For each natural odd number n ≥ 3, we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1. As a consequence, Shafarevich's conjecture holds true for these families. Moreover, it follows from Deligne and Mostow (Publ. Math. IHÉS, 63:5-89, 1986) and Mostow (Publ. Math. IHÉS, 63:91-106, 1986; J. Am. Math. Soc., 1(3): 1988) that, for n = 3, it can be partially compactified to a Shimura family of ball type, and for n = 5, 9, there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.

Let M n,2n+2 be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of P n branched along 2n + 2 hyperplanes in general position. We show that the monodromy group of a good family for M n,2n+2 is Zariski dense in the corresponding symplectic or orthogonal group if n ≥ 3. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever n ≥ 3. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of m ordered points in P n is shown to be large once it is not a point. Similar Zariski-density result is obtained for moduli spaces of CY manifolds arising from cyclic covers of P n branched along m hyperplanes in general position. A classification towards the geometric realization problem of B. Gross for type A bounded symmetric domains is given.

For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigen linear subspace of the middle cohomology of the fiber. We prove the monodromy group is Zariski dense in the corresponding linear group. It can be viewed as a degenerate analogy of Carlson-Toledo's result about the monodromy groups of smooth hypersurfaces [Duke Math. J. 97(3) (1999), 621-648]. The main ingredient in the proof is a Picard-Lefschetz type formula for a suitable degeneration of this family.

To improve the efficiency of the electric vehicle wireless charging system, an optimization design method for the number of coil layers is proposed and studied, which effectively improves the coupling coefficient of the magnetic circuit mechanism. This article first analyzes the energy efficiency characteristics of the wireless charging system for electric vehicles. Then, it analyzes the inductance value changes and magnetic field distribution characteristics of fixed turns coils under different layers. The finite element simulation results performed by MAXWELL show that inducing the number of primary coil layers and increasing the number of secondary coil layers are conducive to the improvement of the coupling coefficient between the coils. Then, based on the theoretical analysis results, the number of coil turns of each layer of the multilayer coil is analyzed and optimized, and a bowl-shaped pair multilayer coil winding method is proposed.

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