...Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences Editor’s Note This book ar... ...OWA 42402 USA GENERALIZED PARTITIONS AND SOME NEW IDEAS ON NUMBER THEORY AND SMARANDACHE SEQUENCES Hexis P... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...e On Maohua Le’s Proof of Murthy’s Conjecture On Reciprocal Partition Theory ………………. 18 1.4 Generalization of Partition Functions, Introducti... ...9 1.5 Open Problems and Conjectures On the Factor/Reciprocal Partition Theory ………………. 28 1.6 A General Result on the Smarandache Star Function... ...rs to the above questions leads to the need for the generalization of the theory of the partition function. Section 2 A Program to Determine t... ...papers, most of which appeared in “Smarandache Notions Journal”, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandac...

... ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 ... ...ache called Smarandache Notions Journal that is edited by Dr. Minh Perez. Information about it and other advances can be found on the web site devot... ...of Inference Section 7 Formal Reasoning Section 8 Quantification Theory Section 9 Uses of Logic In Computer Programming 7 13 14 1... ...o use truth tables to perform the computations. For that we need a formal theory. Definition 1.5.1: A formal theory is a system S constructed from... ...heorem in the system S. Example: The following is a formal axiomatic theory L a) The set of symbols in L are { ¬, →, (, ), T, F, p 1 , p 2 , ... ... . B Definition 1.5.2: The formal axiomatic theory L in the previous example is known as the propositional calculus. ... ... f = 1. B) But to refer to intuitionistic logic, which means incomplete information on a variable, proposition or event one has t + i + f < 1. ... ..., referring to paraconsistent logic, which means contradictory sources of information about a same logical variable, proposition, or event one has t ... ...hen it follows that t 2 = t 3 . However, if f 1 ≤ t 2 , then we have no information about t 3 , so we make no assumptions and set it equal to zero...