at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

The aim of this paper is the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces etc. using corresponding known compact Riemannian ones. This construction is based on the notion of a certain duality between compact and non-compact homogeneous spaces.

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.

helicopter-borne electromagnetic (hem) is a fast and high resolution airborne electromagnetic (aem) method that is frequently used for imaging of the subsurface resistivity structures. this is a versatile and cost effective method, frequently has used in mineral and groundwater exploration and various environmental problems. modern frequency-domain hem systems utilize small electromagnetic, mag...

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...