综合数学
Based on a brief review on developments of number system, a new developed pattern is proposed. The quaternion is extended to a matrix form aI+bC+cB+dA, in which the unit matrix I and three special matrices C,B,A correspond to number 1 and…
If o and * are two binary operations in a number system, then three elements a,b,c in that number system are said to satisfy the distributive property of the operation o over the operation * if, ao(b*c)= (aob)*(aoc) Now, suppose that the…
This paper considers the problem of estimating the population mean using information on auxiliary variable in presence of non response. Exponential ratio and exponential product type estimators have been suggested and their properties are…
This research will be helpful for people to display the 2-dimensiona projective models of 4-variable actual problems in many fields, in order to investigate deeply those actual problems. By using the theory of N-dimensional finite rotation…
Based on the Liouville-Weyl definition of the fractional derivative, a new direct fractional generalization of higher order derivatives is presented. It is shown, that the Riesz and Feller derivatives are special cases of this approach.
By studying the n-dimensional cube, the author finds a new way, and use it to proves that the indefinite equation $x^n+y^n=z^n(n=>3)$ has no any solutions of positive integers.
Using the delta correction to the standard free energy \cite{bc} in the elastic setting with a quadratic foundation term and some parameters, we introduce a one dimension only model for strong segregation in diblock copolymers, whose sharp…
The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…
Investigating Dirichlet L functional equation, the author found the relationship between Dirichlet L functional equation and the prime property function, two new corollaries based on GRH is tenable and the equation of the prime property…
Starting from the Euler's identity, the author improved Riemann's results, discovered the relationship between the Riemann Zeta function and the prime function, and obtained two new corollaries based on Riemann hypothesis is tenable. From…
A question associated with the 2005 open problem of Michael Kinyon (Is every Osborn loop universal?), is answered. Two nice identities that characterize universal (left and right universal) Osborn loops are established. Numerous new…
Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
Two constructed prime number subsets (called prime brother & sisters and prime cousins) lead to a third one (called isolated primes) so that all three disjoint subsets together generate the prime number set. It should be suggested how the…
We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.
We invoke Carlson's theorem to justify and to confirm the results previously obtained on the validity of Riemann Hypothesis via the coupling constant spectrum of the zero energy S-wave Jost function a la N. N. Khuri, for the real, repulsive…
We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the $S$-wave Jost function at zero energy and in identifying it with the Riemann $\xi(s)$…
Recent theologies concerning God's death after Auschwitz are mathematically formalized through a suitable temporalization of G\"{o}del's Ontological Proof.
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…
In this paper we have given an algorithmic proof of an long standing Barnette's conjecture (1969) that every 3-connected bipartite cubic planar graph is hamiltonian. Our method is quite different than the known approaches and it rely on the…