2020 No. 2
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2020, (2): 1-7.
doi: 10.3969/j.issn.1000-5641.201911004
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Abstract:
In this paper, a new spectrum is defined according to the property of the consistent Fredholm index. We establish the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space that satisfies the property\begin{document}$(\omega_1)$\end{document} ![]()
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\begin{document}$(\omega_1)$\end{document} ![]()
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In this paper, a new spectrum is defined according to the property of the consistent Fredholm index. We establish the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space that satisfies the property
2020, (2): 8-14.
doi: 10.3969/j.issn.1000-5641.201911009
Abstract:
Let\begin{document}$ M $\end{document} ![]()
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\begin{document}$ \Phi $\end{document} ![]()
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\begin{document}$ M $\end{document} ![]()
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\begin{document}$ L^2 $\end{document} ![]()
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\begin{document}$ |\Phi| $\end{document} ![]()
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\begin{document}$ M $\end{document} ![]()
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\begin{document}$ \sup_{x\in M}|\Phi|^2(x) $\end{document} ![]()
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\begin{document}$ L^n $\end{document} ![]()
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\begin{document}$ |\Phi| $\end{document} ![]()
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Let
2020, (2): 15-22.
doi: 10.3969/j.issn.1000-5641.201911008
Abstract:
In this paper, exact solutions for a class of population balance equations were investigated. The population balance equation was first transformed to a partial differential equation; symmetries of the partial differential equation were then obtained by use of the classical Lie group analysis method. In addition, the paper presents symmetries, optimal system of subalgebras, reduced ordinary differential integral equations, and group invariant solutions of the population balance equation. Exact solutions of the reduced ordinary differential integral equations were subsequently found using trial functions. Finally, exact solutions for a class of population balance equations are derived.
In this paper, exact solutions for a class of population balance equations were investigated. The population balance equation was first transformed to a partial differential equation; symmetries of the partial differential equation were then obtained by use of the classical Lie group analysis method. In addition, the paper presents symmetries, optimal system of subalgebras, reduced ordinary differential integral equations, and group invariant solutions of the population balance equation. Exact solutions of the reduced ordinary differential integral equations were subsequently found using trial functions. Finally, exact solutions for a class of population balance equations are derived.
Internal layers for a singularly perturbed differential equation with Robin boundary value condition
2020, (2): 23-34.
doi: 10.3969/j.issn.1000-5641.201911043
Abstract:
In this paper, we consider a second order singularly perturbed equation with a discontinuous right-hand function and Robin boundary value condition. Applying the boundary layer function method, we can construct an asymptotical approximation of the solution. We also prove the existence of the solution and obtain an estimation of the remainder based on the matching method.
In this paper, we consider a second order singularly perturbed equation with a discontinuous right-hand function and Robin boundary value condition. Applying the boundary layer function method, we can construct an asymptotical approximation of the solution. We also prove the existence of the solution and obtain an estimation of the remainder based on the matching method.
2020, (2): 35-40.
doi: 10.3969/j.issn.1000-5641.201911007
Abstract:
In Orlicz space, a new norm that is equivalent to the Luxemburg norm is introduced. It is called the Φ-Amemiya norm:\begin{document}${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$\end{document} ![]()
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\begin{document}$\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$\end{document} ![]()
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In Orlicz space, a new norm that is equivalent to the Luxemburg norm is introduced. It is called the Φ-Amemiya norm:
2020, (2): 41-49.
doi: 10.3969/j.issn.1000-5641.201811039
Abstract:
By using the fixed-point index theory of cone mapping, we show the optimal conditions for the existence of positive solutions for second order discrete periodic boundary value problems \begin{document}$\left\{ {\begin{array}{*{20}{l}} {\Delta^2 y(n-1)+a(n)y(n)=g(n)f(y(n)),}&{n\in[1,N]_{\mathbb{Z}},}\\ {y(0)=y(N), \;\;\;\Delta y(0)=\Delta y(N)}&{} \end{array}} \right.$\end{document} ![]()
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with vanishing Green’s function, where \begin{document}$[1,N]_{\mathbb{Z}}=\{1,2,\cdot\cdot\cdot, $\end{document} ![]()
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\begin{document}$N\},\,f:[1,N]_{\mathbb{Z}}\times\mathbb{R}^+\rightarrow\mathbb{R}^+$\end{document} ![]()
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\begin{document}$a: [1,N]_{\mathbb{Z}}\rightarrow(0,+\infty),$\end{document} ![]()
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\begin{document}$\mathop {\max }\limits_{n \in {{[1,N]}_{\mathbb{Z}}}} a(n)\leqslant4\sin^2(\frac\pi{2N}),\,g\in C([1,N]_{\mathbb{Z}},\mathbb{R}^+), $\end{document} ![]()
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\begin{document}$\mathbb{R}^+:=[0,\infty)$\end{document} ![]()
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2020, (2): 50-54.
doi: 10.3969/j.issn.1000-5641.201911006
Abstract:
This paper considers the blow-up phenomena of solutions for nonlocal diffusion equations with a weighted gradient reaction, and gives the sufficient conditions for existence and blow-up. Firstly, the local existence of solutions is proven by using the Banach fixed-point theorem. Secondly, a new auxiliary function is constructed by using eigenfunctions. Finally, the results are combined with the differential inequality technique to obtain the upper bound of the blow-up time.
This paper considers the blow-up phenomena of solutions for nonlocal diffusion equations with a weighted gradient reaction, and gives the sufficient conditions for existence and blow-up. Firstly, the local existence of solutions is proven by using the Banach fixed-point theorem. Secondly, a new auxiliary function is constructed by using eigenfunctions. Finally, the results are combined with the differential inequality technique to obtain the upper bound of the blow-up time.
2020, (2): 55-63.
doi: 10.3969/j.issn.1000-5641.201922010
Abstract:
In this paper, the non-sequential double ionization (NSDI) process of Ar in 800 nm and 400 nm counterrotating circularly polarized two-color(CRTC) laser fields was studied using the classical ensemble model. The dependence of the non-sequential double ionization mechanism and quantum yield on laser intensity, laser intensity ratio, relative phase, and pulse duration of two pulses is calculated and analyzed in detail. The energy evolution of two electrons in the time domain is obtained and two different non-sequential double ionization mechanisms are revealed. The influence of the electron collision energy for different non-sequential double ionization processes is also discussed.
In this paper, the non-sequential double ionization (NSDI) process of Ar in 800 nm and 400 nm counterrotating circularly polarized two-color(CRTC) laser fields was studied using the classical ensemble model. The dependence of the non-sequential double ionization mechanism and quantum yield on laser intensity, laser intensity ratio, relative phase, and pulse duration of two pulses is calculated and analyzed in detail. The energy evolution of two electrons in the time domain is obtained and two different non-sequential double ionization mechanisms are revealed. The influence of the electron collision energy for different non-sequential double ionization processes is also discussed.
2020, (2): 64-69.
doi: 10.3969/j.issn.1000-5641.201922014
Abstract:
As one of the most important optical instruments, molecular (atomic) reflecting mirrors have been broadly applied in experiments for trapping, loading, and guiding of molecules (atoms); however, given that the mirrors can only change the velocity of particles in the longitudinal direction, there is no focusing capability in the lateral direction and particles can subsequently diverge. Using ND3 as an example, we propose a compact micro electrostatic curved mirror to address this issue; we show via theoretical calculations and Monte-Carlo simulations that the proposed mirror can both direct a beam of molecules and achieve transverse bunching of molecules. This kind of reflecting mirror can be used in an extensive range of optical applications for manipulating or loading molecules, composing molecular cavities, and so forth.
As one of the most important optical instruments, molecular (atomic) reflecting mirrors have been broadly applied in experiments for trapping, loading, and guiding of molecules (atoms); however, given that the mirrors can only change the velocity of particles in the longitudinal direction, there is no focusing capability in the lateral direction and particles can subsequently diverge. Using ND3 as an example, we propose a compact micro electrostatic curved mirror to address this issue; we show via theoretical calculations and Monte-Carlo simulations that the proposed mirror can both direct a beam of molecules and achieve transverse bunching of molecules. This kind of reflecting mirror can be used in an extensive range of optical applications for manipulating or loading molecules, composing molecular cavities, and so forth.
2020, (2): 70-75.
doi: 10.3969/j.issn.1000-5641.201922012
Abstract:
Research on spin of Poincaré beams not only has practical engineering applications, but is also important for understanding the nature of light. In this paper, we study the spin density of the tightly focused hybrid-order Poincaré beams (TFPB) and find that it has both longitudinal and transverse components. Unlike tightly focused full Poincaré beams whose longitudinal spin density is on average zero, the total longitudinal spin density of tightly focused hybrid-order Poincaré beams is not zero. The spin density of TFPB has rich controllable spatial patterns; in particular, the longitudinal spin density can be either a ring shape or a regular polygon. These features can be used to separate chiral particles or to manipulate dynamics of ultracold spinot gases.
Research on spin of Poincaré beams not only has practical engineering applications, but is also important for understanding the nature of light. In this paper, we study the spin density of the tightly focused hybrid-order Poincaré beams (TFPB) and find that it has both longitudinal and transverse components. Unlike tightly focused full Poincaré beams whose longitudinal spin density is on average zero, the total longitudinal spin density of tightly focused hybrid-order Poincaré beams is not zero. The spin density of TFPB has rich controllable spatial patterns; in particular, the longitudinal spin density can be either a ring shape or a regular polygon. These features can be used to separate chiral particles or to manipulate dynamics of ultracold spinot gases.
2020, (2): 76-82.
doi: 10.3969/j.issn.1000-5641.201922013
Abstract:
Recent studies have shown that Bose-Einstein condensates (BEC) can act like quantum dielectric materials, which react to light fields, and thus co-manipulation of light-matter waves is possible. So far, the dispersion properties of BEC for optical fields with a large degree of detuning have not been investigated. Accordingly, in this paper, we analytically obtain formulas for the first- and second-order dispersion. Our numerical calculation shows that the refractive index and the second-order dispersion coefficient depend on the properties of red or blue detuning. In the case of red detuning, the refractive index is greater than 1 and the second-order dispersion is normal dispersion. In the case of blue detuning, the refractive index is less than 1 and the second-order dispersion is anomalous dispersion. The second-order dispersion coefficient changes dramatically with changes in detuning. When the detuning quantity is on the order of GHz, the BEC can function as a strong dispersion medium. The first-order dispersion is independent with red detuning or blue detuning; as the amount of detuning increases, the first-order dispersion decreases and the corresponding group velocity increases. Our research shows that BEC is a new dispersion medium for manipulating ultrashort pulse light.
Recent studies have shown that Bose-Einstein condensates (BEC) can act like quantum dielectric materials, which react to light fields, and thus co-manipulation of light-matter waves is possible. So far, the dispersion properties of BEC for optical fields with a large degree of detuning have not been investigated. Accordingly, in this paper, we analytically obtain formulas for the first- and second-order dispersion. Our numerical calculation shows that the refractive index and the second-order dispersion coefficient depend on the properties of red or blue detuning. In the case of red detuning, the refractive index is greater than 1 and the second-order dispersion is normal dispersion. In the case of blue detuning, the refractive index is less than 1 and the second-order dispersion is anomalous dispersion. The second-order dispersion coefficient changes dramatically with changes in detuning. When the detuning quantity is on the order of GHz, the BEC can function as a strong dispersion medium. The first-order dispersion is independent with red detuning or blue detuning; as the amount of detuning increases, the first-order dispersion decreases and the corresponding group velocity increases. Our research shows that BEC is a new dispersion medium for manipulating ultrashort pulse light.
2020, (2): 83-89.
doi: 10.3969/j.issn.1000-5641.201922011
Abstract:
The supernova observations of 1998 show that the universe is accelerating and expanding. Dark energy refers to the cosmic content of the universe's accelerated expansion. The positive cosmological constant Λ is an important factor for dark energy, but the cause of the accelerated expansion of the universe is not Λ. Lorentz invariance is the most accurate symmetry in nature, but all quantum gravitational theories predict the breakup of Lorentz symmetry. Based on the cosmological model of a large-scale Lorentz violation(LSLV), the Friedmann equation modified by effective gravitational theory is discussed and the effect of a large-scale Lorentz violation combined with a cosmological constant term can produce the observed acceleration of the universe.
The supernova observations of 1998 show that the universe is accelerating and expanding. Dark energy refers to the cosmic content of the universe's accelerated expansion. The positive cosmological constant Λ is an important factor for dark energy, but the cause of the accelerated expansion of the universe is not Λ. Lorentz invariance is the most accurate symmetry in nature, but all quantum gravitational theories predict the breakup of Lorentz symmetry. Based on the cosmological model of a large-scale Lorentz violation(LSLV), the Friedmann equation modified by effective gravitational theory is discussed and the effect of a large-scale Lorentz violation combined with a cosmological constant term can produce the observed acceleration of the universe.
2020, (2): 90-97.
doi: 10.3969/j.issn.1000-5641.201922008
Abstract:
The amplitude of the two-loop level in N-N(nucleon-nucleon) scattering is calculated using covariant chiral effective theory. Based on the skeleton of the box diagram, the two-loop diagram results from the correction of pion self-energy. Two subtraction schemes will be employed for comparison:\begin{document}$\overline {{\rm{MS}}}$\end{document} ![]()
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\begin{document}${\rm{E}}\overline {{\rm{MS}}}$\end{document} ![]()
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\begin{document}$\overline {{\rm{MS}}}$\end{document} ![]()
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\begin{document}${\rm{E}}\overline {{\rm{MS}}}$\end{document} ![]()
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The amplitude of the two-loop level in N-N(nucleon-nucleon) scattering is calculated using covariant chiral effective theory. Based on the skeleton of the box diagram, the two-loop diagram results from the correction of pion self-energy. Two subtraction schemes will be employed for comparison:
2020, (2): 98-109.
doi: 10.3969/j.issn.1000-5641.201931002
Abstract:
We arranged 86 1 km × 1 km vegetation surveying plots in Chongqing metropolis using the grid method. The plots were used to investigate the species composition and distribution pattern of weed communities in the context of rapid urbanization. The findings of the study were as follows: ① 301 weed species belonging to 223 genera and 69 families were recorded. Among the recorded species, species of the Compositae and Gramineae were the most abundant; ② Annual weeds and dwarf weeds were the dominant types of weed species; ③ The weed communities in Chongqing metropolis were primarily comprised of native species. There were 31 exotic weed species and 11 invasive weed species recorded in the study; ④ The similarities in weed species composition across high-, medium- and low-urbanization areas were low. Additionally, the composition of dominant species within the weed community varied by area; ⑤ Urbanization had impacted weed biodiversity, evidenced by the lower number of weed species and the Shannon-Wiener diversity index in the high urbanization areas compared to that of the medium and low urbanization areas; ⑥ The number of weed species in the 86 sample plots showed a polycentric pattern with increasing distance between the survey plot and city center. Overall, urbanization had a significant impact on the composition and diversity of weed communities in mountainous multi-center cities, but the urbanization gradient of weed species is different from that of plain single-center cities.
We arranged 86 1 km × 1 km vegetation surveying plots in Chongqing metropolis using the grid method. The plots were used to investigate the species composition and distribution pattern of weed communities in the context of rapid urbanization. The findings of the study were as follows: ① 301 weed species belonging to 223 genera and 69 families were recorded. Among the recorded species, species of the Compositae and Gramineae were the most abundant; ② Annual weeds and dwarf weeds were the dominant types of weed species; ③ The weed communities in Chongqing metropolis were primarily comprised of native species. There were 31 exotic weed species and 11 invasive weed species recorded in the study; ④ The similarities in weed species composition across high-, medium- and low-urbanization areas were low. Additionally, the composition of dominant species within the weed community varied by area; ⑤ Urbanization had impacted weed biodiversity, evidenced by the lower number of weed species and the Shannon-Wiener diversity index in the high urbanization areas compared to that of the medium and low urbanization areas; ⑥ The number of weed species in the 86 sample plots showed a polycentric pattern with increasing distance between the survey plot and city center. Overall, urbanization had a significant impact on the composition and diversity of weed communities in mountainous multi-center cities, but the urbanization gradient of weed species is different from that of plain single-center cities.
2020, (2): 131-139.
doi: 10.3969/j.issn.1000-5641.201933001
Abstract:
In this paper, we discuss ZnO nanostructures synthesized by a hydrothermal method in a droplet microreactor. The microfluidic chip used integrates a multi-function unit that includes a T-channel for droplet formation, a Y-channel for droplet fusion, and an S-channel for rapid mixing and observation of the nanoparticle formation process. By adjusting the flow rates of the aqueous phase and the oil phase, we studied the morphology and size of droplets; fluorescence detection of the ZnO nanostructure synthesized, moreover, was evaluated by an FITC-labeled goat anti-bovine IgG. This work shows that ZnO nanostructures can be prepared by fluid dynamic coupling of droplets and that the morphology and size of the nanostructures vary with droplet size. When the flow rates of the oil phase, ammonia water, and ferric solution were 600, 30, and 90 μL/h, respectively, the ZnO nanostructure synthesized at 75 °C showed optimal fluorescence detection performance.
In this paper, we discuss ZnO nanostructures synthesized by a hydrothermal method in a droplet microreactor. The microfluidic chip used integrates a multi-function unit that includes a T-channel for droplet formation, a Y-channel for droplet fusion, and an S-channel for rapid mixing and observation of the nanoparticle formation process. By adjusting the flow rates of the aqueous phase and the oil phase, we studied the morphology and size of droplets; fluorescence detection of the ZnO nanostructure synthesized, moreover, was evaluated by an FITC-labeled goat anti-bovine IgG. This work shows that ZnO nanostructures can be prepared by fluid dynamic coupling of droplets and that the morphology and size of the nanostructures vary with droplet size. When the flow rates of the oil phase, ammonia water, and ferric solution were 600, 30, and 90 μL/h, respectively, the ZnO nanostructure synthesized at 75 °C showed optimal fluorescence detection performance.
2020, (2): 110-119.
doi: 10.3969/j.issn.1000-5641.201931004
Abstract:
The objective of this study was to clarify the relationship between interspecies associations and species habitat preferences in Tiantong National Forest Park. A total of 109 species of 20 hm2 evergreen broad-leaved forest plots were selected and tested for interspecies associations and species-habitat associations. The results indicated that: ① the ratio of species pairs with significant associations increased with spatial scale and the ratio of negative associations was higher than positive; ② 89.9% of species were significantly correlated with at least one habitat variable, including 73.4% of species positively and 65.1% of species negatively correlated with habitats; ③ at scales larger than 20 m, the results of interspecies associations were consistent with those of species pair habitat preferences; but at smaller scales (i.e., < 5 m), most species pairs did not show significant interspecies associations, indicating there are not habitat preferences but rather other ecological processes influencing interspecies association patterns. The results provide a theoretical basis for further understanding the mechanism of species coexistence in evergreen broad-leaved forests.
The objective of this study was to clarify the relationship between interspecies associations and species habitat preferences in Tiantong National Forest Park. A total of 109 species of 20 hm2 evergreen broad-leaved forest plots were selected and tested for interspecies associations and species-habitat associations. The results indicated that: ① the ratio of species pairs with significant associations increased with spatial scale and the ratio of negative associations was higher than positive; ② 89.9% of species were significantly correlated with at least one habitat variable, including 73.4% of species positively and 65.1% of species negatively correlated with habitats; ③ at scales larger than 20 m, the results of interspecies associations were consistent with those of species pair habitat preferences; but at smaller scales (i.e., < 5 m), most species pairs did not show significant interspecies associations, indicating there are not habitat preferences but rather other ecological processes influencing interspecies association patterns. The results provide a theoretical basis for further understanding the mechanism of species coexistence in evergreen broad-leaved forests.
2020, (2): 120-130.
doi: 10.3969/j.issn.1000-5641.201931003
Abstract:
Sulfosuccinic acid (SSA) can be used as a crosslinking agent and a donor of a hydrophilic group when fabricating a cation exchange membrane. In this study, SSA was crosslinked with polyvinyl alcohol to form a cation exchange membrane for a capacitive deionization system. In this study, the impact of manufacturing parameters (i.e., crosslinker content, crosslinking temperature) on the deionization performance of a composite membrane were investigated in detail. A comparison was made between a capacitive deionization system (CDI) without an ion exchange membrane and a membrane capacitive deionization system (MCDI) coated with a PVA/SSA layer. The results show that the adsorption capacity and charge efficiency can be enhanced by 15% and 25%, respectively, with the PVA/SSA membrane layer; furthermore, the optimal mass fraction of SSA is 5%, and the optimal crosslinking temperature is 100 ℃.
Sulfosuccinic acid (SSA) can be used as a crosslinking agent and a donor of a hydrophilic group when fabricating a cation exchange membrane. In this study, SSA was crosslinked with polyvinyl alcohol to form a cation exchange membrane for a capacitive deionization system. In this study, the impact of manufacturing parameters (i.e., crosslinker content, crosslinking temperature) on the deionization performance of a composite membrane were investigated in detail. A comparison was made between a capacitive deionization system (CDI) without an ion exchange membrane and a membrane capacitive deionization system (MCDI) coated with a PVA/SSA layer. The results show that the adsorption capacity and charge efficiency can be enhanced by 15% and 25%, respectively, with the PVA/SSA membrane layer; furthermore, the optimal mass fraction of SSA is 5%, and the optimal crosslinking temperature is 100 ℃.
