The order of finite algebraic fundamental groups of surfaces with K^2<=3\chi-2
We study the structure of the algebraic fundamental group for minimal surfaces of general type S satisfying K_S^2<=3\chi-2$ and not having any irregular etale cover. We show that, if K_S^2<=3\chi-2, then then the algebraic fundamental group of S has order at most 5, and equality only occurs if S is a Godeaux surface. We also show that if K_S^2<= 3\chi-3 and the algebraic fundamental group of S is not trivial, then it is Z_2, or Z_2^2 or Z_3. Furthermore in this last case one has: 2<=\chi<=4, K^2=3\chi-3 and these possibilities do occur.
Minimal algebraic surfaces of general type with $c^2_1 = 3, p_g = 1 \text{ and } q = 0$, which have non-trivial 3-torsion divisors
We shall give a concrete description of minimal algebraic surfaces X’s defined over C of general type with the first chern number 3, the geometric genus 1 and the irregularity 0, which have non-trivial 3-torsion divisors. Namely, we shall show that the fundamental group is isomorphic to Z/3, and that the canonical model of the universal cover is a complete intersection in P of type (3, 3).
Numerical Simulation of Thermal Sensitivity for Explosives
In order to compare the thermal sensitivity of several typical explosives, this article solved numerically one-dimensional transient heat conduction equation including thermal decomposition for explosives with finite difference method. The explicit difference equations under different boundary conditions were established, and the corresponding stability criterion was derived. The ignition times for typical explosives were calculated, which was used to evaluate thermal sensitivity of explosives.