Unified Equation of Fundamental Forces’ Coupling Values, and the Existence of Subsequent, Fifth and Other, Forces

This paper provides an equation to entangle all known fundamental forces by employing their coupling constants, i.e., strong (αs), electromagnetic (α), weak (αw), and gravitational (αg) interaction coupling values. The constant coupling formulation is further indicative of many other fundamental forces with significantly weaker coupling values. As an example, the fifth fundamental force, Kashi’s Force, is found to have a coupling constant of 10-1446, which is significantly smaller than the smallest known fundamental force, gravitational force, with an approximate coupling constant value of 10-38. Additionally, the paper finds the sum of all fundamental forces based on the equation proposed is equal to 0.118065, which is within the range of effective world value of the strong coupling constant αs(M2z).

BSDES IN GAMES,COUPLED WITH THE VALUE FUNCTIONS.ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.

Investigation of the Spin Crossover Complex [Fe(bapbpy)(NCS)_2 ] in Its Low-spin and Highspin State by DFT/TD-DFT/BS-DFT Calculations

The spin crossover（SCO） compound [Fe（bapbpy）（NCS）2],where bapbpy contains two fused N,N-bis（2-pyridyl）amines,has been studied by DFT/TD-DFT/BS-DFT methods.Several density functionals and basis sets were used in the calculation to obtain optimized geometries of the compound in the low-（LS） and high-spin（HS） states.The vibrational modes and IR spectra,spin splitting energies,excited states and UV/Vis absorption spectra were obtained.The structural parameters of the calculated isolated complex are in good agreement with the X-ray data.We investigate three dimers of [Fe（bapbpy）（NCS）2] complex for their magnetic properties.It has been found that the complex（1,3） has ferromagnetic character while the others are antiferromagnetic in nature by using a broken symmetry approach in the DFT framework（BS-DFT） with support from the coupling constant values（J） and spin density plots.

A DUAL COUPLED METHOD FOR BOUNDARY VALUE PROBLEMS OF PDE WITH COEFFICIENTS OF SMALL PERIOD

In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.