Doubly Reflected BSDEs and Ef{\cal E}^{f}-Dynkin games: beyond the right-continuous case

We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where $\xi$ is right upper-semicontinuous and $\zeta$ is right lower-semicontinuous, the solution is characterized in terms of the value of a corresponding $\mathcal{E}^f$-Dynkin game, i.e. a game problem over stopping times with (non-linear) $f$-expectation, where $f$ is the driver of the doubly reflected BSDE. In the general case where the barriers do not satisfy any regularity assumptions, the solution of the doubly reflected BSDE is related to the value of ''an extension'' of the previous non-linear game problem over a larger set of ''stopping strategies'' than the set of stopping times. This characterization is then used to establish a comparison result and \textit{a priori} estimates with universal constants

Reflected BSDEs when the obstacle is not right-continuous and optimal stopping

In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate Banach spaces. The result is established by using some tools from the general theory of processes such as Mertens decomposition of optional strong (but not necessarily right-continuous) supermartingales, some tools from optimal stopping theory, as well as an appropriate generalization of It{\^o}'s formula due to Gal'chouk and Lenglart. In the second part of the paper, we provide some links between the RBSDE studied in the first part and an optimal stopping problem in which the risk of a financial position $\xi$ is assessed by an $f$-conditional expectation $\mathcal{E}^f(\cdot)$ (where $f$ is a Lipschitz driver). We characterize the "value function" of the problem in terms of the solution to our RBSDE. Under an additional assumption of left upper-semicontinuity on $\xi$, we show the existence of an optimal stopping time. We also provide a generalization of Mertens decomposition to the case of strong $\mathcal{E}^f$-supermartingales

The method of meshless fundamental solutions with sources at infinity

The method of external source collocation is used to solve a discretised boundary value problem, ∇2U = 0, where U is the potential in a two-dimensional simply-connected region D, subject to a mixture of Neumann and Dirichlet boundary conditions. Numerical analysis has, to date, been hindered by an accumulation of round-off error, which has made it impossible to investigate accuracy of the Meshless Fundamental Solutions method unless sources are near the boundary. Symbolic analysis allows a full investigation of ill-conditioned systems in which sources can be placed "at infinity". This analysis provides an indication of how many sources must be used and where they should be placed

The legal framework for private sector development in a transitional economy : the case of Poland

The economies of Central and Eastern Europe are in the midst of a historic transition from central planning and state ownership to development of a market-driven private sector. This transition requires comprehensive changes in"rules of the game"- including the legal framework for economic activity. A market economy presupposes a set of property rights and a system of laws or customs that allow the exchange of those rights. The legal framework in a market economy has at least three basic functions: defining the universe of property rights; setting the rules for entry into and exit from productive activities; and setting the rules of market exchange. These legal tasks are accomplished by areas of law such as: company, foreign investment, bankruptcy, contract and competition law. Poland has a rich legal tradition dating from pre-socialist times, which was suppressed but not eliminated during its forty years of socialism. This tradition is being revised as the country moves toward a private market economy. The current legal framework in Poland closely follows other continental jurisdictions and has a clear and reasonable internal logic. Many of the laws are old, but most are flexible enough to permit a wide range of modern, market-oriented activity. Property law, however, remains a"jungle". The wide discretion and general lack of precedent create tremendous legal uncertainty that is sure to hamper private sector development.Environmental Economics&Policies,Banks&Banking Reform,Municipal Housing and Land,Legal Products,Land and Real Estate Development

Experimental and numerical investigation of a new MOF based adsorption water desalination system

In this research, performance of adsorption desalination systems is investigated numerically and experimentally through number of techniques including the use of advanced adsorbent materials known as metal organic frameworks (MOFs), various cycle configurations and operating conditions. A Simulink model was developed to simulate the heat and mass transfer processes associated with the adsorption/desorption processes, evaporation of seawater and condensation of potable water. This model has been used to investigate a number of new adsorbents; "AQSOA-Z02", "Aluminum Fumarate", "CP0-27Ni" and "MIL-l 01 Cr" for the purposes of water desalination and cooling as a secondary output. Number of operating parameters have been investigated including; effect of condenser, evaporator and bed's heating secondary fluid temperatures as well as half cycle time. It was concluded that decreasing condenser temperature, enhances cycle performance, therefore, a new system configuration was developed that enables decreasing the condenser temperature by utilizing all or part of the cooling effect produced in the evaporator which resulted in 314% increase in water production than conventional cycle. Two experimental testing facilities were developed to investigate CP0-27Ni and Al-Fumarate which resulted in maximum daily water production (SDWP) of 22.8 and 25.3 m3 .tonne·'.day·' respectively, while the maximum SDWP reported experimentally for Silica-gel is 13.46 m3 .tonne·' .day·'

Assessment of geometrical characteristics of dental endodontic micro-instruments utilizing X-ray micro computed tomography

OBJECTIVE: The aim of this study was to quantify the surface area, volume and specific surface area of endodontic files employing quantitative X-ray micro computed tomography (mXCT). MATERIAL AND METHODS: Three sets (six files each) of the Flex-Master Ni-Ti system (Nº 20, 25 and 30, taper .04) were utilized in this study. The files were scanned by mXCT. The surface area and volume of all files were determined from the cutting tip up to 16 mm. The data from the surface area, volume and specific area were statistically evaluated using the one-way ANOVA and SNK multiple comparison tests at α=0.05, employing the file size as a discriminating variable. The correlation between the surface area and volume with nominal ISO sizes were tested employing linear regression analysis. RESULTS: The surface area and volume of Nº 30 files showed the highest value followed by Nº 25 and Nº 20 and the differences were statistically significant. The Nº 20 files showed a significantly higher specific surface area compared to Nº 25 and Nº 30. The increase in surface and volume towards higher file sizes follows a linear relationship with the nominal ISO sizes (r²=0.930 for surface area and r²=0.974 for volume respectively). Results indicated that the surface area and volume demonstrated an almost linear increase while the specific surface area exhibited an abrupt decrease towards higher sizes. CONCLUSIONS: This study demonstrates that mXCT can be effectively applied to discriminate very small differences in the geometrical features of endodontic micro-instruments, while providing quantitative information for their geometrical properties