This paper refers to studying some types of ideals, specifically cubic bipolar ideals and cubic bipolar T-ideals of TM algebra. It also introduces a cubic bipolar sub-TM-algebra and several important properties of these concepts. The relationships between these ideals and characterizations of cubic bipolar T-ideals are investigated.

Remote surveying of unknown bound geometries, such as the mapping of underground water supplies and tunnels, remains a challenging task. The obstacles and absorption in media make the long-distance telecommunication and localization process inefficient due to mobile sensors’ power limitations. This work develops a new short-range sequential localization approach to reduce the required amount of signal transmission power. The developed algorithm is based on a sequential localization process that can utilize a multitude of randomly distributed wireless sensors while only employing several anchors in the process. Time delay elliptic and frequency range techniques are employed in developing the proposed algebraic closed-form solution.

In this paper, we define a cubic positive implicative-ideal, a cubic implicative-ideal and a cubic commutative-ideal of a semigroup in KU-algebra as a generalization of a fuzzy (positive implicative-ideal, an implicative-ideal and a commutative-ideal) of a semigroup in KU-algebra. Some relations between these types of cubic ideals are discussed. Also, some important properties of these ideals are studied. Finally, some important theories are discussed. It is proved that every cubic commutative-ideal, cubic positive implicative-ideal, and cubic implicative-ideal are a cubic ideal, but not conversely. Also, we show that if Θ is a cubic positive implicative-ideal and a cubic commutative-ideal then Θ is a cubic implicative-ideal. Some example

In this paper, an efficient method for compressing color image is presented. It allows progressive transmission and zooming of the image without need to extra storage. The proposed method is going to be accomplished using cubic Bezier surface (CBI) representation on wide area of images in order to prune the image component that shows large scale variation. Then, the produced cubic Bezier surface is subtracted from the image signal to get the residue component. Then, bi-orthogonal wavelet transform is applied to decompose the residue component. Both scalar quantization and quad tree coding steps are applied on the produced wavelet sub bands. Finally, adaptive shift coding is applied to handle the remaining statistical redundancy and attain e

The study of homomorphism and Cartesian product is one of the most important mathematical tools that preserve algebraic structures. In this work, a new definition of the concept of a cubic bipolar-ideal under homomorphism in a TM-algebra is introduced. Some important theorems are presented. The notion of Cartesian product for cubic bipolar-ideals and cubic bipolar T-ideals is studied. Also, several properties of the Cartesian product for cubic bipolar-ideals are investigated. Furthermore, the level subsets of the Cartesian product of two cubic bipolar-ideals are defined.

An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.