The ultimate goal of any sale contract is to maximize the combined returns of the parties, knowing that these returns are not realized (in long-term contracts) except in the final stages of the contract. Therefore, this requires the parties to the contract to leave some elements open, including the price, because the adoption of a fixed price and inflexible will not be appropriate to meet their desires when contracting, especially with ignorance of matters beyond their will and may affect the market conditions, and the possibility of modifying the fixed price through The elimination is very limited, especially when the parties to the contract are equally in terms of economic strength. Hence, in order to respond to market uncertainties, the

In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

The significance fore supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extension to supra open sets, including supra semi open sets, supra per open and others. In this research, a notion for ⱨ-supra open created within the generalizations of the supra topology of sets. Our investigation involves harnessing this style of sets to introduce modern notions in these spaces, specifically supra ⱨ - interior, supra ⱨ - closure, supra ⱨ - limit points, supra ⱨ - boundary points and supra ⱨ - exterior of sets. It has been examining the relationship with supra open. The research was also enriched with many

Recently, Image enhancement techniques can be represented as one of the most significant topics in the field of digital image processing. The basic problem in the enhancement method is how to remove noise or improve digital image details. In the current research a method for digital image de-noising and its detail sharpening/highlighted was proposed. The proposed approach uses fuzzy logic technique to process each pixel inside entire image, and then take the decision if it is noisy or need more processing for highlighting. This issue is performed by examining the degree of association with neighboring elements based on fuzzy algorithm. The proposed de-noising approach was evaluated by some standard images after corrupting them with impulse

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

This work aims to develop a secure lightweight cipher algorithm for constrained devices. A secure communication among constrained devices is a critical issue during the data transmission from the client to the server devices. Lightweight cipher algorithms are defined as a secure solution for constrained devices that require low computational functions and small memory. In contrast, most lightweight algorithms suffer from the trade-off between complexity and speed in order to produce robust cipher algorithm. The PRESENT cipher has been successfully experimented on as a lightweight cryptography algorithm, which transcends other ciphers in terms of its computational processing that required low complexity operations. The mathematical model of