Paul’s Use of Leviticus 19:18: A Comparative Analysis with Select Second Temple Jewish Texts

Paul’s use of Leviticus 19:18 in Romans 13:8-10 and Galatians 5:13-15 begs the question of how a command that is not repeated in the Old Testament came to the position of prominence as the summarizing and fulfilling statement of the whole law. This study aims to analyze select Second Temple Jewish texts and Paul’s letters to the Romans and Galatians in order to trace the uses of or allusions to Leviticus 19:18 and determine how Paul’s use of Leviticus 19:18 compares and differs from the selected texts. The Second Temple Jewish texts that are analyzed include the Testaments of the Twelve Patriarchs, Tobit 4:15, Bavli Shabbat 31a, the Damascus Document, and the Community Rule. The comparative analysis reveals that Paul’s use of Leviticus 19:18 in Romans 13:8-10 and Galatians 5:13-15 is shaped by the crucifixion of Jesus Christ and is thus unique when compared to preceding and contemporary Second Temple Jewish texts

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter beta>0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. We prove that the method is strongly stable when beta > -lambda_k where lambda_k is the k'th Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.Comment: 14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 k

Eigenfunctions for smooth expanding circle maps

We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.Comment: 10 pages, 2 figure

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the Molecular Dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.Comment: 21 pages, 2 figures, Revtex. Submitted to Phys. Rev.

A Geometric, Dynamical Approach to Thermodynamics

We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself micro-canonically observable. In particular, temperature, specific heat and higher order derivatives of the entropy can be observed dynamically. We give perturbative, asymptotic formulas by which the canonical ensemble itself can be reconstructed from micro-canonical measurements only. In a purely micro-canonical approach we rederive formulas by Lebowitz et al \cite{LPV}, relating e.g. specific heat to fluctuations in the kinetic energy. We show that under natural assumptions on the fluctuations in the kinetic energy the micro-canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy.Comment: 7 pages, LaTeX, uses RevTex. New sections and examples using fluctuations in the kinetic energy adde

Measuring Nonequilibrium Temperature of Forced Oscillators

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We invent a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.Comment: 8 page

A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures, compressed and encoded with uufiles, 170 k