The deformation is the mathematical concept. The Sylvester-Gallai Theorem is that a finite set of points in the plane have the proper line through any two of them, and it passes through a third point of the set. Moreover, it must be on the same line. P is the the noncollinear finite set. S(P) is the set of connecting lines in P. p∈P, s∈S(P) p and s are perpendicular, so they are not the ordinary line. (s*,p*) is the smallest distance, and s* is in the ordinary line. l∩P={p} l must be the ordinary line. This is the contradiction. l∩S(P) There is the cyclically intersection points (p,x1). x1,・・・xk is on l. Moreover it crosses S. This must be ordinary. You also see the extra dimensions. i lines are determined by P.
Hybrid orbitals are the explanation of molecular geometry and atomic bonding. This is Montgomery's pair correlation conjecture, which is the pair correlation between pairs of zeros of the Riemann zeta function . γ and γ' are imaginary. This is like piling prime numbers . Methane and hydrogen are gasses. C=C is carbon bonding which is in surface. Gasses move like ↑ ↑ ↓. This is called π bond.
MOF is the metal–organic framework. Chemistry is recently calculating. NM125-TiO2 is the MOF-metal oxide composite material. The sensing ability of NM125-TiO2 for over 100 human-breath compounds spanning 13 different diseases is examined. gray = carbon, white = hydrogen, red = oxygen, blue = nitrogen The black line is the DOS which is density of states, the red line is the Gaussian function , and the blue line is the Gaussian-weighted DOS. The DOS of the NM125-TiO2 structure is calculated.
コメント