This paper devoted to the analysis of regular singular boundary value problems for ordinary differential equations with a singularity of the different kind , we propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the regular singular points and its numerical approximation. Many examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

Complex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

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

The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

     The primary purpose of this subject is to define new games in ideal spaces via set. The relationships between games that provided and the winning and losing strategy for any player were elucidated.