Rings Over Which Cyclics are Direct Sums of Projective and CS or Noetherian

R is called a right WV -ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV -ring, then R is right uniform or a right V -ring. It is shown that for a right WV-ring R, R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS or noetherian module. For a finitely generated module M with projective socle over a V -ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X \oplus T, where X is semisimple and T is noetherian with zero socle. In the case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring, and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian.Comment: A Para\^itre Glasgow Mathematical Journa

A Characterization of Infinite LSP Words

G. Fici proved that a finite word has a minimal suffix automaton if and only if all its left special factors occur as prefixes. He called LSP all finite and infinite words having this latter property. We characterize here infinite LSP words in terms of $S$-adicity. More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and all its directive words are recognizable by ${\cal A}$

Activity Dependent Branching Ratios in Stocks, Solar X-ray Flux, and the Bak-Tang-Wiesenfeld Sandpile Model

We define an activity dependent branching ratio that allows comparison of different time series $X_{t}$. The branching ratio $b_x$ is defined as $b_x= E[\xi_x/x]$. The random variable $\xi_x$ is the value of the next signal given that the previous one is equal to $x$, so $\xi_x=\{X_{t+1}|X_t=x\}$. If $b_x>1$, the process is on average supercritical when the signal is equal to $x$, while if $b_x<1$, it is subcritical. For stock prices we find $b_x=1$ within statistical uncertainty, for all $x$, consistent with an ``efficient market hypothesis''. For stock volumes, solar X-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, $b_x$ is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power law behavior. For solar X-ray flux and the BTW model, there is a broad regime of activity where $b_x \simeq 1$, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for $X_t$, and for $\xi_x$. For the BTW model the distribution of $\xi_x$ is Gaussian, for $x$ sufficiently larger than one, and its variance grows linearly with $x$. Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where $b_x$ is close to one disappears once bulk dissipation is introduced in the BTW model -- supporting our hypothesis that it is an indicator of criticality.Comment: 7 pages, 11 figure

The Structure of a Low-Metallicity Giant Molecular Cloud Complex

To understand the impact of low metallicities on giant molecular cloud (GMC) structure, we compare far infrared dust emission, CO emission, and dynamics in the star-forming complex N83 in the Wing of the Small Magellanic Cloud. Dust emission (measured by Spitzer as part of the S3MC and SAGE-SMC surveys) probes the total gas column independent of molecular line emission and traces shielding from photodissociating radiation. We calibrate a method to estimate the dust column using only the high-resolution Spitzer data and verify that dust traces the ISM in the HI-dominated region around N83. This allows us to resolve the relative structures of H2, dust, and CO within a giant molecular cloud complex, one of the first times such a measurement has been made in a low-metallicity galaxy. Our results support the hypothesis that CO is photodissociated while H2 self-shields in the outer parts of low-metallicity GMCs, so that dust/self shielding is the primary factor determining the distribution of CO emission. Four pieces of evidence support this view. First, the CO-to-H2 conversion factor averaged over the whole cloud is very high 4-11 \times 10^21 cm^-2/(K km/s), or 20-55 times the Galactic value. Second, the CO-to-H2 conversion factor varies across the complex, with its lowest (most nearly Galactic) values near the CO peaks. Third, bright CO emission is largely confined to regions of relatively high line-of-sight extinction, A_V >~ 2 mag, in agreement with PDR models and Galactic observations. Fourth, a simple model in which CO emerges from a smaller sphere nested inside a larger cloud can roughly relate the H2 masses measured from CO kinematics and dust.Comment: 17 pages, 10 figures (including appendix), accepted for publication in the Astrophysical Journa

Lingulodinium machaerophorum expansion over the last centuries in the Caspian Sea reflects global warming

This article is made available through the Brunel Open Access Publishing Fund. Copyright @ Author(s) 2012. This work is distributed under the Creative Commons Attribution 3.0 License.We analysed dinoflagellate cyst assemblages in four short sediment cores, two of them dated by radionuclides, taken in the south basin of the Caspian Sea. The interpretation of the four sequences is supported by a collection of 27 lagoonal or marine surface sediment samples. A sharp increase in the biomass of the dinocyst occurs after 1967, especially owing to Lingulodinium machaerophorum. Considering nine other cores covering parts or the whole of Holocene, this species started to develop in the Caspian Sea only during the last three millennia. By analysing instrumental data and collating existing reconstructions of sea level changes over the last few millennia, we show that the main forcing of the increase of L. machaerophorum percentages and of the recent dinocyst abundance is global climate change, especially sea surface temperature increase. Sea level fluctuations likely have a minor impact. We argue that the Caspian Sea has entered the Anthropocene

Rotational cooling of molecules using lamps

We investigate theoretically the application of tailored incoherent far-infrared fields in combination with laser excitation of a single rovibrational transition for rotational cooling of translationally cold polar diatomic molecules. The cooling schemes are effective on a timescale shorter than typical unperturbed trapping times in ion traps and comparable to obtainable confinement times of neutral molecules.Comment: 5 pages, 2 figure

Solar rotation rate and its gradients during cycle 23

Available helioseismic data now span almost the entire solar activity cycle 23 making it possible to study solar-cycle related changes of the solar rotation rate in detail. In this paper we study how the solar rotation rate, in particular, the zonal flows change with time. In addition to the zonal flows that show a well known pattern in the solar convection zone, we also study changes in the radial and latitudinal gradients of the rotation rate, particularly in the shear layer that is present in the immediate sub-surface layers of the Sun. In the case of the zonal-flow pattern, we find that the band indicating fast rotating region close to the equator seems to have bifurcated around 2005. Our investigation of the rotation-rate gradients show that the relative variation in the rotation-rate gradients is about 20% or more of their average values, which is much larger than the relative variation in the rotation rate itself. These results can be used to test predictions of various solar dynamo models.Comment: To appear in ApJ. Fig 5 has been corrected in this versio

Can we estimate the impact of small targeted dietary changes on human health and environmental sustainability?

A recent analysis by Stylianou et al. (2021) estimated the impact of small dietary changes in the consumption of individual foods on human health and the environment, expressed as minutes of healthy life lost or gained daily combined with dietary carbon footprints. While an appealing concept given its simplistic interpretation, we aim to draw the attention of nLCA practitioners and developers to the significant limitations and uncertainties of this analysis, based on existing evidence. Stylianou's approach produces results that fail to recognize the importance of essential nutrient density and the risks associated with ultra-processed foods, added sugar, and refined starches. The novel impact assessment undoubtedly brings a new perspective to the growing field of nutritional Life Cycle Assessment. However, the authors neglect numerous methodological limitations, fail to direct the readers' attention to (mis)interpretation risks, and draw highly definitive recommendations aiming to directly influence consumer choices and policymaking. Due to extensive data limitations and associated uncertainties in extant databases (both environmental and nutritional), we recommend caution in the use of this (or any other) food classification system to inform consumer behavior, front-of-package labelling, policies, and programs