Petak, 05. maj 2006. u 14h, sala 2 MI SANU BG:

Predrag Tanovic, Matematicki institut SANU
PREBROJIVA ELEMENTARNA PROSIRENJA STRUKTURA PRVOG REDA

Sadrzaj: Neka je M=(M,...) bilo koja struktura prvog reda. Za njena dva elementarna prosirenja $M_1\succ^ŮM$ i $M_2^Ů\succ M$ kazemo da su izomorfna nad M ako postoji izomorfizam koji fiksira M ta?ku po ta?ku. Glavna tema predavanja je hipoteza koju je Anand Pillay postavio 1976. godine:

Pillay-eva hipoteza Svaka prebrojiva (beskona?na) struktura prvog reda M ima beskona?no mnogo u parovima neizomorfnih nad M elementarnih prosirenja.

Hipoteza je do sada potvrdjena u nekim posebnim slu?ajevima, na primer u slu?ajevima kada je M grupa ili polje. Predavanje ?e sadrzati pregled do sada poznatih rezultata na ovu temu kao i najavu kona?ne potvrde ove pretpostavke.

Sreda, 10. maj 2006. u 12h, sala 2 MI SANU:

??? OBRATITE PAZNJU NA TERMIN??? (zajedni?ki sastanak sa Odeljenjem za mehaniku) Alessandro M. Forte, GEOTOP - Département des Sciences de la Terre et de l'Atmosphčre Université du Québec ŕ Montréal, Québec, Canada
A NUMERICAL INVESTIGATION OF TIME-DEPENDENT THERMAL CONVECTION IN EARTH'S INTERIOR

Abstract: The physical and mathematical formulation of a model of thermal convection in a viscous fluid will be presented. This model will be used to explore the dynamics in Earth's 3000 kilometre-thick rocky shell called the mantle. The discussion will first focus on the mathematical and numerical development of a model of time-dependent, compressible thermal convection in 3-D spherical geometry which is based on a pseudo-spectral solution of the coupled equations of energy and momentum conservation assuming a linear viscous rheology. The equations of mass and momentum conservation are solved only once using generalized spherical harmonic basis functions to obtain spectral Green functions. These Green functions describe the viscous impulse response of the mantle and they are used to mathematically predict the flow induced by an arbitrary distribution of density perturbations. With this approach, the thermal convection problem is effectively reduced to the solution of the conservation of energy equation. The present-day distribution of temperature anomalies in Earth's mantle may be derived from global seismic tomographic images of three-dimensional (3-D) structure inside our planet. These estimates of mantle thermal structure provide a starting point for numerical reconstructions of the spatial and temporal evolution of the 3-D structure and flow in the mantle. The Rayleigh number which characterizes the convective vigour in the mantle is estimated to be very high and therefore the effect of thermal diffusion will be much weaker than thermal advection in most of the mantle. This assumption will be used as a basis for reconstructing past thermal states in the mantle.

Petak, 19. maj 2006. u 14h, sala 2 MI SANU:


VREDNOVANJE NAU?NIH REZULTATA I NAU?NOG DOPRINOSA. STRATEGIJA RAZVOJA MATEMATIKE U SRBIJI
(zajedni?ki sastanak sa Odeljenjem za mehaniku)

Vrednovanje nau?nih projekata i istra^Ţiva?a u proteklom periodu je izazivalo polemike u matemati?koj javnosti. Sastanak Odeljenja ?e biti otvoren za predloge kako unaprediti kriterijume vrednovanja nau?nog rada u Srbiji u oblasti matematike. Sastanak ?e voditi upravnici Odeljenja.

Petak, 26. maj 2006. u 14h, sala 718, MF BGD:

Slavisa Presi?, Matemati?ki fakultet, Beograd
O TAKOZVANIM ZBIROVSKIM FORMAMA I NJIHOVOJ PRIMENI

Sadrzaj: Izlaze se jedan algoritam pomo?u koga se, na primer, moze
1) na?i obrazac za $\sum_{i=1}^{n}p(i)$, gde je $p(i)=a_ki^k+\cdots+a_0$ zadan polinom
2) u formuli
$$ 1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}=\frac{\pi^2}{6}+o(1), n\to \infty, $$
se o(1) "moze efektivno udrobiti" u obliku
$$ \frac{\alpha_1}{n}+\frac{\alpha_2}{n^2}+\cdots+\frac{\alpha_s}{n^s}+ \frac{k_{s+1}}{n^{s+1}} (s=1,2,\ldots), $$
sa nekim nalazivim, konstantama $\alpha_i$. Uz to $k_{s+1}$ je ograni?en.

OBAVESTENJE

Profesor A. Forte gostuje u Beogradu 8-12. maja 2006. godine i odrzace jos dva predavanja

Katedra za astronomiju, Matemati?ki fakultet, 09.05.2006. u 18h

PERTURBATIONS IN EARTH'S ORBITAL PARAMETERS AND EARTH ROTATION DUE TO THERMAL CONVECTION IN EARTH'S MANTLE

Abstract: Changes in Earth's external shape due to the process of thermal convection in Earth's mantle may have a large influence on variations in Earth's obliquity and axial precession rate. Mantle convection may also produce significant true polar wander on geological time scales. A new numerical model of thermal convection, based on seismic tomographic images of Earth's internal structure, will be used to predict variations in Earth's dynamic ellipticity and inertia tensor in the geologic past. Using the many-body orbital solution of Laskar et al [1993], we determine the consequences of convection-induced variations in Earth flattening on changes in Earth's orbital parameters. A spectral S-transform analysis of the predicted orbital perturbations will be employed to discover whether the changes in Earth's dynamical ellipticity are sufficiently large to produce a resonant interaction with the planets Jupiter and Saturn, as discovered in a previous study [Forte and Mitrovica, 1997]. This resonance can strongly perturb Earth's precession rate and obliquity, yielding significant changes in high-latitude summer insolation in the geologic past. The impact of convection on Earth's inertia tensor will also be considered from the perspective of paleomagnetic reconstructions of true polar wander.

Institut za geofiziku, RGF, ?u^Úina 7, 11.05.2006. u 14h

SEISMIC AND GEODYNAMIC CONSTRAINTS ON PRESENT-DAY DYNAMICS IN EARTH'S MANTLE

Abstract: Seismic tomography provides models of global, three-dimensional (3-D) mantle structure with increasingly improved vertical and horizontal resolution. These seismic models of heterogeneity in the mantle may be interpreted in terms of the density perturbations which drive the convective flow in the mantle. Direct calculations of this flow are shown to provide very good matches to a variety of important geophysical surface 'observables', such as the geoid or free-air gravity anomalies, core-mantle boundary topography, and dynamic surface topography. These tomography-based convective flow calculations require, as necessary inputs, the depth dependence of the effective mantle viscosity and the scaling coefficient between perturbations of seismic velocity and density. The convection-related geophysical data may therefore be employed, in inverse calculations, to constrain both the rheological and thermo-chemical structure of the mantle. The tomography-based mantle flow models have been reformulated to handle very large radial gradients in viscosity and they incorporate surface tectonic plates whose movements are predicted, rather than imposed. This viscous flow theory, in combination with mantle density anomalies derived from 3-D seismic tomography models, is used to invert a wide range of surface convection data to obtain new inferences of the radial profile of mantle viscosity. These viscosity inversions have revealed the presence of a strong maximum in viscosity in the lower mantle, near 2000 km depth. This rheological stratification provides an obstacle to convective mixing and it yields a transition to a flow patters in the deep mantle which is strongly dominated by the longest horizontal wavelengths.