Extension theorems for functions of vanishing mean oscillation

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^d converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O(ρ(l(Q))) where l(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0⁺) = 0.

We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.

Efficient laser oscillation of Yb : Y3Al5O12 single crystal grown by temperature gradient technique

Low-threshold and highly efficient continuous-wave laser performance of Yb:Y3Al5O12 (Yb:YAG) single crystal grown by a temperature gradient technique (TGT) was achieved at room temperature. The laser can be operated at 1030 and 1049 nm by varying the transmission of the output coupler. Slope efficiencies of 57% and 68% at 1049 and 1030 nm, respectively, were achieved for 10 at. % Yb:YAG sample in continuous-wave laser-diode pumping. The effect of pump power on the laser emission spectrum of both wavelengths is addressed. The near-diffraction-limited beam quality for different laser cavities was achieved. The excellent laser performance indicates that TGT-grown Yb:YAG crystals have very good optical quality and can be potentially used in high-power solid-state lasers.

Variation in yellowfin tuna (Thunnus albacares) catches related to El Niño-Southern Oscillation events at the entrance to the Gulf of California

Fishery catch data on yellowfin tuna (Thunnus albacares) were examined to study the effects of El Niño events between 1990 and 1999 for an area in the northeastern tropical Pacific (18−24°N, 112−104°W). The data were extracted from a database of logbook records from the Mexican tuna purse-seine f leet. Latitudinal distribution of the catches increased from south to north for the 10-year period. Highest catches and effort were concentrated between 22°N and 23°N. This area accumulated 48% of the total catch over the 10year period. It was strongly correlated with El Niño-Southern Oscillation (ENSO) events. At least two periods of exceptionally high catches occurred following El Niño events in 1991 and 1997. Peaks of catches were triggered by the arrival of positive anomalies of sea surface temperature (SST) to the area. A delay of two to four months was observed between the occurrence of maximum SST anomalies at the equator and peaks of catch. Prior to these two events, negative SST anomalies were the dominant feature in the study area and catch was extremely low. This trend of negative SST anomalies with low catches followed by positive SST anomalies and high catches may be attributed to northward yellowfin tuna migration patterns driven by El Niño forcing, a result that contrasts with the known behavior of decreasing relative abundance of these tuna after El Niño events in the eastern Pacific. However, this decrease in relative abundance may be the result of a local or subregional effect.

Co-oscillation of a fjord basin’s circulation with decade-long oceanographic, hydrologic, and climatic regimes: Puget Sound 1916-'87 [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Oceanographic, hydrologic, and climatic data collected during 1916-'87 in Puget Sound's Main Basin (~200 m x 5 km x 100 km) and approaches oscillate at low frequency between two regimes (I, II). The oscillation accounts for a large fraction of the interannual variability (41-75%) and the zero crossings between regimes span approximately a decade. ... The transition between regimes is accompanied by substantial changes in the horizontal pressure and density fields between the Pacific coast and the mixing zones leading to the Basin, as well as within the Basin itself.

Effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean off Java

The effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean (EIO) off Java were evaluated through the use of remotely sensed environmental data (sea-surface-height anomaly [SSHA], sea-surface temperature [SST], and chlorophyll a concentration), and Bigeye Tuna catch data. Analyses were conducted for the period of 1997–2000, which included the 1997–98 El Niño and 1999–2000 La Niña events. The empirical orthogonal function (EOF) was applied to examine oceanographic parameters quantitatively. The relationship of those parameters to variations in catch distribution of Bigeye Tuna was explored with a generalized additive model (GAM). The mean hook rate was 0.67 during El Niño and 0.44 during La Niña, and catches were high where SSHA ranged from –21 to 5 cm, SST ranged from 24°C to 27.5°C, and chlorophyll-a concentrations ranged from 0.04 to 0.16 mg m–3. The EOF analysis confirmed that the 1997–98 El Niño affected oceanographic conditions in the EIO off Java. The GAM results indicated that SST was better than the other environmental factors (SSHA and chlorophyll-a concentration) as an oceanographic predictor of Bigeye Tuna catches in the region. According to the GAM predictions, the highest probabilities (70–80%) for Bigeye Tuna catch in 1997–2000 occurred during oceanographic conditions during the 1997–98 El Niño event.

Uncovering North American temperature and precipitation patterns associated with the Southern Oscillation

The extreme phases of the Southern Oscillation (SO) have been linked to fairly persistent classes of circulation anomalies over the North Pacific and parts of North America. It has been more difficult to uncover correspondingly consistent patterns of surface temperature and precipitation over much of the continent. The few regions that appear to have consistent SO-related patterns of temperature and precipitation anomalies are identified and discussed. Also discussed are regions that appear to have strong SO-related surface anomalies whose sign varies from episode to episode.

El Niño-Southern Oscillation (ENSO) phenomena and forest fires in the southwestern United States

Fire statistics (area burned) and fire-scar chronologies from tree rings show reduced fire activity during El Niño-Southern Oscillation (ENSO) in forests of Arizona and New Mexico. This relationship probably stems from increased fuel moisture after a wet winter and spring, but also could involve climatic controls on lightning activity at the onset of the monsoon season.

Centennial oscillation of the climatic crescendo during the last glacial maximum: evidence from Lake Estancia, central New Mexico

Sediments deposited in late Pleistocene Lake Estancia, central New Mexico, contain a paleoclimatic record that includes the last glacial maximum and deglacial episode. Stratigraphic reconstruction of an interval representing the highstand of the lake that occurred during the last glacial maximum reveals ~2000-, ~600-, and ~200-year oscillations in lake level and climate. Shifting position of the polar jetstream in response to expansion and contraction of the North American ice sheet may be partly responsible for the millenial-scale changes in Lake Estancia but probably does not explain the centennial-scale oscillations.

South American streamflow and the extreme phases of the Southern Oscillation

This study investigates the extent of the affect [sic] of the El Niño/Southern Oscillation on South American streamflow. The response of South American precipitation and temperature to the extreme phases of ENSO (El Niño and La Niña events) is well documented; but the response of South American hydrology has been barely studied. Such paucity of research contrasts sharply with that available on the response of North American streamflow to ENSO events.

Temperature dependences of oscillation parameters in ferroelectric liquid crystals

Oscillation processes have been revealed in the course of reversible polarization study in ferroelectric liquid crystals. The oscillation frequency of polarization vector has been found to be from 1 to 30 kHz. The oscillation parameters were studied as functions of temperature. Temperature dependences of the oscillation amplitude and damping decrement have been measured.