Cosmical Imaginary and Gravitational Particles and Their Scientific Analytical Calculuses

The linear and spatial and temporal motions can all twin rotation and vibration. The entanglement of the former twins relies on the latter two, and entangles fundamental forces in sequence. The latter two entangle imaginary and gravitational particles sequentially, the comprehensive dimensionalities of their entanglements reveal various physical essences, hence it creates the resplendent world of matter and energy. These entanglements bring about the expansion of Special Relativity to General Relativity. These particles possess the differential and dimensional variabilities, which require to manipulate the differential variations (namely differential increment and domain) to maximally optimize differentiation, and govern the dimensional variations (videlicet dimensional exchange and involution) to timely replace integration, and eradicate the approximate estimation of limit theory to completely exterminate errors. The scientific analytical calculus emerges as these requirements, its integration embraces the extensive operations (e.g., summation, factorial, function, wavelet, etc.). The equations of these particles are confirmed by the theoretical inferences and experimental data and results. The evolutionary Euler's formula shines upon particle and wave as well as dimensionality of particle, the subtraction and addition of the analytical formula of quadratic difference in Einstein's linear motional corrective equation (namely high and low frequencies of wavelet) reveal rotation and vibration, the orbital radii and motions of the Earth and electron glimpse the gravitational constant, all of them demystify these particles from different perspectives.