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A multitude of uncertainty models, such as fuzzy, neutrosophic, and plithogenic sets, have emerged in the domain of fuzzy sets and their extensions. This diversity, while reflecting an active research community, can lead to conceptual overlap. To address this, the authors propose a unified framework for the systematic management of these "Uncertain Sets" by defining the Uncertain Model, the U-Structure, and the U-Off Structure. The paper revisits and extends the definitions of HyperUncertain, SuperUncertain, SuperHyperUncertain, Tree Uncertain, and Forest Uncertain structures, along with their "Off" variants. To encompass systems beyond Uncertain Sets, the concepts of Functorial Set and Functorial Structure are also introduced. This comprehensive approach aims to establish a robust foundation for organizing and applying uncertainty models across various mathematical and applied domains.
In June 1997, fifty-seven of the world's best students gathered at TASI '97 in Boulder, Colorado, USA, to attend an intensive series of lectures on the theory and phenomenology of supersymmetry, supergravity and supercolliders. This book contains the proceedings of that school. It is aimed at advanced graduate students as well as postdoctoral and other researchers. It provides a snapshot of the state-of-the-art in an active area of high energy particle theory, and may perhaps serve as a preview of physics to be discovered in the next decade.
During the last three decades supersymmetry has grown into one of the busiest theoretical avenues of particle physics. Supersymmetric ideas dominate the scenario of “beyond the standard model phenomenology”, in spite of the thirty-year-old experimental opacity, a situation that could change within the following decade. One additional important reason for the good health of supersymmetry must be found in the most speculative areas of particle physics. Much of its success comes from superstring theory.The Advanced School on Supersymmetry in the Theories of Fields, Strings and Branes attempted to provide an up-to-date perspective of the role played by supersymmetry in these subjects. The le...
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Neutrosophic Sets and Systems, Volume 91 (2025), presents recent advances in neutrosophic theory and its diverse applications across mathematics, computer science, engineering, and the social sciences. The issue brings together contributions that extend classical models of uncertainty—fuzzy, intuitionistic, and probabilistic—through refined neutrosophic frameworks, including plithogenic, superhyper, quadripartitioned, and n-valued models. Articles explore novel applications of neutrosophic integrals, Markov decision processes, network flows, and dynamical systems, addressing challenges in real-time safety evaluation, vocational education, innovation and entrepreneurship training, curricu...
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This book describes quantum geometry in the framework of Matrix Theory, which offers a quantum theory of space-time and matter.
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