On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

2000 Mathematics Subject Classification: 12D10.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

A kvázi- és általánosított hiperbolikus diszkontálás hosszú távon (Quasi- and Generalized Hyperbolic Discounting in Long Term)

Az intertemporális döntések fontos szerepet játszanak a közgazdasági modellezésben, és azt írják le, hogy milyen átváltást alkalmazunk két különböző időpont között. A közgazdasági modellezésben az exponenciális diszkontálás a legelterjedtebb, annak ellenére, hogy az empirikus vizsgálatok alapján gyenge a magyarázó ereje. A gazdaságpszichológiában elterjedt általánosított hiperbolikus diszkontálás viszont nagyon nehezen alkalmazható közgazdasági modellezési célra. Így tudott gyorsan elterjedni a kvázi-hiperbolikus diszkontálási modell, amelyik úgy ragadja meg a főbb pszichológiai jelenségeket, hogy kezelhető marad a modellezés során. A cikkben azt állítjuk, hogy hibás az a megközelítés, hogy hosszú távú döntések esetén, főleg sorozatok esetén helyettesíthető a két hiperbolikus diszkontálás egymással. Így a hosszú távú kérdéseknél érdemes felülvizsgálni a kvázi-hiperbolikus diszkontálással kapott eredményeket, ha azok az általánosított hiperbolikus diszkontálási modellel való helyettesíthetőséget feltételezték. ____ Intertemporal choice is one of the crucial questions in economic modeling and it describes decisions which require trade-offs among outcomes occurring in different points in time. In economic modeling the exponential discounting is the most well known, however it has weak validity in empirical studies. Although according to psychologists generalized hyperbolic discounting has the strongest descriptive validity it is very complex and hard to use in economic models. In response to this challenge quasi-hyperbolic discounting was proposed. It has the most important properties of generalized hyperbolic discounting while tractability remains in analytical modeling. Therefore it is common to substitute generalized hyperbolic discounting with quasi-hyperbolic discounting. This paper argues that the substitution of these two models leads to different conclusions in long term decisions especially in the case of series; hence all the models that use quasi-hyperbolic discounting for long term decisions should be revised if they states that generalized hyperbolic discounting model would have the same conclusion.

A globálisan növekvő hulladékmennyiség és a kezelésére irányuló nemzetközi törekvések (International efforts to cope with globally increasing waste amounts)

Sokoldalú nemzetközi megállapodások és programok foglalkoznak a hulladékok keletkezésének és az országhatárokon átterjedő hatásainak problémájával, a nemzetközi együttműködést szükségessé tevő megoldásokkal. A leginkább átfogó megközelítést a probléma hajtóerőinek szentelt globális programok tartalmazzák, de a fenntarthatóság alapelveire támaszkodó termelési eljárásokra és fogyasztási szokásokra, a zöld gazdaságra való áttérést szorgalmazó dokumentumok nem tartalmaznak számon kérhető kötelezettségeket. A konkrétabb hulladékkeletkezési és hatásterjedési ügyekben – mindenekelőtt a veszélyes hulladékok és a nemzeti fennhatóság alá nem tartozó területekre eljutó vagy ott keletkező hulladékok esetében – jóval konkrétabb nemzetközi megállapodások és programok léteznek. Ezek szabályozási, szakpolitikai, technológiai célokat, feladatokat határoznak meg az országok és az érintett ágazati szereplők szintjén is. Egyes problémák kapcsán és egyes térségekben a hulladékgazdálkodás jelentős eredményeket tud felmutatni, de általában véve a nemzetközi megállapodások hatékony végrehajtásával komoly gondok vannak. Továbbá a meglévő nemzetközi eszközök összességükben még teljes körű végrehajtásuk esetén sem lennének képesek ellensúlyozni a hulladékprobléma globális szintű növekedését. Következésképpen további erőfeszítésekre van szükség – minden kormány, érintett nem-kormányzati szervezet és az ágazatok részéről – különösen a megelőzés vonatkozásában. ____ Various multilateral agreements and programmes deal with the problems of waste generation and its transboundary impacts, and those solutions, which necessitate international co-operation. Those global programmes include the most comprehensive approach, which are dedicated to the drivers of these problems, however, these documents promoting the transition to sustainable production and consumption, or to the green economy do not consist of binding commitments. In case of more concrete issues of waste generation and transboundary impacts there are much more concrete international agreements and programmes, especially, for the hazardous waste streams and the waste transmitted to and/or generated in areas outside national jurisdiction. These determine regulatory, policy, technological goals and tasks for the participating countries and the relevant sectors. Significant progress is demonstrated for some specific problems and in certain regions, but in general, there are serious concerns about the efficient implementation of the international agreements in their entirety. Moreover, even if those were fully accomplished, the existing set of the international instruments would be unable to counterweigh the global increase of the waste problem. Consequently, further efforts are needed by all countries, the relevant non-governmental organisations and sectors, primarily in order to prevent the further global escalation of the problem.

Seagrass ecosystems as a globally significant carbon stock

The protection of organic carbon stored in forests is considered as an important method for mitigating climate change. Like terrestrial ecosystems, coastal ecosystems store large amounts of carbon, and there are initiatives to protect these ‘blue carbon’ stores. Organic carbon stocks in tidal salt marshes and mangroves have been estimated, but uncertainties in the stores of seagrass meadows—some of the most productive ecosystems on Earth—hinder the application of marine carbon conservation schemes. Here, we compile published and unpublished measurements of the organic carbon content of living seagrass biomass and underlying soils in 946 distinct seagrass meadows across the globe. Using only data from sites for which full inventories exist, we estimate that, globally, seagrass ecosystems could store as much as 19.9 Pg organic carbon; according to a more conservative approach, in which we incorporate more data from surface soils and depth-dependent declines in soil carbon stocks, we estimate that the seagrass carbon pool lies between 4.2 and 8.4 Pg carbon. We estimate that present rates of seagrass loss could result in the release of up to 299 Tg carbon per year, assuming that all of the organic carbon in seagrass biomass and the top metre of soils is remineralized.

Environmental stability affects phenotypic evolution in a globally distributed marine picoplankton

Marine phytoplankton can evolve rapidly when confronted with aspects of climate change because of their large population sizes and fast generation times. Despite this, the importance of environment fluctuations, a key feature of climate change, has received little attention-selection experiments with marine phytoplankton are usually carried out in stable environments and use single or few representatives of a species, genus or functional group. Here we investigate whether and by how much environmental fluctuations contribute to changes in ecologically important phytoplankton traits such as C:N ratios and cell size, and test the variability of changes in these traits within the globally distributed species Ostreococcus. We have evolved 16 physiologically distinct lineages of Ostreococcus at stable high CO2 (1031±87?µatm CO2, SH) and fluctuating high CO2 (1012±244?µatm CO2, FH) for 400 generations. We find that although both fluctuation and high CO2 drive evolution, FH-evolved lineages are smaller, have reduced C:N ratios and respond more strongly to further increases in CO2 than do SH-evolved lineages. This indicates that environmental fluctuations are an important factor to consider when predicting how the characteristics of future phytoplankton populations will have an impact on biogeochemical cycles and higher trophic levels in marine food webs.

Some near horizon studies onWeyl and Vaidya spacetimes

This thesis comprises some studies on the Weyl, Vaidya and Weyl distorted Schwarzschild (WDS) spacetimes. The main focal areas are : a) construction of near horizon metric(NHM) for WDS spacetime and subsequently a "stretched horizon" prescribed by the membrane formalism for black holes, b) application of membrane formalism and construction of stretched horizons for Vaidya spacetime and c) using the thin shell formalism to construct an asymptotically flat spacetime with a Weyl interior where the construction does not violate energy conditions. For a), a standard formalism developed in [1] has been used wherein the metric is expanded as a Taylor series in ingoing Gaussian null coordinates with the affine parameter as the expansion parameter. This expansion is used to construct a timelike "stretched horizon" just outside the true horizon to facilitate some membrane formalism studies, the theory for which was first introduced in [2]. b) applies the membrane formalism to Vaidya spacetime and also extends a part of the work done in [1] in which event horizon candidates were located perturbatively. Here, we locate stretched horizons in close proximity to every event horizon candidate located in [1]. c) is an attempt to induce Weyl distortions with a thin shell of matter in an asymptotically flat spacetime without violating energy conditions.

Vacuum spacetimes with constant Weyl eigenvalues

Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant A) with constant non-zero Weyl eigenvalues are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2A/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant.

Adaptation of a globally important coccolithophore to ocean warming and acidification

Regulating intracellular pH (pHi) is critical for optimising the metabolic activity of corals, yet mechanisms involved in pH regulation and the buffering capacity within coral cells are not well understood. Our study investigated how the presence of symbiotic dinoflagellates affects the response of pHi to pCO2-driven seawater acidification in cells isolated from Pocillopora damicornis. Using the fluorescent dye BCECF-AM, in conjunction with confocal microscopy, we simultaneously characterised the response of pHi in host coral cells and their dinoflagellate symbionts, in symbiotic and non-symbiotic states under saturating light, with and without the photosynthetic inhibitor DCMU. Each treatment was run under control (pH 7.8) and CO2 acidified seawater conditions (decreasing pH from 7.8 - 6.8). After two hours of CO2 addition, by which time the external pH (pHe) had declined to 6.8, the dinoflagellate symbionts had increased their pHi by 0.5 pH units above control levels. In contrast, in both symbiotic and non-symbiotic host coral cells, 15 min of CO2 addition (0.2 pH unit drop in pHe) led to cytoplasmic acidosis equivalent to 0.4 pH units. Despite further seawater acidification over the duration of the experiment, the pHi of non-symbiotic coral cells did not change, though in host cells containing a symbiont cell the pHi recovered to control levels. This recovery was negated when cells were incubated with DCMU. Our results reveal that photosynthetic activity of the endosymbiont is tightly coupled with the ability of the host cell to recover from cellular acidosis after exposure to high CO2 / low pH.

Reduced resilience of a globally distributed coccolithophore to ocean acidification: Confirmed up to 2000 generations

Ocean acidification (OA), induced by rapid anthropogenic CO2 rise and its dissolution in seawater, is known to have consequences for marine organisms. However, knowledge on the evolutionary responses of phytoplankton to OA has been poorly studied. Here we examined the coccolithophore Gephyrocapsa oceanica, while growing it for 2000 generations under ambient and elevated CO2 levels. While OA stimulated growth in the earlier selection period (from generations 700 to 1550), it reduced it in the later selection period up to 2000 generations. Similarly, stimulated production of particulate organic carbon and nitrogen reduced with increasing selection period and decreased under OA up to 2000 generations. The specific adaptation of growth to OA disappeared in generations 1700 to 2000 when compared with that at 1000 generations. Both phenotypic plasticity and fitness decreased within selection time, suggesting that the species' resilience to OA decreased after 2000 generations under high CO2 selection.

Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

Black hole's response to external perturbations will carry significant information about these exotic objects. Its response, shortly after the initial `kick', is known to be ruled by the damped oscillation of the perturbating eld, called quasinormal modes(QNMs), followed by the tails of decay and is the characteristic of the background black hole spacetime. In the last three decades, several shortcomings came out in the Einstein's General Theory of Relativity(GTR). Such issues come, especially, from observational cosmology and quantum eld theory. In the rst case, for example, the observed accelerated expansion of the universe and the hypothesized mysterious dark energy still lack a satisfactory explanation. Secondly, GTR is a classical theory which does not work as a fundamental theory, when one wants to achieve a full quantum description of gravity. Due to these facts modi cation to GTR or alternative theories for gravity have been considered. Two potential approaches towards these problems are the quintessence model for dark energy and Ho rava-Lifshitz(HL) gravity. Quintessence is a dynamical model of dark energy which is often realized by scalar eld mechanism. HL gravity is the recently proposed theory of gravity, which is renormalizable in power counting arguments. The two models are considered as a potential candidate in explaining these issues.