We consider an equivariant analogue of a conjecture of Borcherds. Let (Y, σ) be a real K3 surface without real points. We shall prove that the equivariant determinant of the Laplacian of (Y, σ) with respect to a σ-invariant Ricci-flat Kähler metric is expressed as the norm of the Borcherds Φ-function at the “period point”. Here the period of (Y, σ) is not the one in algebraic geometry.

We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews’s determinant.

The angular distributions of photoelectrons from atomic oxygen, nitrogen and carbon are calculated. Both Hartree-Fock and Hartree-Slater (Herman-Skillman) wave functions are used for oxygen, and the agreement is excellent; thus only Hartree-Slater functions are used for carbon and nitrogen. The pitch angle distribution of photoelectrons is discussed and it is shown that previous approximations ...

chrome c in solution is reduced very rapidly by a number of reducing agents, e.g. ascorbic acid which reduce the cytochrome c in the heart-muscle preparation much more slowly (Slater, 1949 b). Thus the various 'cytochrome reductases' which have been isolated may be the appropriate diaphorase, which when reduced, can be reoxidized either by methylene blue or cytochrome c in solution, but which i...

The form of a real AT-body fermion wave function when expanded in Slater determinants of natural orbitals is investigated using a computer. I t is found that in the case when the number of natural orbitals is N f 2 there is a considerable reduction in the number of Slater determinants required. This offers the possibility of calculating atomic wave functions which are significantly more accurat...

In this Review we show several mathematical techniques that can be used in molecular calculations using Slater orbitals, like the transformation of the Hamiltonian, derivatives of spherical harmonics with respect to the angles, and angular transformations. We treat several kinds of integrals in detail: the exchange, Coulomb and hybrid repulsion and exchange correlated integrals, and the three-c...

We study a mixed–state Schrödinger–Poisson–Slater system (SPSS). This system combines the nonlinear and nonlocal Coulomb interaction with a local potential nonlinearity known as the ”Slater exchange term” which models a fermionic effect. The origin of the model is explained and related models are also proposed. Existence, uniqueness and regularity of local–in–time and global solutions are analy...

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the N -particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of...