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.

(Supplementary Material 2) Landmark coordinates of the analyzed specimens with associated metadata

The use of planktonic foraminifera in paleoceanographic studies relies on the assumption that morphospecies represent biological species with ecological preferences that are stable through time and space. However, genetic surveys unveiled a considerable level of diversity in most morphospecies of planktonic foraminifera. This diversity is significant for paleoceanographic applications because cryptic species were shown to display distinct ecological preferences that could potentially help refine paleoceanographic proxies. Subtle morphological differences between cryptic species of planktonic foraminifera have been reported, but so far their applicability within paleoceanographic studies remains largely unexplored. Here we show how information on genetic diversity can be transferred to paleoceanography using Globorotalia inflata as a case study. The two cryptic species of G. inflata are separated by the Brazil-Malvinas Confluence (BMC), a major oceanographic feature in the South Atlantic. Based on this observation, we developed a morphological model of cryptic species detection in core top material. The application of the cryptic species detection model to Holocene samples implies latitudinal oscillations in the position of the confluence that are largely consistent with reconstructions obtained from stable isotope data. We show that the occurrence of cryptic species in G. inflata, can be detected in the fossil record and used to trace the migration of the BMC. Since a similar degree of morphological separation as in G. inflata has been reported from other species of planktonic foraminifera, the approach presented in this study can potentially yield a wealth of new paleoceanographical proxies.

Seawater carbonate chemistry and morphometric coordinates and morphology of the control 8-arm pluteus of brittlestar Ophiothrix fragilis, 2008

The world's oceans are slowly becoming more acidic. In the last 150 yr, the pH of the oceans has dropped by ~0.1 units, which is equivalent to a 25% increase in acidity. Modelling predicts the pH of the oceans to fall by 0.2 to 0.4 units by the year 2100. These changes will have significant effects on marine organisms, especially those with calcareous skeletons such as echinoderms. Little is known about the possible long-term impact of predicted pH changes on marine invertebrate larval development. Here we predict the consequences of increased CO2 (corresponding to pH drops of 0.2 and 0.4 units) on the larval development of the brittlestar Ophiothrix fragilis, which is a keystone species occurring in high densities and stable populations throughout the shelf seas of northwestern Europe (eastern Atlantic). Acidification by 0.2 units induced 100% larval mortality within 8 d while control larvae showed 70% survival over the same period. Exposure to low pH also resulted in a temporal decrease in larval size as well as abnormal development and skeletogenesis (abnormalities, asymmetry, altered skeletal proportions). If oceans continue to acidify as expected, ecosystems of the Atlantic dominated by this keystone species will be seriously threatened with major changes in many key benthic and pelagic ecosystems. Thus, it may be useful to monitor O. fragilis populations and initiate conservation if needed.

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds