CD Manuscript B and the Community Rule – Reflections on a Literary Relationship

This article begins by noting the proliferation of textual overlap between the Damascus Document and the Rule of the Community. Some examples of such overlap, such as the penal code, have received a large amount of scholarly attention in the wake of the publication of all the Cave 4 manuscripts. This study returns to a passage from CD manuscript B (CD 20:1b-8a) that has long been recognized as closely related to 1QS 8-9 and offers a reconsideration of the relationship between both texts in the light of the full publication of all the S manuscripts. The analysis offered here uncovers a complex inter-relationship between both texts as well as some intriguing pointers towards a complex literary history within the S tradition

Almost group theory

The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup of such groups is shown to be nilpotent and a theorem of Hall for nilpotent groups is generalized to ind-definable almost nilpotent subgroups of $\widetilde{\mathfrak M}\_c$-groups

Nucleon self-energies for supernova equations of state

Nucleon self-energies and interaction potentials in supernova (SN) matter, which are known to have an important effect on nucleosynthesis conditions in SN ejecta are investigated. Corresponding weak charged-current interaction rates with unbound nucleons that are consistent with existing SN equations of state (EOSs) are specified. The nucleon self-energies are made available online as electronic tables. The discussion is mostly restricted to relativistic mean-field models. In the first part of the article, the generic properties of this class of models at finite temperature and asymmetry are studied. It is found that the quadratic expansion of the EOS in terms of asymmetry works reasonably well at finite temperatures and deviations originate mostly from the kinetic part. The interaction part of the symmetry energy is found to be almost temperature independent. At low densities, the account of realistic nucleon masses requires the introduction of a linear term in the expansion. Finally, it is shown that the important neutron-to-proton potential difference is given approximately by the asymmetry of the system and the interaction part of the zero-temperature symmetry energy. The results of different interactions are then compared with constraints from nuclear experiments and thereby the possible range of the potential difference is limited. In the second part, for a certain class of SN EOS models, the formation of nuclei is considered. Only moderate modifications are found for the self-energies of unbound nucleons that enter the weak charged-current interaction rates. This is because in the present approach the binding energies of bound states do not contribute to the single-particle energies of unbound nucleons.Comment: 25 pages, 12 figures, v3: editorial corrections, matches published versio

On n-dependent groups and fields

First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IPn property for all natural numbers n and certain properties of dependent (NIP) valued fields extend to the n-dependent context

The Earthly Essene Nucleus of 1QSA

This article makes the case that the regulations for communal life in the central portions of 1QSa are much more closely related to the Damascus Document than to the Rule of the Community to which the text was physically attached. In particular, attention is drawn to shared characteristics such as, an all-Israel perspective; the presupposition of family life; a proliferation of congregation terminology in both 1QSa and D in contrast to the Community Rule; references to the Book of Hagi; and prescriptions for exclusion from the congregation of members with physical or mental disabilities. I conclude that 1QSa 1:6-2:11a comprises communal legislation that originated with the parent movement of the Yaḥad – also attested in the communal legislation in the Damascus Document – which was secondarily inserted into its present eschatological context. <br/

Spectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview

We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to weak coupling between the period cells. Weak coupling of periodic systems frequently produces spectral gaps or spectral concentration. Our examples include Schr\"odinger operators, elliptic operators in divergence form, Laplace-Beltrami-operators, Schr\"odinger and Pauli operators with periodic magnetic fields. There are corresponding applications in heat and wave propagation, quantum mechanics, and photonic crystals.Comment: 12 pages, 1 eps-figure, LaTe