In the last decades, there is a lot of discussion in many scientific fields, about the high importance of water as a basic element for the existence and the maintenance of life, aiming to the right and proper usage of...In the last decades, there is a lot of discussion in many scientific fields, about the high importance of water as a basic element for the existence and the maintenance of life, aiming to the right and proper usage of water in our everyday basic water-needs due to its limited resources and the growing demand. This research deals with simple ways and technological systems applicable in urban residential buildings for the better management of domestic fresh water, as far as its maintenance and sustainability. Main aim of the survey is the effective minimization of urban daily water usage. All measurements of water quantities have estimated in the imperial gallon （1 gallon = 4.546 liter）, and in liter （1 liter = 0.2 gallon）.展开更多
This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward gener...This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.展开更多
文摘In the last decades, there is a lot of discussion in many scientific fields, about the high importance of water as a basic element for the existence and the maintenance of life, aiming to the right and proper usage of water in our everyday basic water-needs due to its limited resources and the growing demand. This research deals with simple ways and technological systems applicable in urban residential buildings for the better management of domestic fresh water, as far as its maintenance and sustainability. Main aim of the survey is the effective minimization of urban daily water usage. All measurements of water quantities have estimated in the imperial gallon （1 gallon = 4.546 liter）, and in liter （1 liter = 0.2 gallon）.
基金supported by the National Science Foundation under Grant Nos. #DMS 0505472, 0806017,and#DMS 0604309
文摘This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.
