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Articles 31 - 33 of 33
Full-Text Articles in Number Theory
Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan
Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan
Branch Mathematics and Statistics Faculty and Staff Publications
The first chapter, Characterizations of regular and duo semigroups based on int-soft set theory, investigates the relations among int-soft semigroup, int-soft (generalized) bi-ideal, int-soft quasi-ideal and int-soft interior ideal. Using int-soft left (right) ideal, an int-soft quasi-ideal is constructed. We show that every int-soft quasi-ideal can be represented as the soft intersection of an int-soft left ideal and an int-soft right ideal. Using int-soft quasiideal, an int-soft bi-ideal is established. Conditions for a semigroup to be regular are displayed.
Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. I, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali
Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. I, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor [1]. Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set [2–4]. This book contains the successful invited submissions [5–56] to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic …
On The Density Of The Odd Values Of The Partition Function, Samuel Judge
On The Density Of The Odd Values Of The Partition Function, Samuel Judge
Dissertations, Master's Theses and Master's Reports
The purpose of this dissertation is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo $2$. We provide a doubly-indexed, infinite family of conjectural identities in the ring of series $\Z_2[[q]]$, which relate $p(n)$ with suitable $t$-multipartition functions, and show how to, in principle, prove each such identity. We will exhibit explicit proofs for $32$ of our identities. However, the conjecture remains open in full generality. A striking consequence of these conjectural identities is that, under suitable …