companies. In this paper utilizing the statistical procedures to find the attribute quality control charts for through fuzzified the real data which we got it from Baghdad Soft Drink Company in Iraq, by using triangular membership function to obtain the fuzzy numbers then employing the proposed ranking function to transform to traditional sample. Then, compare between crisp and fuzzy attribute quality control.

The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner,  Taylor manner and block- by- block(2, 3, 5).

Blockchain is an innovative technology that has gained interest in all sectors in the era of digital transformation where it manages transactions and saves them in a database. With the increasing financial transactions and the rapidly developed society with growing businesses many people looking for the dream of a better financially independent life, stray from large corporations and organizations to form startups and small businesses. Recently, the increasing demand for employees or institutes to prepare and manage contracts, papers, and the verifications process, in addition to human mistakes led to the emergence of a smart contract. The smart contract has been developed to save time and provide more confidence while dealing, as well a

The main objective of" this paper is to study a subclass of holomrphic and univalent functions with negative coefficients in the open unit disk U= defined by Hadamard Product. We obtain coefficients estimates, distortion theorem , fractional derivatives, fractional integrals, and some results.

The issue of image captioning, which comprises automatic text generation to understand an image’s visual information, has become feasible with the developments in object recognition and image classification. Deep learning has received much interest from the scientific community and can be very useful in real-world applications. The proposed image captioning approach involves the use of Convolution Neural Network (CNN) pre-trained models combined with Long Short Term Memory (LSTM) to generate image captions. The process includes two stages. The first stage entails training the CNN-LSTM models using baseline hyper-parameters and the second stage encompasses training CNN-LSTM models by optimizing and adjusting the hyper-parameters of