Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

Existence of a solution to Hartree-Fock equations with decreasing magnetic field

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge Z of K nuclei exceeds N−1, where N is the number of electrons. In the opposite direction, no ground state exists if N>2Z+K

Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations

We establish existence of infinitely many distinct solutions to the Hartree-Fock equations for Coulomb systems with quasi-relativistic kinetic energy \sqrt{ -\a^{-2} D_{x_{n}} + \a^{-4}} -\a^{-2} for the $n^{\rm th}$ electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge $Z_{\rm tot}$ of $K$ nuclei is greater than or equal to the total number of electrons $N$ and that $Z_{\rm tot}$ is smaller than some critical charge $Z_{\rm c}$. The proofs are based on critical point theory in combination with density operator techniques

Uncertainty quantification of propagation in evaporation ducting

The Fourier split-step method is used for solving parabolic equations in, for example, computational electromagnetics. In this paper we develop a spectral based Fourier split-step method that will take a limited degree of information with regard to the refractive index of the atmosphere into account

Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators

We consider a system of nonlinear coupled equations involving magnetic Schrödinger operators and general potentials. We provide the criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of infinitely many distinct solutions within Hartree and Hartree–Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a “physically measurable” magnetic field

A spectral expansion-based Fourier split-step method for uncertainty quantification of the propagation factor in a stochastic environment

A chaos expanded Fourier split-step method is derived and applied to a narrow-angle parabolic equation. The parabolic equation has earlier been used to study deterministic settings. In this paper we develop a spectral-based Fourier split-step method that will take a limited degree of information about the environment into account. Our main focus is on proposing an efficient method for computational electromagnetics in stochastic settings. In this paper we study electromagnetic wave propagation in the troposphere in the case when the refraction index belongs to a uniform distribution

High throughput generation of a resource of the human secretome in mammalian cells

The proteins secreted by human tissues and blood cells, the secretome, are important both for the basic understanding of human biology and for identification of potential targets for future diagnosis and therapy. Here, a high-throughput mammalian cell factory is presented that was established to create a resource of recombinant full-length proteins covering the majority of those annotated as ‘secreted’ in humans. The full-length DNA sequences of each of the predicted secreted proteins were generated by gene synthesis, the constructs were transfected into Chinese hamster ovary (CHO) cells and the recombinant proteins were produced, purified and analyzed. Almost 1,300 proteins were successfully generated and proteins predicted to be secreted into the blood were produced with a success rate of 65%, while the success rates for the other categories of secreted proteins were somewhat lower giving an overall one-pass success rate of ca. 58%. The proteins were used to generate targeted proteomics assays and several of the proteins were shown to be active in a phenotypic assay involving pancreatic β-cell dedifferentiation. Many of the proteins that failed during production in CHO cells could be rescued in human embryonic kidney (HEK 293) cells suggesting that a cell factory of human origin can be an attractive alternative for production in mammalian cells. In conclusion, a high-throughput protein production and purification system has been successfully established to create a unique resource of the human secretome.ISSN:1871-6784ISSN:1876-434