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
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
The super junction(SJ) has been recognized as the "milestone" of the power MOSFET, which is the most important innovation concept of the voltage-sustaining layer(VSL). The basic structure of the SJ is a typical ...The super junction(SJ) has been recognized as the "milestone" of the power MOSFET, which is the most important innovation concept of the voltage-sustaining layer(VSL). The basic structure of the SJ is a typical junction-type VSL(J-VSL) with the periodic N and P regions. However, the conventional VSL is a typical resistance-type VSL(R-VSL) with only an N or P region. It is a qualitative change of the VSL from the R-VSL to the JVSL, introducing the bulk depletion to increase the doping concentration and optimize the bulk electric field of the SJ. This paper firstly summarizes the development of the SJ, and then the optimization theory of the SJ is discussed for both the vertical and the lateral devices, including the non-full depletion mode, the minimum specific on-resistance optimization method and the equivalent substrate model. The SJ concept breaks the conventional"silicon limit" relationship of R_(on)∝V_B^(2.5), showing a quasi-linear relationship of R_(on)∝V_B^(1.03).展开更多
The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and ...The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method, Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young's moduli of the beads were determined from the force versus displacement data using the Hertz's contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50% with the exception of copper-alginate beads for which yield occured at lower deformation, Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young's modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.展开更多
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εhl1(x) + ε2hl2(x),y=-x- ε(fn1(x)y(2p+1) + gm1(x))...Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εhl1(x) + ε2hl2(x),y=-x- ε(fn1(x)y(2p+1) + gm1(x)) + ∈2(fn2(x)y(2p+1) + gm2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.展开更多
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 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The super junction(SJ) has been recognized as the "milestone" of the power MOSFET, which is the most important innovation concept of the voltage-sustaining layer(VSL). The basic structure of the SJ is a typical junction-type VSL(J-VSL) with the periodic N and P regions. However, the conventional VSL is a typical resistance-type VSL(R-VSL) with only an N or P region. It is a qualitative change of the VSL from the R-VSL to the JVSL, introducing the bulk depletion to increase the doping concentration and optimize the bulk electric field of the SJ. This paper firstly summarizes the development of the SJ, and then the optimization theory of the SJ is discussed for both the vertical and the lateral devices, including the non-full depletion mode, the minimum specific on-resistance optimization method and the equivalent substrate model. The SJ concept breaks the conventional"silicon limit" relationship of R_(on)∝V_B^(2.5), showing a quasi-linear relationship of R_(on)∝V_B^(1.03).
基金the Ministry of Higher Education (MOHE),Malaysia for providing financial support under Fundamental Research Grant Scheme
文摘The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method, Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young's moduli of the beads were determined from the force versus displacement data using the Hertz's contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50% with the exception of copper-alginate beads for which yield occured at lower deformation, Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young's modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.
文摘Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εhl1(x) + ε2hl2(x),y=-x- ε(fn1(x)y(2p+1) + gm1(x)) + ∈2(fn2(x)y(2p+1) + gm2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.