Special Dual Like Numbers And Lattices

In this book the authors introduce the new notions of subset polynomial semirings and subset matrix semirings. Solving subset polynomial equations is an interesting exercise. Open problems about the solution set of subset polynomials are proposed.

In this book authors introduce the notion of subset vertex multigraphs for the first time. The study of subset vertex graphs was introduced in 2018, however they are not multiedged, further they were unique once the vertex subsets are given. These subset vertex multigraphs are also unique once the vertex subsets are given and the added advantage is that the number of common elements between two vertex subsets accounts for the number of edges between them, when there is no common element there is no edge between them.

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied and resolved using similar of different methods. Therefore, more research should to be done in the field of neutrosophics. The author introduces for the first time the notions of neutrosophic mereo-limit, neutrosophic mereo-continuity (in a different way from the classical semi-continuity), neutrosophic mereo-derivative and neutrosophic mereo-integral (both in different ways from the fractional calculus), besides the classical definitions of limit, continuity, derivative, and integral respectively. Future research may be done in the neutrosophic fractional calculus. It means that in neutrosophic calculus there are limits, continuity, derivatives, and integrals that are not complete, i.e. there are neutrosophic functions that at a given point may have a degree of a limit (not 100%) called mereo-limit, or may be continuous in a certain degree (not 100%) called mereo-continuity, or may be differentiable or integrable in a certain degree (not 100%) called mereo-derivatives and respectively mereo-integrals. These occur because of indeterminacies...

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.