Journal of Kufa for Mathematics and Computer

Abstract— The problem of transportation is studied in many areas, most importantly in the field of logistics and
operations management. The distribution problem of goods and commodities from sources to destinations is an
important problem where many methods have been used to obtain its optimum solution, which represents the
minimum cost of distribution the goods from sources to destinations. Generally, the transportation classical cost of
one unit of a good is depending on the source and the destination. In this paper, we suggest an approach to obtain a
solution to the transportation problem consisting of two products or more and then by using the modified Kruskal’s
algorithm we find the minimum feasible solution.

Abstract--- Prepare network sensor as a context to achieve network community everywhere , it has made
technological innovations sensor smaller and more efficient to use in the discovery of the ocean and gain valuable
information, it can be as simple as a temperature gauge or as complicated as if used in military and dangerous areas
In order to transmit information safely and without any loss, it is necessary to study a dedicated processing
mechanism for calculating the encryption taking into account the reduction of power consumption of the sensor node.
the network has been simulated using QualNet.

The transfer of information using the signal needs speed, which leads to the compression of the information.
It is only possible through the process of using a mathematical technique at work.
To demonstrate an increase in theory efficiency, it was used in signal processing, compression, and good results. In
section 4 Matrix was used because M=3 was taken, where six functions were obtained, when these functions
were integrated, the operations matrix of integration was added, which was added to solve Boundary Value
Problems (BVPs) numerically. In addition to solving problems numerically, using the proposed technique, which is
signal processing, to demonstrate the efficiency of the proposed theory as indicated in section 2, wavelets are built on
the dependence of the four effects . In addition, the number of equations obtained is calculated based on the
value of where six functions are obtained and the greater value of is obtained More
functions, leading to greater accuracy in obtaining the best results.

In this study, Multiple-Chaotic maps were merged by using multiplicative-additive form to generate the
chaotic sequences which are used to track the addresses of shuffled bits in steganography. Three techniques are
introduced for image steganography in the spatial domain. The first system is based on the well-known LSB
technique, the second system is based on looking for the identical bits between the secret message and the cover
image and the third system is based on the concept of LSB substitution, it is employed the mapping of secret data bits
with cover pixel bits. It was tested and evaluated security levels for the proposed techniques by using the Peak
Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), histogram analysis and correlative analysis and tested the
Chaotic sequences generated by using correlation, Lypaunov exponents, Poincaré section and 0-1Test. The results
show that the proposed methods perform better than existed systems.