Disaster relief logistics is a significant element in the management of disaster relief operations.In this paper,the operational decisions of relief logistics are considered in the distribution of resources to the aff...Disaster relief logistics is a significant element in the management of disaster relief operations.In this paper,the operational decisions of relief logistics are considered in the distribution of resources to the affected areas to include scheduling,routing,and allocation decisions.The proposed mathematical model simultaneously captures many aspects relevant to real life to face the challenging situation of disasters.Characteristics such as multiple uses of vehicles and split delivery allow for better use of vehicles as one of the primary resources of disaster response.A multi-period multi-criteria mixed-integer programming model is introduced to evaluate and address these features.The model utilizes a rolling horizon method that provides possibilities to adjust plans as more information becomes available.Three objectives of efficiency,effectiveness,and equity are jointly considered.The augmented epsilon constraint method is applied to solve the model,and a case study is presented to illustrate the potential applicability of our model.Computational results show that the model is capable of generating efficient solutions.展开更多
In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a ...In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.展开更多
Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We c...Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.展开更多
This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solut...This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.展开更多
In 2013, World-Universe Model (WUM) made one of the most important predictions: “Macroobjects of the World have cores made up of the discussed DM (Dark Matter) particles. Other particles, including DM and baryonic ma...In 2013, World-Universe Model (WUM) made one of the most important predictions: “Macroobjects of the World have cores made up of the discussed DM (Dark Matter) particles. Other particles, including DM and baryonic matter, form shells surrounding the cores” [1]. Prof. R. Genzel and A. Ghez confirmed this prediction: “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020). On May 12, 2022, astronomers, using the Event Horizon Telescope, released the first image of the accretion disk around the Sagittarius A* (Sgr A*) produced using a worldwide network of radio observatories made in April 2017. These observations were obtained by a global array of millimeter wavelength telescopes and analyzed by an international research team that now numbers over 300 people, which claimed that Sgr A* is a Supermassive Black Hole (SBH). In the present paper, we analyze these results in frames of WUM. Based on the totality of all accumulated experimental results for the Center of the Milky Way Galaxy we conclude that Sgr A* is the DM Core of our Galaxy.展开更多
An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight...An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.展开更多
This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's ...This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.展开更多
文摘Disaster relief logistics is a significant element in the management of disaster relief operations.In this paper,the operational decisions of relief logistics are considered in the distribution of resources to the affected areas to include scheduling,routing,and allocation decisions.The proposed mathematical model simultaneously captures many aspects relevant to real life to face the challenging situation of disasters.Characteristics such as multiple uses of vehicles and split delivery allow for better use of vehicles as one of the primary resources of disaster response.A multi-period multi-criteria mixed-integer programming model is introduced to evaluate and address these features.The model utilizes a rolling horizon method that provides possibilities to adjust plans as more information becomes available.Three objectives of efficiency,effectiveness,and equity are jointly considered.The augmented epsilon constraint method is applied to solve the model,and a case study is presented to illustrate the potential applicability of our model.Computational results show that the model is capable of generating efficient solutions.
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA079 and ZR2021MG049)the National Social Science Funding of China(Grant No.21CJY027)the TianYuan Special Funds of the National Natural Science Foundation of China(Grant No.11626146)。
文摘In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.
文摘Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10171059,10371084&10525105)the National Natural Science Foundation of Spain(Grant No.MTM2005-00714)+1 种基金the Program for New Century Excellent Talents in University of China(Grant No.NCET-04-0882)the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant Nos.200119&200218).
文摘This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.
文摘In 2013, World-Universe Model (WUM) made one of the most important predictions: “Macroobjects of the World have cores made up of the discussed DM (Dark Matter) particles. Other particles, including DM and baryonic matter, form shells surrounding the cores” [1]. Prof. R. Genzel and A. Ghez confirmed this prediction: “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020). On May 12, 2022, astronomers, using the Event Horizon Telescope, released the first image of the accretion disk around the Sagittarius A* (Sgr A*) produced using a worldwide network of radio observatories made in April 2017. These observations were obtained by a global array of millimeter wavelength telescopes and analyzed by an international research team that now numbers over 300 people, which claimed that Sgr A* is a Supermassive Black Hole (SBH). In the present paper, we analyze these results in frames of WUM. Based on the totality of all accumulated experimental results for the Center of the Milky Way Galaxy we conclude that Sgr A* is the DM Core of our Galaxy.
基金This work is partially supported by the National Key Project of Chinathe National Nature Science Foundation of China No.19901030NSF of the Chinese State Education Ministry and Lab.of Math.for Nonlinear Sciences at Fudan University
文摘An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.
文摘This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.
