Divisiveness, National Narratives, and the Establishment Clause

The Supreme Court habitually justifies the Establishment Clause as a means to prevent political division, protect the civil peace, and forestall citizen alienation. In spite of this popularity among the judiciary, legal scholars have emphatically rejected the political division theory. They state that religion is not especially divisive, and that even if it was, there is no reason to think non-establishment will prevent such political harm. This rejection relies on the misconception that the validity of the political division theory requires that all forms of religion must foment civil strife. This is a mistake. Often, laws apply to a wider category than to the core of what they seek to address. If this is the case, then even if non-establishment comes to merely prevent an especially erosive type of state and religion involvement, it may still be a valid and useful theory. In this Article, I argue that the political division theory is compelling when it is applied to a religion which seeks to collapse the distinction between politics and religion. To achieve this, I portray one such form of establishment of religion: American Christian Nationality, an ideology which sees the United States as having deep religious meaning and promotes Christianity as the central attribute of American identity. This Article will show that the combination between nationality and religion is uniquely divisive because it promotes a religious-based exclusionary understanding of who is a “real” American citizen. Many of the canonical Establishment Clause doctrines seem tailored to protect against government involvement in such religious movements

Legendre Polynomials Roots and the FF-Pure Threshold of bivariate Forms

We provide a direct computation of the $F$-pure threshold of degree four homogeneous polynomial in two variables and, more generally, of certain homogeneous polynomials with four distinct roots. The computation depends on whether the cross ratio of the roots satisfies a specific M\"{o}bius transformation of a Legendre polynomial. We then make a connection between a long lasting open question, involving the relationship between the $F$-pure and the log canonical threshold, and roots of Legendre polynomials over $\mathbb{F}_p$

Four-Brane and Six-Brane Interactions in M(atrix) Theory

We discuss the proposed description of configurations with four-branes and six-branes in m(atrix) theory. Computing the velocity dependent potential between these configurations and gravitons and membranes, we show that they agree with the short distance string results computed in type IIa string theory. Due to the ``closeness'' of these configuration to a supersymmetric configuration the m(atrix) theory reproduces the correct long distance behavior.Comment: 14 pages, late

Lepton Masses and Mixing Angles with Spontaneously Broken O(3) Flavor Symmetry

We present a model based on an O(3) flavor symmetry and a minimal extension of the scalar sector to induce hierarchical breaking, O(3) -> O(2) -> SO(2) -> nothing. The model naturally accounts for all the known lepton parameters and yields various interesting predictions for others: (i) Neutrinos are nearly degenerate, m_\nu \sim 0.1 eV; (ii) The solar neutrino problem is solved by the MSW small mixing angle solution; (iii) The MNS mixing angle theta_{13} is unobservably small, theta_{13} = O(10^{-5}).Comment: 8 pages, LaTeX2e, published version, typos corrected and some of the notations were improve