This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperat...This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperations in oil fields. The main phenomena governing the behavior of the electrostatic coalescer are denscribed, starting from fundamental laws. In addition, the gradual coalescence of the emulsion droplets isconsidered in the mathematical modeling in a dynamic fashion, as the phenomenon is identified as a keystep in the overall yield of the unit operation. The resulting differential system with boundary conditionsis then integrated via performing numerical libraries, and the simulation results confirm the available lit-erature and the industrial data. A sensitivity analysis is provided with respect to the main parameters. Themathematical model results in a flexible tool that is useful for the purposes of design, unit behavior predic-tion. performance rnoniroring, and ontimization.展开更多
A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange ter...A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange term KaQ and the kernel for the fermion line renormalization K_(fr).It is shown that according to our method,not only K_(an) but also K_(sc) and K_(fr) can be given rigorously in a form which depends only on one ω(energy)-variable and they all take account of the retardation effect properly.展开更多
Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gra...Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gratings (SG), which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. The numerical investigations for the diffraction spectra of SG by our theoretical and computer programs are in good agreement with the results of classical RCWA in the condition when a Sandwish grating is simplified to a classical one-layer grating. The calculations by our programs of another condition when a Sandwish grating is degenerated to a classical single planar structure also conform to the results of classical electromagnetic theory. The research results above indicate that the extended theoretical formula has backwards compatibility and is self-consistent with the classical theory.展开更多
In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and e...In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and establish evaluation standard based on the relationship between refractive index and reflectivity and responses of reflection efficiency to refractive index,grating thickness and incident angles,etc.The results suggest that reflection efficiency varies significantly as a function of the natural jadeite quality,which can provide a new method to evaluate natural jadeite.展开更多
Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)...Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)the number of distinct sites visited in time t,and P(t)the probability of return at time t.The spatial disorder turns out to be predominant for long time.展开更多
In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but a...In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because pedagogically the calculus books still use circular reasoning today to prove the area inside a circle (also that of an ellipse) on this important historical topic, first illustrated by Archimedes. I offer an innovative approach through the introduction of a theorem, which will lead to proving the area inside a circle avoiding circular argumentation.展开更多
Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components durin...Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components during this period subject to the constraint:Earth’s hydrosphere conserves water.The newly simultaneously adjusted trends of the budget components suggest a larger correction for the global mean sea level trend implicated by the other budget components’trends under the budget constraint.The simultaneous estimation of the linear trends of the budget components subject to the constraint for closure improves their uncertainties and enables a holistic assessment of the global mean sea budget,which has implications for future sea level science studies,including the future Intergovernmental Panel on Climate Change(IPCC)Assessment Reports,and the US Climate Assessment Reports.展开更多
The paper analyzes the practical use of management mode of small-scale farmland irrigation works in China,and studies various problems existing in the present management mode.It puts forward a mode named Water-consume...The paper analyzes the practical use of management mode of small-scale farmland irrigation works in China,and studies various problems existing in the present management mode.It puts forward a mode named Water-consumer Association which is the most practical one at present.It points out some rules which must be mastered in solving problems appearing in using this mode.展开更多
In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwis...In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.展开更多
The proposal that"the rural governance system based on the combination of self-governance,rule of law and rule of virtue should be completed"was put forward in the report of the 19th National Congress of the...The proposal that"the rural governance system based on the combination of self-governance,rule of law and rule of virtue should be completed"was put forward in the report of the 19th National Congress of the Communist Party of China.There are many challenges for the development and difficulties for the governance of rural social transformation in the new era,so"the combination of self-governance,rule of law and rule of virtue"is realistically essential,having the objective inevitability and practical possibility.The fundamental and central role of the villagers'self-governance should be brought into full play to construct"the rural governance system based on the combination of self-govermance,rule of law and rule of virtue"under the guidance of the spirit of the 19th National Congress ofthe Communist Party of China,by taking the rule of law as the legal assurance and rule of virtue as the social affection support,managing to complete and optimize the rural governance system,realize the good and right governance in the rural society,boost the modernization construction process of the national governance ability,and realize the great objective of comprehensive rural vitalization of the"stability of the rural areas,development of the agriculture and happiness of the farmers".展开更多
文摘This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperations in oil fields. The main phenomena governing the behavior of the electrostatic coalescer are denscribed, starting from fundamental laws. In addition, the gradual coalescence of the emulsion droplets isconsidered in the mathematical modeling in a dynamic fashion, as the phenomenon is identified as a keystep in the overall yield of the unit operation. The resulting differential system with boundary conditionsis then integrated via performing numerical libraries, and the simulation results confirm the available lit-erature and the industrial data. A sensitivity analysis is provided with respect to the main parameters. Themathematical model results in a flexible tool that is useful for the purposes of design, unit behavior predic-tion. performance rnoniroring, and ontimization.
基金Supported by the National Natural Science Foundation of China and the Foundation of State Education Commission.
文摘A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange term KaQ and the kernel for the fermion line renormalization K_(fr).It is shown that according to our method,not only K_(an) but also K_(sc) and K_(fr) can be given rigorously in a form which depends only on one ω(energy)-variable and they all take account of the retardation effect properly.
文摘Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gratings (SG), which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. The numerical investigations for the diffraction spectra of SG by our theoretical and computer programs are in good agreement with the results of classical RCWA in the condition when a Sandwish grating is simplified to a classical one-layer grating. The calculations by our programs of another condition when a Sandwish grating is degenerated to a classical single planar structure also conform to the results of classical electromagnetic theory. The research results above indicate that the extended theoretical formula has backwards compatibility and is self-consistent with the classical theory.
文摘In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and establish evaluation standard based on the relationship between refractive index and reflectivity and responses of reflection efficiency to refractive index,grating thickness and incident angles,etc.The results suggest that reflection efficiency varies significantly as a function of the natural jadeite quality,which can provide a new method to evaluate natural jadeite.
文摘Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)the number of distinct sites visited in time t,and P(t)the probability of return at time t.The spatial disorder turns out to be predominant for long time.
文摘In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because pedagogically the calculus books still use circular reasoning today to prove the area inside a circle (also that of an ellipse) on this important historical topic, first illustrated by Archimedes. I offer an innovative approach through the introduction of a theorem, which will lead to proving the area inside a circle avoiding circular argumentation.
基金partially supported by the Natural Science Foundation of China(Grant No.41974040)。
文摘Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components during this period subject to the constraint:Earth’s hydrosphere conserves water.The newly simultaneously adjusted trends of the budget components suggest a larger correction for the global mean sea level trend implicated by the other budget components’trends under the budget constraint.The simultaneous estimation of the linear trends of the budget components subject to the constraint for closure improves their uncertainties and enables a holistic assessment of the global mean sea budget,which has implications for future sea level science studies,including the future Intergovernmental Panel on Climate Change(IPCC)Assessment Reports,and the US Climate Assessment Reports.
基金Supported by Provincial Water Conservancy Research and Technology Promotion Project:Research on Key Technical Problems of Farmland Water Conservancy Projects in Shandong Province(SDSLKY201401)
文摘The paper analyzes the practical use of management mode of small-scale farmland irrigation works in China,and studies various problems existing in the present management mode.It puts forward a mode named Water-consumer Association which is the most practical one at present.It points out some rules which must be mastered in solving problems appearing in using this mode.
基金supported by the National Natural Science Foundation of China(Grant No.11771265).
文摘In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.
文摘The proposal that"the rural governance system based on the combination of self-governance,rule of law and rule of virtue should be completed"was put forward in the report of the 19th National Congress of the Communist Party of China.There are many challenges for the development and difficulties for the governance of rural social transformation in the new era,so"the combination of self-governance,rule of law and rule of virtue"is realistically essential,having the objective inevitability and practical possibility.The fundamental and central role of the villagers'self-governance should be brought into full play to construct"the rural governance system based on the combination of self-govermance,rule of law and rule of virtue"under the guidance of the spirit of the 19th National Congress ofthe Communist Party of China,by taking the rule of law as the legal assurance and rule of virtue as the social affection support,managing to complete and optimize the rural governance system,realize the good and right governance in the rural society,boost the modernization construction process of the national governance ability,and realize the great objective of comprehensive rural vitalization of the"stability of the rural areas,development of the agriculture and happiness of the farmers".