CUBIC Z-SUBALGEBRAS IN Z-ALGEBRAS

In this article, the notions of Cubic Z-Subalgebras in Z-algebras is introduced and some of their properties are investigated. The Z-homomorphic image and inverse image of cubic Z-Subalgebras in Z-algebras is investigated. Also, the cartesian product of cubic Z-Subalgebras in Z-algebras is also discussed.

Application Multi-Fuzzy Soft Sets in Hypermodules

The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy soft hyperstructure. We investigate the notion of multi-fuzzy soft hypermodules and some of their structural properties are discussed. We discuss the behavior image and inverse image of a multi-fuzzy soft set under the multi-fuzzy soft function. According to Zadeh’s extension principle, we prove that the image and inverse image of a multi-fuzzy soft hypermodules are further multi-fuzzy soft hypermodule.

Degree 2 transformation semigroups as continuous maps on graphs: Foundations and structure

We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elements. We show that the graph of fibers of such an action gives a deep connection between semigroup theory and graph theory. It is known that the Krohn–Rhodes complexity of a degree 2 action is at most 2. We show that the monoid of continuous maps on a graph is the translational hull of an appropriate 0-simple semigroup. We show how group mapping semigroups can be considered as regular covers of their right letter mapping image and relate this to their graph of fibers.

Intuitionistic anti fuzzy normed ideals

In this paper, we introduce the notion of intuitionistic anti fuzzy normed subrings and intuitionistic anti fuzzy normed ideals and various properties of intuitionistic anti fuzzy normal subrings and ideals are examined. Also, we prove that the intersection of two intuitionistic anti fuzzy normed ideals is also an intuitionistic anti fuzzy normed ideal. Besides, we define the anti level subsets and identify the relationship between these sets and intuitionistic anti fuzzy normed ideals. In addition, we define the anti-image of intuitionistic anti fuzzy normed ideals and discuss the inverse image and anti-image for intuitionistic anti fuzzy normed ideals under epimorphism mapping.

Real-time magnetic resonance imaging in pediatric radiology — new approach to movement and moving children

The recent development of highly undersampled radial gradient echo sequences in combination with nonlinear inverse image reconstruction now allows for MRI examinations in real time. Image acquisition times as short as 20 ms yield MRI videos with rates of up to 50 frames per second with spin density, T1- and T2-type contrast. The addition of an initial 180° inversion pulse achieves accurate T1 mapping within only 4 s. These technical advances promise specific advantages for studies of infants and young children by eliminating the need for sedation or anesthesia. Our preliminary data demonstrate new diagnostic opportunities ranging from dynamic studies of speech and swallowing processes and body movements to a rapid volumetric assessment of brain cerebrospinal fluid spaces in only few seconds. Real-time MRI of the heart and blood flow can be performed without electrocardiogram gating and under free breathing. The present findings support the idea that real-time MRI will complement existing methods by providing long-awaited diagnostic options for patients in early childhood. Major advantages are the avoidance of sedation or anesthesia and the yet unexplored potential to gain insights into arbitrary body functions.

A note on complex fuzzy subfield

In this paper, we introduce idea of complex fuzzy subfield and discuss its various algebraic aspects. We prove that every complex fuzzy subfield generate two fuzzy fields and shows that intersection of two complex fuzzy subfields is also complex fuzzy subfields. We also present the concept of level subsets of complex fuzzy subfield and shows that level subset of complex fuzzy subfield form subfield. Furthermore, we extend this idea to define the notion of the direct product of two complex fuzzy subfields and also investigate the homomorphic image and inverse image of complex fuzzy subfield.

Weak Essential Fuzzy Submodules Of Fuzzy Modules

Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

Anti complex fuzzy subgroups under \(s\)-norms

In this study, we define anti complex fuzzy subgroups and normal anti complex fuzzy subgroups under \(s\)-norms and investigate some of characteristics of them. Later we introduce and study the intersection and composition of them. Next, we define the concept normality between two anti complex fuzzy subgroups by using \(s\)-norms and obtain some properties of them. Finally, we define the image and the inverse image of them under group homomorphisms.