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- Neutrosophic logic (5)
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Articles 1 - 11 of 11
Full-Text Articles in Algebra
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …
Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy
Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place the fundamental theorem of algebra, “a nth degree polynomial has n and only n roots”, n is untrue in case of polynomial in polynomial quaternion rings in general. Further the very concept of derivative and integrals of these polynomials are untrue. Finally interval pseudo quaternion rings also behave in an erratic way. Not …
Algebraic Structures On Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Algebraic Structures On Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
Study of MOD planes happens to a very recent one. Authors have studied several properties of MOD real planes Rn(m); 2 ≤ m ≤ ∞. In fact unlike the real plane R × R which is unique MOD real planes are infinite in number. Likewise MOD complex planes Cn(m); 2 ≤ m ≤ ∞, are infinitely many. The MOD neutrosophic planes RnI(m); 2 ≤ m ≤ ∞ are infinite in number where as we have only one neutrosophic plane R(I) = 〈R ∪ I〉 = {a + bI | I2 = I; a, b ∈ R}. Further three other new …
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m …
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD …
Multidimensional Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Multidimensional Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors name the interval [0, m); 2 ≤ m ≤ ∞ as mod interval. We have studied several properties about them but only here on wards in this book and forthcoming books the interval [0, m) will be termed as the mod real interval, [0, m)I as mod neutrosophic interval, [0,m)g; g2 = 0 as mod dual number interval, [0, m)h; h2 = h as mod special dual like number interval and [0, m)k, k2 = (m − 1) k as mod special quasi dual number interval. However there is only one real interval (∞, ∞) but …
Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz
Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz
Branch Mathematics and Statistics Faculty and Staff Publications
Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and articial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion. To overcome these di¢ culties of uncertainties, many theories have been developed such as rough sets theory, probability theory, fuzzy sets theory, theory of vague sets, theory of soft ideals and the theory of intuitionistic fuzzy sets, theory of neutrosophic sets, Dezert-Smarandache Theory (DSmT), etc. Zadeh introduced the degree of membership/truth (t) in 1965 and dened …
Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan
Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan
Branch Mathematics and Statistics Faculty and Staff Publications
It is common knowledge that common models with their limited boundaries of truth and falsehood are not su¢ cient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and impaction. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not su¢ cient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh [67] introduced the concept of …
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache
Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.