A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
Refs 1 and 2 provide the definition of the concepts of‘potential infinity’(poi)and actual infinity(aci);Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate(p,-p)....Refs 1 and 2 provide the definition of the concepts of‘potential infinity’(poi)and actual infinity(aci);Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate(p,-p).The second part of this paper,i.e.,§2,further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that,in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A).Finally,on the basis of this conclusion,we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions.展开更多
An H infinity(H∞)controller for a sandwiched maglev positioning stage is proposed.The maglev positioning stage has a special structure:a sandwiched maglev stage,consisting of repulsive linear motors and attractive li...An H infinity(H∞)controller for a sandwiched maglev positioning stage is proposed.The maglev positioning stage has a special structure:a sandwiched maglev stage,consisting of repulsive linear motors and attractive linear motors,which have better levitation performance.Forces on the sandwiched maglev stage are analyzed and modeled.The positioning controller is designed based on the feedback linearized model with a dynamic damping system.The design of the H infinity controller for stage positioning is derived as a series of linear matrix inequalities(LMIs)which are efficiently solved in Matlab.The proposed controller and its effectiveness is demonstrated compared to PID method.展开更多
From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the m...From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz's secant and tangent lines in the medium logic system from the perspective of logical mathematics.展开更多
In this paper, a stand-alone hybrid microgrid consisting of wind turbines, photovoltaic (PV) arrays and storage battery banks is developed for use in Qinghai Province, China. With the help of Software Homer and Matlab...In this paper, a stand-alone hybrid microgrid consisting of wind turbines, photovoltaic (PV) arrays and storage battery banks is developed for use in Qinghai Province, China. With the help of Software Homer and Matlab, different variables such as annual average wind speed, annual average load demand, and annual capacity shortage are considered. The net present value is then used during an entire project lifetime for the optimization solution.展开更多
This paper presents a design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in rural area in Jordan. The complete design steps for the suggested house...This paper presents a design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in rural area in Jordan. The complete design steps for the suggested household loads are carried out. Site radiation data and the electrical load data of a typical household in the considered site are taken into account during the design steps. The reliability of the system is quantified by the loss of load probability. A computer program is developed to simulate the PV system behavior and to numerically find an optimal combination of PV array and battery bank for the design of stand-alone photovoltaic systems in terms of reliability and costs. The program calculates life cycle cost and annualized unit electrical cost. Simulations results showed that a value of loss of load probability LLP can be met by several combinations of PV array and battery storage. The method developed here uniquely determines the optimum configuration that meets the load demand with the minimum cost. The difference between the costs of these combinations is very large. The optimal unit electrical cost of 1 kWh for LLP = 0.049 is $0.293;while for LLP 0.0027 it is $0.402. The results of the study encouraged the use of the PV systems to electrify the remote sites in Jordan.展开更多
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
基金Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)Supported by the Beihang University and by the National High Technology Research and Development Program of China(863 Program)(2009AA043303)
文摘Refs 1 and 2 provide the definition of the concepts of‘potential infinity’(poi)and actual infinity(aci);Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate(p,-p).The second part of this paper,i.e.,§2,further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that,in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A).Finally,on the basis of this conclusion,we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions.
基金Supported by the National Natural Science Foundation of China(51375052)
文摘An H infinity(H∞)controller for a sandwiched maglev positioning stage is proposed.The maglev positioning stage has a special structure:a sandwiched maglev stage,consisting of repulsive linear motors and attractive linear motors,which have better levitation performance.Forces on the sandwiched maglev stage are analyzed and modeled.The positioning controller is designed based on the feedback linearized model with a dynamic damping system.The design of the H infinity controller for stage positioning is derived as a series of linear matrix inequalities(LMIs)which are efficiently solved in Matlab.The proposed controller and its effectiveness is demonstrated compared to PID method.
基金Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)Supported by the National High Technology Research and Development Program of China (863 Program)(2009AA043303)
文摘From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz's secant and tangent lines in the medium logic system from the perspective of logical mathematics.
文摘In this paper, a stand-alone hybrid microgrid consisting of wind turbines, photovoltaic (PV) arrays and storage battery banks is developed for use in Qinghai Province, China. With the help of Software Homer and Matlab, different variables such as annual average wind speed, annual average load demand, and annual capacity shortage are considered. The net present value is then used during an entire project lifetime for the optimization solution.
文摘This paper presents a design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in rural area in Jordan. The complete design steps for the suggested household loads are carried out. Site radiation data and the electrical load data of a typical household in the considered site are taken into account during the design steps. The reliability of the system is quantified by the loss of load probability. A computer program is developed to simulate the PV system behavior and to numerically find an optimal combination of PV array and battery bank for the design of stand-alone photovoltaic systems in terms of reliability and costs. The program calculates life cycle cost and annualized unit electrical cost. Simulations results showed that a value of loss of load probability LLP can be met by several combinations of PV array and battery storage. The method developed here uniquely determines the optimum configuration that meets the load demand with the minimum cost. The difference between the costs of these combinations is very large. The optimal unit electrical cost of 1 kWh for LLP = 0.049 is $0.293;while for LLP 0.0027 it is $0.402. The results of the study encouraged the use of the PV systems to electrify the remote sites in Jordan.
