Sharif Digital Repository

In 1952, Choquet-Bruhat proved the well-posedness of the Cauchy problem for Einstein’s equation, and demonstrated that a given initial data on a Cauchy hypersurface in spacetime propagates forward in time as a solution to the wave equation. It took nearly half a century for mathematicians to build the necessary tools and techniques for proving the stability of the most basic solution of Einstein’s vacuum equations (EVE), namely Minkowski spacetime. In 1993, Christodoulou and Klainerman showed the global nonlinear stability of this solution using the concept of a double null gauge. The Schwarzschild solution, introduced by Karl Schwarzschild in 1916 for spherically symmetric spacetimes as an... 

Probabilistic graphical models have great applications in studying and analyzing realworld data. For instance, these models have been used in reconstructing gene regularity networks. Specifically, learning the edges’ structure of graphical models is of great importance.Knowledge about the underlying structure of a graphical model brings about a valuable framework for the decomposition of the model’s distribution and reveals important information such as dependency among dimensions of samples, etc. Most existing methods for structure learning obtain the underlying structure of the model in a centralized fashion and without considering noise in data. In many applications, data exist in a... 

Sustainable agricultural development in the country without regard to water supply problems in terms of time and place is not possible. Construction of water storage tanks filled with water and seasonal use in dry seasons in the effective action in the optimal use of water in the climate of (low and irregular rainfall) is. The most important step in the construction of water storage tanks to choose the best point for the construction of the reservoir basin in order to reduce costs and increase efficiency. Chndmyarh different methods to decide the best option for finding a few options from there. Among these methods can be Tapsys two methods (TOPSIS) and hierarchical analysis (AHP) pointed... 

“Sustainable development” is a frequently used phrase, but the idiom has been experienced little since it was coined by the Brundtland, due to its intrinsic complications. The issue is going to compromise two key components; economy and ecology. One of the solutions based on concept of sustainable development that has been proposed for maintaining water quality at acceptable levels is to cap pollutant emissions at a sustainable level, then establish an economic market in which the right to discharge pollutants is traded according to market supply and demand mechanisms. Water quality trading or pollution trading is one such kind of market-based program that has also been described using names... 

One of the main challenges of Water Resources Planning and Management (WRPM) is to balance water allocation between different uses. Usually, due to political and economic power of other uses, ecosystem receives less attention. Environmental flow is the allocated flow to ecosystem. Ecosystem provides a wide range of services to humanity. Therefore, environmental flow is not exclusively a matter of sustaining ecosystem but also a matter of providing humans with better life. Several methods have been developed to determine the environmental flow but only a few consider its socio-economic aspects. Consideration of these aspects could assist decision-makers with determining the optimum flow and...