General Mathematics
Contemporary geometers do not acknowledge nonaxomatizable geometries. This fact means that our knowledge of geometry is poor. A perfect knowledge of geometry is important for "consumers of geometry" (physicists dealing with geometry of…
A set theory is developed based on the approximations of sets and denoted by AS. In AS the set of all sets exists but the argument for Russell's and Cantor's paradox fail. The Axioms of Separation, Replacement and Foundation are not valid.…
We derive consequences from the existence of a term which satisfies Mal'cev identities (characterizing permutability) modulo two functions F and G from admissible relations to admissible relations. We also provide characterizations of…
There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an…
Using the $\zeta$ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the $\zeta$ zeros is established. We then demonstrate that on the critical line, $|\zeta|$ is convex, and that in the…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Some open questions related to prime reciprocal digit frequencies with potential applications to cryptography are presented.
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
We prove that if a completely non-unitary contraction T in L(H) has a non-trivial algebraic element h, then T has a non-trivial invariant subspace.
In this paper we talk about the so-called SuperMathematics Functions (SMF), which often constiture the base for generating technical neo-geometrical objects.
A functional Menger system is a set of $n$-place functions containing $n$ projections and closed under the so-called Menger's composition of $n$-place functions. We give the abstract characterization for subsets of these functional systems…
In this book, we introduce the notion of Smarandache special definite algebraic structures. We can also call them equivalently as Smarandache definite special algebraic structures. These new structures are defined as those strong algebraic…
In this paper relations of non-empty intersection, inclusion end equality of domains of functions for $(2,n)$-semigroups of partial $n$-place functions are investigated.
I show--contrary to common beliefs tolerated by the 'bosses'--that any interpretation of ZF that admits Aristotle's particularisation is not sound; that the standard interpretation of PA is not sound; that PA is consistent but…
Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty…
A method is presented for using the consistent part of inconsistent axiomatic systems.
This paper has been withdrawn by the author, due to a crucial error in page 5.
We proposed a new type of soliton equation, whose solutions may describe some statistical distributions, for example, Cauchy distribution, normal distribution and student distribution, etc. The equation possesses two characters. Further,…
In this paper exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown population variance $S_y^2$. Problem is extended to the case of two-phase sampling. Theoretical…
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…