We have not yet obtained a simple, complete and accurate method for determining if an integer number specifically an odd number that does not digitally sum to 3,6,9, whether it is prime, and that does not involve trial & error and/or as by a sieving method or factoring. This after thousand(s) of...

The calculation of risk and its pricing has been of great interest to the financial field(s) of economics. As issuance of bonds, loans, mortgages etc. has accelerated so have schemes to bundle, diversify and hedge such 'assets' and with a similarly accelerated 'need' or ever more accurate...

Primes constitute a subset of all integers. Integers that are not prime are composite numbers, constituted of primes. Studies of numbers have been ongoing for millenia, and with recent advances making large strides forward in understanding and in connections between various viewpoints and...

There is enormous invested interest and capital in national and global economies. Deriving an accurate mathematics theory of economy and with sufficient detail such that various observables indicators of an economy can be inter-related at the same time with the control methods and overall...

Some nonlinear PDEs partial differential equations are exactly solvable. As an example, nonlinear PDEs such as the Soliton equation were shown to be exactly solvable by quantum operator methods. More recently the Boltzmann equation was solved exactly as well. A question is are other equations...

There is an interest in quantifying the impact of natural disasters. The impact not limited to physical destructiveness. The impact extends to economy in the long term, and the psychology of the population. In this article we derive a general theory of quantification of the impact of natural...

Recently there has been an interest in utilizing recent advances in nonlinear partial differential equations solution methods, the equivalent description by stochastic calculus methods, and the state function level of information entropy to the solution of several nonlinear PDEs that are well...

Recently the approach of the Feynman parametrization of the wave equation for the obtaining of the photon propagator has been noted as a parametrization much similar to a derivation of the wave equation as a 4D 1p thermodynamics derived diffusion-Schroedinger equation. The 5D equation analogous...

We apply the Non-equilibrium Green's functions formalism (NEGF) to the case of Ferro Magnet-Insulator-Ferro Magnet (FM-I-FM) and the Ferro magnet-Ballistic Conductor-Ferro magnet (FM-BC-FM) heterostructures. The spin dependence in the Ferro-magnetic reservoirs respectively. The current-voltage...

The interest in the microscopic modeling of the dynamics of the social interactions of human beings from the interacting statistical approach has seen increased application due to its success. Recent approaches have included multi-agent models, generalized spin models, genetic algorithms, etc.....