Primary ideal theory for quadratic Jordan algebras

AbstractThe notion of a primary ideal was originally introduced in the study of noetherian rings, i.e., commutative associative rings with unity which have the maximum condition on ideals. In more recent years, this notion has been carried over to noncommutative associative rings and nonassociative rings (see [3]). In this paper, we shall give a definition and basic properties for (inner) primary ideals in a quadratic Jordan algebra based on the concept of prime ideals in Jordan algebras as discussed in [10]. We then give a necessary and sufficient condition for those algebras in which the well-known Lasker-Noether decomposition theorem holds. Finally, the analog of the tertiary ideal is discussed, and we show that in any quadratic Jordan algebra which has the maximum condition on ideals, all ideals can be represented as a finite intersection of tertiary ideals

Anomalous physical properties of underdoped weak-ferromagnetic superconductor RuSr2_2EuCu2_{2}O8_{8}

Similar to the optimal-doped, weak-ferromagnetic (WFM induced by canted antiferromagnetism, T$_{Curie}$ = 131 K) and superconducting (T$_{c}$ = 56 K) RuSr$_{2}$GdCu$_{2}$O$_{8}$, the underdoped RuSr$_{2}$EuCu$_{2}$O$_{8}$ (T$_{Curie}$ = 133 K, T$_{c}$ = 36 K) also exhibited a spontaneous vortex state (SVS) between 16 K and 36 K. The low field ($\pm$20 G) superconducting hysteresis loop indicates a weak and narrow Meissner state region of average lower critical field B$_{c1}^{ave}$(T) = B$_{c1}^{ave}$(0)[1 - (T/T$_{SVS}$)$^{2}$], with B$_{c1}^{ave}$(0) = 7 G and T$_{SVS}$ = 16 K. The vortex melting transition (T$_{melting}$ = 21 K) below T$_{c}$ obtained from the broad resistivity drop and the onset of diamagnetic signal indicates a vortex liquid region due to the coexistence and interplay between superconductivity and WFM order. No visible jump in specific heat was observed near T$_{c}$ for Eu- and Gd-compound. This is not surprising, since the electronic specific heat is easily overshadowed by the large phonon and weak-ferromagnetic contributions. Furthermore, a broad resistivity transition due to low vortex melting temperature would also lead to a correspondingly reduced height of any specific heat jump. Finally, with the baseline from the nonmagnetic Eu-compound, specific heat data analysis confirms the magnetic entropy associated with antiferromagnetic ordering of Gd$^{3+}$ (J = S = 7/2) at 2.5 K to be close to $\it{N_{A}k}$ ln8 as expected.Comment: 7 figure

b-quark decay in the collinear approximation

The semileptonic decay of a b-quark, b--> c l nu, is considered in the relativistic limit where the decay products are approximately collinear. Analytic results for the double differential lepton energy distributions are given for finite charm-quark mass. Their use for the fast simulation of isolated lepton backgrounds from heavy quark decays is discussed.Comment: 7 pages, 1 figure, submitted to Phys.Rev.

Dynamical Properties of a Growing Surface on a Random Substrate

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force $F$ and temperature $T$. A continuous transition is found from high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.Comment: 10 pages, latex, 3 figures, to appear in Phys. Rev. E (RC

Expected seismicity and the seismic noise environment of Europa

Seismic data will be a vital geophysical constraint on internal structure of Europa if we land instruments on the surface. Quantifying expected seismic activity on Europa both in terms of large, recognizable signals and ambient background noise is important for understanding dynamics of the moon, as well as interpretation of potential future data. Seismic energy sources will likely include cracking in the ice shell and turbulent motion in the oceans. We define a range of models of seismic activity in Europa's ice shell by assuming each model follows a Gutenberg-Richter relationship with varying parameters. A range of cumulative seismic moment release between $10^{16}$ and $10^{18}$ Nm/yr is defined by scaling tidal dissipation energy to tectonic events on the Earth's moon. Random catalogs are generated and used to create synthetic continuous noise records through numerical wave propagation in thermodynamically self-consistent models of the interior structure of Europa. Spectral characteristics of the noise are calculated by determining probabilistic power spectral densities of the synthetic records. While the range of seismicity models predicts noise levels that vary by 80 dB, we show that most noise estimates are below the self-noise floor of high-frequency geophones, but may be recorded by more sensitive instruments. The largest expected signals exceed background noise by $\sim$50 dB. Noise records may allow for constraints on interior structure through autocorrelation. Models of seismic noise generated by pressure variations at the base of the ice shell due to turbulent motions in the subsurface ocean may also generate observable seismic noise.Comment: 24 pages, 11 figures, Added in supplementary information from revision submission, including 3 audio files with sonification of Europa noise records. To view attachments, please download and extract the gzipped tar source file listed under "Other formats

Site amplification, attenuation, and scattering from noise correlation amplitudes across a dense array in Long Beach, CA

For accurate seismic hazard evaluation, both the spatial and frequency-dependent variabilities in the amplitudes of earthquake ground motions are needed. While this information is rarely fully available due to the paucity of relevant seismic data, dense arrays like the 5200-geophone array in Long Beach, California provide the opportunity to study this amplitude variability. Here we show that ambient noise correlation amplitudes from the Long Beach array can be used to directly determine frequency-dependent site amplification factors. We analyze Rayleigh-wavefield amplitude gradients from ambient noise correlations that are processed so that relative amplitudes satisfy the wave equation and are therefore meaningful. Ultimately, we construct maps of site amplification across Long Beach at frequencies of 0.67, 1.0, and 2.0 Hz. These maps correlate well with local structure, notably the Newport-Inglewood Fault and also to known velocity structure. Through this process, we also obtain constraints on average attenuation structure and local scattering