Stability in Terms of Two Measures for Differential Equations with “Maxima”

Атанаска Георгиева, Стела Глухчева, Снежана Христова - Изследвана е устойчивостта на нелинейни диференциални уравнения с “максимуми” по отношение на две мерки. Приложени са две различни мерки за началните условия и за решението. Използван е методът на Разумихин, а също така и методът на сравнението на обикновени скаларни диференциални уравнения. Приложението на получените резултати и достатъчни условия за устойчивост е илюстрирано с пример.

Integral Inequalities and Applications to Partial Differential Equations with “Maxima”

Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Revisiting Offspring Maxima in Branching Processes

2000 Mathematics Subject Classification: 60J80; 60G70.

Spatial and seasonal variability in elemental content, δ13C, and δ15N ofThalassia testudinum from South Florida and its implications for ecosystem studies

Elemental and isotopic composition of leaves of the seagrassThalassia testudinum was highly variable across the 10,000 km2 and 8 years of this study. The data reported herein expand the reported range in carbon:nitrogen (C:N) and carbon:phosphorus (C:P) ratios and δ13C and δ15N values reported for this species worldwide; 13.2–38.6 for C:N and 411–2,041 for C:P. The 981 determinations in this study generated a range of −13.5‰ to −5.2‰ for δ13C and −4.3‰ to 9.4‰ for δ15N. The elemental and isotope ratios displayed marked seasonality, and the seasonal patterns could be described with a simple sine wave model. C:N, C:P, δ13C, and δ15N values all had maxima in the summer and minima in the winter. Spatial patterns in the summer maxima of these quantities suggest there are large differences in the relative availability of N and P across the study area and that there are differences in the processing and the isotopic composition of C and N. This work calls into question the interpretation of studies about nutrient cycling and food webs in estuaries based on few samples collected at one time, since we document natural variability greater than the signal often used to imply changes in the structure or function of ecosystems. The data and patterns presented in this paper make it clear that there is no threshold δ15N value for marine plants that can be used as an unambiguous indicator of human sewage pollution without a thorough understanding of local temporal and spatial variability.

Cyclostratigraphy and eccentricity tuning of the early Oligocene through early Miocene record from Walvis Ridge

Few astronomically calibrated high-resolution (<=5 kyr) climate records exist that span the Oligocene-Miocene time interval. Notably, available proxy records show responses varying in amplitude at frequencies related to astronomical forcing, and the main pacemakers of global change on astronomical time-scales remain debated. Here we present newly generated X-ray fluorescence core scanning and benthic foraminiferal stable oxygen and carbon isotope records from Ocean Drilling Program Site 1264 (Walvis Ridge, southeastern Atlantic Ocean). Complemented by data from nearby Site 1265, the Site 1264 benthic stable isotope records span a continuous ~13-Myr interval of the Oligo-Miocene (30.1-17.1 Ma) at high resolution (~3.0 kyr). Spectral analyses in the stratigraphic depth domain indicate that the largest amplitude variability of all proxy records is associated with periods of ~3.4 m and ~0.9 m, which correspond to 405- and ~110-kyr eccentricity, using a magnetobiostratigraphic age model. Maxima in CaCO3 content, d18O and d13C are interpreted to coincide with ~110 kyr eccentricity minima. The strong expression of these cycles in combination with the weakness of the precession- and obliquity-related signals allow construction of an astronomical age model that is solely based on tuning the CaCO3 content to the nominal (La2011_ecc3L) eccentricity solution. Very long-period eccentricity maxima (~2.4-Myr) are marked by recurrent episodes of high-amplitude ~110-kyr d18O cycles at Walvis Ridge, indicating greater sensitivity of the climate/cryosphere system to short eccentricity modulation of climatic precession. In contrast, the responses of the global (high-latitude) climate system, cryosphere, and carbon cycle to the 405-kyr cycle, as expressed in benthic d18O and especially d13C signals, are more pronounced during ~2.4-Myr minima. The relationship between the recurrent episodes of high-amplitude ~110-kyr d18O cycles and the ~1.2-Myr amplitude modulation of obliquity is not consistent through the Oligo-Miocene. Identification of these recurrent episodes at Walvis Ridge, and their pacing by the ~2.4-Myr eccentricity cycle, revises the current understanding of the main climate events of the Oligo-Miocene.

Dissolved Zinc in the Southern Ocean measured on water bottle samples during POLARSTERN cruise ANT-XXIV/3

The distribution of dissolved zinc (Zn) was investigated in the Atlantic sector of the Southern Ocean in the austral autumn of 2008 as part of the IPY GEOTRACES expedition ZERO & DRAKE. Research focused on transects across the major frontal systems along the Zero Meridian and across the Drake Passage. There was a strong gradient in surface zinc concentrations observed across the Antarctic Polar Front along both transects and high zinc levels were found in surface waters throughout the Southern Ocean. Vertical profiles for dissolved Zinc showed the presence of local minima and maxima in the upper 200 m consistent with significant uptake by phytoplankton and release by zooplankton grazing, respectively. Highest deep water zinc concentrations were found in the centre of the Weddell Gyre associated with Central Intermediate Water (CIW), a water mass which is depleted in O2, elevated in CO2 and is regionally a CFC minimum. Our data suggests that the remineralization of sinking particles is a key control on the distribution of Zn in the Southern Ocean. Disappearance ratios of zinc to phosphate (Zn:P) in the upper water column increased southwards along both transects and based on laboratory studies they suggest slower growth rates of phytoplankton due to iron or light limitation. Zinc and silicate were strongly correlated throughout the study region but the disappearance ratio (Zn:Si) was relatively uniform overall except for the region close to the ice edge on the Zero Meridian.

Statistique de maxima et modèles graphiques multi-échelles : application à la turbulence

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Statistique de maxima et modèles graphiques multi-échelles : application à la turbulence

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Carbon and oxygen isotope ratios, and geochemistry of the Precambrian-Cambrian Sukharikha River section, northwestern Siberian platform

A high-resolution carbon isotope profile through the uppermost Neoproterozoic-Lower Cambrian part of the Sukharikha section at the northwestern margin of the Siberian platform shows prominent secular oscillations of d13C with peak-to-peak range of 6-10 ?. There are six minima, 1n-6n, and seven maxima 1p-7p, in the Sukharikha Formation and a rising trend of d13C from the minimum 1n of -8.6 ? to maximum 6p of +6.4 ?. The trough 1n probably coincides with the isotopic minimum at the Precambrian-Cambrian boundary worldwide. Highly positive d13C values of peaks 5p and 6p are typical of the upper portion of the Precambrian-Cambrian transitional beds just beneath the Tommotian Stage in Siberia. A second rising trend of d13C is observed through the Krasnoporog and lower Shumny formations. It consists of four excursions with four major maxima that can be cor related with Tommotian-Botomian peaks II, IV, V, and VII of the reference profile from the southeastern Siberian platform. According to the chemostratigraphic cor relation, the first appearances of the index forms of archaeocyaths are earlier in the Sukharikha section than in the Lena-Aldan region.

Age control points and sedimentation rates of ODP Hole 145-887B (Table 1)

Hole 887B of the Ocean Drilling Program (ODP) comprises a 44 m (750 kyr) long continuous section recovered from the Patton-Murray Rise, an elevated plateau that is largely isolated from turbidite deposition. The Patton-Murray area is centered under the Alaska Gyre, a region characterized by the domal upwelling of nutrient-rich waters. Marked increases in productivity and rapid settling of biogenic matter are suggested throughout the section by the episodic accumulation of diatomaceous oozes up to ~1 m thick that are accompanied by barium enrichments. Significant delta13Corg maxima in the major diatomaceous bands suggest that mixedlayer [CO2(aq)] may have been drawn down significantly during some of the productivity events. The episodes of enhanced productivity at Site 887 occur synchronously with short-lived minima in planktonic foram delta18O, suggesting a direct link to low salinity, or less likely, warming, events in the Gulf of Alaska. There is no obvious explanation for the events, but they may be related to seasonal incursions of meltwater from Alaska. We speculate that episodic input of meltwater- or dust-borne iron from Asian or Alaskan sources may have promoted the extraordinary diatom production events recorded in the sedimentary record.

Abundance of organic-walled dinoflagellate cysts of sediment core GeoB3603-2

Here, we reconstruct the varying influence of the Agulhas Current (AgC), the South Atlantic Current and the Antarctic Circumpolar Current on the Agulhas Retroflection (AgR) in the eastern South Atlantic Ocean for the last 160,000 years on the basis of the dinoflagellate cysts, pollen and spores present in a sediment core (GeoB 3603-2) from the southeastern Cape Basin offshore South Africa, where the Agulhas Current enters the Atlantic Ocean. Our analyses reveal strong orbital forcing on the heat exchange between the Indian Ocean and the South Atlantic Ocean during the Late Quaternary. Maxima in local productivity appear to be primarily related to a strengthening of the ocean circulation as a result of the high seasonal contrast during precession maxima. During precession minima, seasonal contrast was low and stratified, oligo- to mesotrophic conditions prevailed, notably when these minima coincided with the glacial terminations. The clear presence of periodicities on a sub-Milankovitch scale as well as modulations of the primary frequencies demonstrate that the Agulhas Retroflection furthermore is modulated substantially by complex interactions between the subtropical, 'precession-driven', climate and ocean circulation systems, and the southern, 'obliquity-driven', high latitudes.

(Table 2) Age model and sedimentation rate of sediment core GeoB5559-2

The Canary Basin lies in a region of strong interaction between the atmospheric and ocean circulation systems: Trade winds drive seasonal coastal upwelling and dust storm outbreaks from the neighbouring Sahara desert are the major source of terrigenous sediment. To investigate the forcing mechanisms for dust input and wind strength in the North Canary Basin, the temporal pattern of variability of sedimentological and geochemical proxy records has been analysed in two sediment cores between latitudes 30°30'N and 31°40'N. Spectral analysis of the dust proxy records indicates that insolation changes related to eccentricity and precession are the main periods of temporal variation in the record. Si/Al and grain-size of the terrigenous fraction show an increase in glacial-interglacial transitions while Al concentration and Fe/Al ratio are both in phase with minima in the precessional index. Hence, the results obtained show that the wind strength was intensified at Terminations. At times of maxima of Northern Hemisphere seasonal insolation, when the African monsoon was enhanced, the North Canary Basin also received higher dust input. This result suggests that the moisture brought by the monsoon may have increased the availability of dust in the source region.