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This work represents a contribution to the study of the theory of multidual integers. We start by introducing the concept of multidual integers and we show some of their algebraic properties. We focus on the description of their ideals and subrings. We will devote ourselves to highlight algebraic results, like divisibility in the ring of multidual integers. Moreover, various isomorphism results are provided.

The purpose of this paper is to participate to the study of the theory of multidual algebra, which has been introduced in the paper [7]. We start by recalling some notions of multidual numbers and their properties. We focus on the description of their ideals and subalgebra. Various properties were shown. In addition, the new concept of subalgebra of multidual geometric numbers has been developed.

The purpose of this paper is to introduce and develop the new concept of generalized hyperbolic numbers, which generalize together dual numbers and hyperbolic numbers. We start by define, generalized hyperbolic numbers and their basic properties. In addition, we give another representation of generalized hyperbolic numbers basing on matrices. We extend the concept of holomorphicity to generalized hyperbolic functions. Moreover, a general explicit representation of generalized hyperbolic functions has been obtained. Finally and as concrete examples, some usual real functions have been extended to the algebra of generalized hyperbolic numbers.

The paper is devoted to the study of transmission problem between two Herschel-Bulkley fluids with different viscosities, yield limits and power law index.