For any positive real number n one defines SSp n as the smallest. For any positive real number n one defines ISs n as the largest. For any positive real number n one defines SSs n as the smallest.

Account Options

The first values of this function are: For any positive real number n one defines ISc n as the largest. For any positive real number n one defines ISf n as the largest. For any positive real number n one defines SSf n as the smallest. This is a generalization of the fractional part of a number. In a similar way one defines:.


  • 6 Days To Slim: The Amazing Mediterranean Detox Diet: Lose up to 12lbs in 6 Days and Keep it Off!
  • Dereks Bliss: (Gay Futuristic Scifi Erotic Romance) (The Unwanted Book 2).
  • Mathematics > General Mathematics.
  • ?

Superior Fractional S-Cubic Part of Then we say that f: The following functions are obviously S-multiplicative:. Certainly, many properties of multiplicative functions can be translated for.

Then SI1 d n is the smallest number of iterations k such that d d Let n be an integer and gd n be the greatest divisor of n, less than n,. Press, Vail, USA, Other e-books on Smarandache Functions and Sequences can be downloaded from.

Submission history

Mathematics Magazine for Grades Characterization of a prime number: Smarandache Ceil Functions of k-th Order: Definition Let be a non-empty set, and GNSS and in the form , , then we may consider two possible definitions for subsets may be defined as and and Proposition For any generalized neutrosophic set the following are holds Definition Let be a non-empty set, and , are GNSS Then maybe defined as: Let and given by: We can easily generalize the operations of generalized intersection and union in definition 3. Definition Let be a arbitrary family of in , then maybe defined as: Generalized Neutrosophic Topological Spaces Here we extend the concepts of and intuitionistic fuzzy topological space [5, 7], and neutrosophic topological Space [ 9] to the case of generalized neutrosophic sets.

Definition A generalized neutrosophic topology GNT for short an a non empty set is a family of generalized neutrosophic subsets in satisfying the following axioms In this case the pair is called a generalized neutrosophic topological space G for short and any neutrosophic set in is known as neuterosophic open set for short in. The elements of are called open generalized neutrosophic sets, A generalized neutrosophic set F is closed if and only if it C F is generalized neutrosophic open.

Publications

Remark A generalized neutrosophic topological spaces are very natural generalizations of intuitionistic fuzzy topological spaces allow more general functions to be members of intuitionistic fuzzy topology. Example Let and Then the family of G in is generalized neutrosophic topology on Example Let be a fuzzy topological space in Changes [4] sense such that is not indiscrete suppose now that then we can construct two G on as follows Proposition Let be a GNT on , then we can also construct several GNTSS on in the following way: Since , we have This similar to a Definition Let be two generalized neutrosophic topological spaces on.

Then is said be contained in in symbols if for each. In this case, we also say that is coarser than.

Full text of "Smarandache Function, book series, Vol. , "

Proposition Let be a family of on. Then is A generalized neutrosophic topology on. Furthermore, is the coarsest NT on containing all.


  • ;
  • Roman life in the days of Cicero (TREDITION CLASSICS)!
  • Playas de Sangre (Spanish Edition).
  • .

Obvious Definition The complement of C A for short of is called a generalized neutrosophic closed set G for short in. Now, we define generalized neutrosophic closure and interior operations in generalized neutrosophic topological spaces: Then the generalized neutrosophic closer and generalized neutrosophic interior of Aare defined by G G.


  1. ?
  2. - Document - On the numerical function [theranchhands.com]!
  3. ;

    4. It can be also shown that It can be also shown that is and is a G in is in if and only if G. Proposition For any generalized neutrosophic set in we have a G b G Proof. Let and suppose that the family of generalized neutrosophic subsets contained in are indexed by the family if G contained in are indexed by the family. Then we see that and hence. Since and and for each , we obtaining.

    Smarandache Function

    Hence follows immediately This is analogous to a. Proposition Let be a G and be two neutrosophic sets in. Then the following properties hold: