A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc − I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Šajna in 2004. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In par...

The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method. We explore the internal xc hole components, showing that they share properties with thos...

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density-functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a spaceand frequency-dependent discontinuity of the XC kernel that diverges as r → ∞. In a combined donor-acceptor syst...

Let XR be the zero locus in RP n of one or two independently and Weyl distributed random real quadratic forms. Denoting by XC the complex part in CP n of XR and by b(XR) and b(XC) the sums of their Betti numbers, we prove that: (1) lim n→∞ Eb(XR) n = 1. In particular for one quadric hypersurface asymptotically Smith’s inequality b(XR) ≤ b(XC) is expected to be sharp. The methods we use combine ...

In this work, we report on the deposition of microcrystalline silicon (µc-Si:H) films produced from silane (SiH4), hydrogen (H2), and argon (Ar) mixtures using plasma-enhanced chemical vapor (PECVD) technique at 200 °C. Particularly, studied effect RF power crystalline fraction (XC) deposited films, have correlated XC with their optical, electrical, structural characteristics. Different types c...

It is shown that the errors of present-day exchange-correlation (XC) functionals are rather short ranged. For extended systems, the correction can therefore be evaluated by analyzing properly chosen clusters and employing highest-quality quantum chemistry methods. The XC correction rapidly approaches a universal dependence with cluster size. The method is applicable to bulk systems as well as t...

Bond-dilution effects on spin-1/2 spin-gapped Heisenberg antiferromagnets of coupled alternating chains on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that, in contrast with the site-diluted system having an infinitesimal critical concentration, the bond-diluted system has a finite critical concentration of diluted bonds, xc, above which the system ...

Let Σ be a compact orientable surface with genus g and n boundary components B = (B1, . . . , Bn). Let c = (c1, . . . , cn) ∈ [−2, 2]n. Then the mapping class group MCG of Σ acts on the relative SU(2)-character variety XC := HomC(π,SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(Bi)) = ci. This action preserves a symplectic structure on the smooth part of XC , and the ...