Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_D$ and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle's death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.Comment: Published in at http://dx.doi.org/10.1214/12-AOP778 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sensorless torque estimation in multidegree-of-freedom flexible systems

This paper presents a sensorless torque estimation algorithm for multidegree-of-freedom flexible systems. The proposed algorithm makes it possible to estimate externally applied torques due to flexible system s interaction with the environment without taking any measurement from the system. The algorithm is based on modifying the disturbance observer in order to decouple the reflected torque waves out of the total disturbance on the actuator. Then Reflected torque waves are used along with the actuator s current and velocity to estimate flexible system parameters, dynamics and the external torques or disturbances. Several experimental results are included in order to confirm the validity of the proposed torque estimation algorithm

Sedimentological and stratigraphic framework of the several hundred thousand years old lacustrine record from Lake Van, Turkey

Within the frame of the International Continental scientific Drilling Program (ICDP) project PALEOVAN, a long and continuous sediment record from Lake Van, a closed lake situated in a climatically sensitive semiarid and tectonically active region in Eastern Anatolia, has been drilled in summer 2010. At two sites, Ahlat Ridge and Northern Basin, sedimentary records of 220 and 140 m were recovered, respectively. With basal ages possibly around 500'000 years, these records span several glacial-interglacial cycles and reach back until the lake’s initial transgression in the Middle Pleistocene. First results from ongoing analysis of core-catcher samples and newly opened cores document the sedimentological and geochemical succession. Two composite profiles of the drill sites were defined. Core catcher-based geochemical data such as proxies of lake’s productivity and catchment alterations show large variations and reflect a rich paleoenvironmental history. Most of the 220 m thick succession consists of carbonate mud, mostly sub-mm-thick laminated and interbedded by either homogenous mud or pyroclastic cm-thick layers. The lowermost sediments from the Ahlat Ridge site represent the initial lake transition as the drilling could not penetrate further and the seismic data indicates coincidence with the ‘acoustic’ basement. Such an early transgressive state of the lake’s history is also supported by the lithology consisting of a gravel unit as an indicator of a beach-like environment, which is overlain by sand deposits containing fresh-water gastropods (Bithynia). Above 200 mblf, the laminated mud clearly indicates that the lake was already deep enough to form anoxic bottom water as the laminations were preserved. This unique paleoclimate archive indicates that great changes of the depositional conditions occurred that hint to a fascinating evolution of the environment and has ideal prerequisites for the investigation of the Quaternary climate evolution in the Near East

Differential Subordinations Involving Generalized Bessel Functions

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.Comment: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences Societ