we observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds are left-invariant. The main purpose of this note is to give an example of a six-dimensional compact solvmanifold which admits a continuous family of non-leftinvariant complex structures. We also determine all three-dimensional compact complex-homogeneous pseudo-Kähler solvmanifolds.

Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct boundary element method, we numerically obtain the low-lying eigenmodes on a com...

We investigate the sample complexity for learning using higher-order neurons. We calculate upper and lower bounds on the Vapnik-Chervonenkis dimension and the pseudo dimension for higher-order neurons that allow unrestricted interactions among the input variables. In particular, we show that the degree of interaction is irrelevant for the VC dimension and that the individual degree of the varia...

In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based on a new closure relation that involves not only the average degree but also the second and third moments of the degree distribution. Its derivation uses an...

the effective removal of dyes from aqueous wastewaters is among the most important issues formany industrialized countries. removal of congo red (cr) dye from aqueous solutions was studiedusing nickel oxide nanoparticles. the operating variables studied were initial ph of solution,adsorbents dosage, temperature and contact time. the morphological information of nickel oxidenanoparticles were ch...