A general velocity profile for a laminar flow over a flat plate with zero incidence is obtained by employing a new boundary condition to the other available boundary conditions. The general velocity profile is mathematically simple and nearest to the exact solution. Also other related values, boundary layer thickness, displacement thickness, momentum thickness and coefficient of friction are nearest to the exact solution compared with other corresponding values for other researchers.

    In this study, the concept of fuzzy α-topological vector space is introduced by using the concept  fuzzy α-open set , some properties of fuzzy α-topological vector spaces are proved .We also show that the space is -space iff every singleton set is fuzzy α- closed .Finally, the convex property and its relation with the interior points are discussed.

     The most common artifacts in ultrasound (US) imaging are reverberation and comet-tail. These are multiple reflection echoing the interface that causing them, and result in ghost echoes in the ultrasound image. A method to reduce these unwanted artifacts using a Otsu thresholding to find region of interest (reflection echoes) and output applied to median filter to remove noise. The developed method significantly reduced the magnitude of the reverberation and comet-tail artifacts. Support Vector Machine (SVM) algorithm is most suitable for hyperplane differentiate. For that, we use image enhancement, extraction of feature, region of interest, Otsu thresholding, and finally classification image datasets to normal or abnormal image.

     The main aim of this work is to investigate the existence and approximate controllability of mild solutions of impulsive fractional nonlinear control system with a nonsingular kernel in infinite dimensional space. Firstly, we set sufficient conditions to demonstrate the existence and uniqueness of the mild solution of the control system using the Banach fixed point theorem. Further, we prove the approximate controllability of the control system using the sequence method.

Let 


 
, 1
( )
1 2 ,
( , ) 1 2
m n
s s
m n
f s s a e m n   , (s   it , j 1,2) j j j  ,  
m 1  and
 
n 1  being an increasing sequences of positive numbers and a E m n  , where E
is Banach algebra, represent a vector valued entire Dirichlet functions in two
variables. The space  of all such entire functions having order at most equal to 
is considered in this paper. A metric topology using the growth parameters of f is
defined on  and its various properties are obtained. The form of linear operator on
the space  is characterized and proper bases are also characterized in terms of
growth parameters  .

In this research, the problem of multi- objective modal transport was formulated with mixed constraints to find the optimal solution. The foggy approach of the Multi-objective Transfer Model (MOTP) was applied. There are three objectives to reduce costs to the minimum cost of transportation, administrative cost and cost of the goods. The linear membership function, the Exponential membership function, and the Hyperbolic membership function. Where the proposed model was used in the General Company for the manufacture of grain to reduce the cost of transport to the minimum and to find the best plan to transfer the product according to the restrictions imposed on the model.

    Cryptography can be thought of as a toolbox, where potential attackers gain access to various computing resources and technologies to try to compute key values. In modern cryptography, the strength of the encryption algorithm is only determined by the size of the key. Therefore, our goal is to create a strong key value that has a minimum bit length that will be useful in light encryption. Using elliptic curve cryptography (ECC) with Rubik's cube and image density, the image colors are combined and distorted, and by using the Chaotic Logistics Map and Image Density with a secret key, the Rubik's cubes for the image are encrypted, obtaining a secure image against attacks. ECC itself is a powerful algorithm that generates a pair of p