THE JEWISH DIETARY LAWS AND THEIR FOUNDATION

While food and drug law has made its greatest contributions to the health and welfare of society over the past two centuries, it is indisputable that the history of this body of law is much older than two hundred years.1 Soon after man realized he needed to eat, he recognized a need to establish rules and regulations governing the sale, preparation and handling of food. Perhaps the oldest documented set of food laws are the Jewish dietary laws, also known by the Hebrew term, kashrut, from which the word "kosher" is derived. Unlike most laws related to food, which are enacted by society through government or other rule-making bodies, Jewish dietary laws are believed to be conceptualizations of divine will that were expressed to Moses at Mount Sinai and transcribed in the Old Testament.2 Intellectual curiosity and an interest in the evolution of food and drug law compel both Jews and Gentiles to study the Jewish dietary laws. For observant Jews, however, Jewish dietary laws possess unique significance. Kashrut is one of the pillars of Jewish religious life and virtually every aspect of eating and preparing food implicates some Jewish dietary law. While the First Amendment prevents any governmental enforcement of religious law, for those who are strict practitioners of the Jewish religion, the observance of Jewish dietary laws is every bit as important and compelling as is the observance of secular law. Despite the important role Jewish dietary laws play in the lives of many, few give much thought to the foundations of and rationales for kashruz. After describing the Jewish dietary laws and their origin, this paper will present and analyze some Judaic and secular scholarly attempts at explaining the underpinnings of these laws. The Pentateuch does not explicitly explain the reasons for the laws, which has made this issue a popular topic for debate among Biblical scholars. While the arguments these scholars make for their positions are logical and often convincing, it is important to remember that an accepted principle of jurisprudence and legal philosophy is that "unless a code of law itself states the underlying idea of a law, any theory about that idea remains conjecture

Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases

We report on the observation of sympathetic cooling of a cloud of fermionic 6-Li atoms which are thermally coupled to evaporatively cooled bosonic 87-Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |a_s|=20_{-6}^{+9} a_B. We found that the presence of residual rubidium atoms in the |2,1> and the |1,-1> Zeeman substates gives rise to important losses due to inelastic collisions.Comment: 4 pages, 3 figure

Broken symmetries and pattern formation in two-frequency forced Faraday waves

We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.Comment: 4 pages, 6 figure

Super-lattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the non-monotonic dispersion relation of a ferrofluid

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

НАУКОВІ ДОСЛІДЖЕННЯ ВЧЕНИХ КВГУ-КГІ-ДГІ В ГАЛУЗІ МЕТАЛУРГІЇ (1900-1930 рр.)

Перші зародки промислового вуглевидобутку на Півдні Російської імперії (Лисячий Байрак під Лисичанськом) і виробництва металу (м. Луганськ) виник-ли у 90-х роках ХVІІІ с. У наступні десятиліття ці взаємопов’язані галузі розвивалися дуже повільно. А трохи раніше спроба почати видобуток залізної руди і виплавку з неї гарматних ядер на Криворіжжі була невдалою, тому майже на сто років про ці поклади руд забули

The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur

Bifurcations of periodic orbits with spatio-temporal symmetries

Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on bifurcations of group orbits of spatially symmetric equilibria. Two examples, two-dimensional pulsating waves (PW) and three-dimensional alternating pulsating waves (APW), have discrete spatio-temporal symmetries characterized by the cyclic groups Z_n, n=2 (PW) and n=4 (APW). These symmetries force the Poincare' return map M to be the nth iterate of a map G: M=G^n. The group orbits of PW and APW are generated by translations in the horizontal directions and correspond to a circle and a two-torus, respectively. An instability of pulsating waves can lead to solutions that drift along the group orbit, while bifurcations with Floquet multiplier +1 of alternating pulsating waves do not lead to drifting solutions. The third example we consider, alternating rolls, has the spatio-temporal symmetry of alternating pulsating waves as well as being invariant under reflections in two vertical planes. This leads to the possibility of a doubling of the marginal Floquet multiplier and of bifurcation to two distinct types of drifting solutions. We conclude by proposing a systematic way of analysing steady-state bifurcations of periodic orbits with discrete spatio-temporal symmetries, based on applying the equivariant branching lemma to the irreducible representations of the spatio-temporal symmetry group of the periodic orbit, and on the normal form results of Lamb (1996). This general approach is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems