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25 January 2020, Volume 2020 Issue 1
Mathematics
 Normal families of meromorphic functions and omitted functions YANG Qi, YANG Jinhua 2020, 2020 (1):  1-6.  doi: 10.3969/j.issn.1000-5641.201811043 Abstract ( 26 )   HTML ( 1 )   PDF (607KB) ( 24 )   In this paper, we study the normal criterion of meromorphic functions concerning omitted functions. By using P-Z lemma and the method of proof by contradiction, we obtain a new normal criterion: if the zeros of the families of meromorphic functions are all have multiplicity at least 3, then the families of meromorphic functions concerning omitted functions are normal.
 The polar form of hyperbolic commutative quaternions KONG Xiangqiang 2020, 2020 (1):  16-23.  doi: 10.3969/j.issn.1000-5641.201911001 Abstract ( 15 )   HTML ( 0 )   PDF (656KB) ( 10 )   Firstly, this paper presents the e1-e2 representation and matrix representation of hyperbolic commutative quaternions. Secondly, the polar form theorem of hyperbolic commutative quaternion is presented; the existence and uniqueness of the respective polar form are proven, and a series of properties for the hyperbolic commutative quaternion polar form are obtained. Lastly, the relationship between the polar form, e1-e2 representation and matrix representation of hyperbolic commutative quaternions are discussed. Hence, the paper provides a theoretical basis for further research on the application of hyperbolic commutative quaternions.
 An algorithm for finding all polynomial solutions of nonlinear difference equations Jiangtao YU, Yinping LIU 2020, 2020 (1):  24-39.  doi: 10.3969/j.issn.1000-5641.201811037 Abstract ( 21 )   HTML ( 1 )   PDF (1210KB) ( 23 )   Difference equations are a major aspect of computer algebra; yet, there are currently few studies on solving general nonlinear difference equations. Inspired by the homogeneous balance principle that works well for solving nonlinear differential equations, we use it to find polynomial solutions for a wide range of nonlinear difference equations, in which a new n-order expansion method is proposed to process the powerless cases of the homogeneous balance principle. They are combined together as an algorithm that can be used to find all polynomial solutions of nonlinear difference equations. The algorithm is implemented in Maple, and the experiments show that it is effective and efficient.
 I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm DONG Xiaoli, GONG Wanzhong 2020, 2020 (1):  40-50.  doi: 10.3969/j.issn.1000-5641.201811042 Abstract ( 21 )   HTML ( 1 )   PDF (608KB) ( 7 )   There are some equivalent definitions for I-convexity and Q-convexity. In this context, if (Ω, Σ, μ) is a finite measure space, the Orlicz-Bochner function space L(M)(μ, X) endowed with the Luxemburg norm is I-convex if and only if M ∈ △2(∞) ∩ ▽2(∞) and X is I-convex; similarly, L(M)(μ, X) is Q-convex if and only if M ∈ △2(∞) ∩ ▽2(∞) and X is Q-convex.
 Topological graph passwords based on the gracefulness of disconnected graphs with circles MU Yarong, LIU Xinsheng, YAO Bing 2020, 2020 (1):  51-57.  doi: 10.3969/j.issn.1000-5641.201811045 Abstract ( 14 )   HTML ( 0 )   PDF (959KB) ( 7 )   Graph labeling is an important branch of graph theory. We use disconnected graphs to start our study, and show that disconnected graphs G = (C4, Kr)∪∪t=1kKm,nt and G = (C4, Kr)∪K1,n∪∪t=1kTt allow graceful labelings. Algorithms can be used to provide a theoretical basis for proving the application of disconnected graphs to networks.
Physics and Electronics
 Atomic distortion in CrN: A first-principle investigation WANG Qianqian, ZHAO Zhenjie, LI Xin, XIE Wenhui 2020, 2020 (1):  58-66.  doi: 10.3969/j.issn.1000-5641.201922002 Abstract ( 8 )   HTML ( 2 )   PDF (816KB) ( 4 )   First principle calculations indicate that Cr and N atoms in the orthorhombic phase of CrN (Chromium Nitride) tend to shift from their ideal positions along the [100] direction. This shift can induce zigzag Cr-N-Cr chains in the orthorhombic phase; these atomic distortions have not been taken into account in previous studies. The atomic distortions may decrease the total energy of the orthorhombic phase by 0.125 eV/formula unit and make the structure more stable. Lattice constants, moreover, may also be in better agreement with experiment results when considering these atomic distortions. Further, the bulk modulus K0 decreases significantly when considering the atomic distortions and is closer to the experimental value. The atomic distortions are induced by the asymmetric magnetic forces between asymmetric magnetic layers in the special antiferromagnetic order of the orthorhombic phase, which compensates for the magnetic forces between the layers. The atomic distortions would not change the Mott-insulator property of the orthorhombic phase but may reduce the band gap slightly.
 Study on the covariant chiral effective field theory of vector meson WANG Yan, YANG Jifeng 2020, 2020 (1):  67-75.  doi: 10.3969/j.issn.1000-5641.201922007 Abstract ( 7 )   HTML ( 2 )   PDF (607KB) ( 3 )   In this paper, we employ covariant chiral effective field theory to explore the prescriptions in the loops involving spin 1 vector fields. The self-energy diagram for a Goldstone boson containing a vector meson line is studied, and consistent results are obtained in two representations of the vector field. Our calculation shows that the EOMS[1](Extended On-Mass Shell) proposed indeed removes the terms that violate chiral power counting. Closer examination, however, shows that the problematic sources are actually localized; thus, we propose a simpler EMS (extended MS) cheme, which is further validated using a vertex diagram. Compared to EOMS, this scheme eliminates the localized terms that violate chiral power counting without additional manipulation or modification of the non-local terms. This feature would bring about better convergence of the chiral expansion and is more suitable for studying heavy hadrons with chiral effective theory.
 The complexity of Kerr-AdS black holes DING Yuchen, WANG Tao 2020, 2020 (1):  76-82.  doi: 10.3969/j.issn.1000-5641.201922004 Abstract ( 7 )   HTML ( 1 )   PDF (533KB) ( 5 )   Gauge/gravity duality has shed light on physics research. It reveals that conformal field theory on the boundary is equivalent to the bulk of anti-de Sitter space-time, which brings us great convenience for studying the conformal field on the boundary. Recently, Susskind et al. proposed a conjecture for complexity/action duality, which states that the quantum computational complexity of the boundary state of a black hole is equivalent to the action in a Wheeler-DeWitt patch. The complexity represents the difficulty of performing quantum computing, which means that black holes may be linked to quantum computing. This provides us with deeper insights on black holes. Based on this conjecture and taking the contribution of null joints into consideration, we improve the original method of Susskind et al., and recalculate the action growth rate of the Wheeler-DeWitt patch of Kerr-AdS black holes more accurately. Finally, we get the complexity of the state on the boundary of Kerr-AdS black hole space-time.
 Novel polymer semiconductor films and related field effect transistor devices YE Jianchun, ZHOU Lizhao, LI Wenwu, OU-YANG Wei 2020, 2020 (1):  83-92.  doi: 10.3969/j.issn.1000-5641.201922006 Abstract ( 12 )   HTML ( 2 )   PDF (1121KB) ( 7 )   Thin films using a novel organic polymer semiconductor (DPPTTT(poly(3,6-di(2-thien-5-yl)-2,5-di(2-octyldodecyl)-pyrrolo[3,4-c]pyrrole-1,4-dione) thieno [3,2-b] thiophene)) were prepared by a solution process and characterized through different techniques. It was found that the thickness, surface roughness, and Raman peak strength of the semiconductor films changed with the solution concentration and rotation rate. The polymer semiconductor was used to prepare the active layer for p-type organic field effect transistors; with these, the influence of channel length on critical transistor parameters (i.e., carrier mobility and threshold voltage) was studied. It was found that the effective carrier mobility was the highest at 0.12 cm2/Vs when the channel length was reduced to 50 μm. With a decrease in channel length, both carrier mobility and threshold voltage tended to increase, which was contrary to the short channel effect. This paper may provide new perspectives for better understanding the physics of field effect transistor devices.
 Application of TiO2 nanotube arrays for bipolar photocatalytic fuel cells WANG Jianqiao, LIU dong, ZHOU Jun, XI Qinghua, NIE Er, SUN Zhuo 2020, 2020 (1):  93-102.  doi: 10.3969/j.issn.1000-5641.201922005 Abstract ( 8 )   HTML ( 0 )   PDF (1118KB) ( 5 )   Photocatalytic fuel cell (PFC) technology is a combination of photocatalytic technology and fuel cell technology, which can degrade wastewater and generate electricity at the same time. The influence of the preparation process for photoanodes of TiO2 Nanotube Arrays (TNAs) on its morphology and structure was explored; a positive correlation between the electrolysis time and the tube length of TNAs was confirmed by a Field Emission Scanning Electron Microscope (FESEM). We can combine TNAs with Cu2O photoelectrodes to obtain a system with stronger photocatalytic activity, confirming the existence of a PFC synergistic effect. The optimal electrolysis process was 4 h, and the photocatalytic degradation rate of the electrode prepared by this process was more than 79% within 2 h. Analysis of the three standards showed an excellent linear correlation between the photocurrent of PFC and the chemical oxygen demand (COD); as the degradation proceeds, the mass transfer process is reduced and the correlation between the two is weakened.
Ecological and Environmental Sciences
 Performance of lime-based algae control in urban landscape water ZHOU Yunchang, HE Yan, CHEN Jinghan, HUANG Minsheng 2020, 2020 (1):  103-109.  doi: 10.3969/j.issn.1000-5641.201831012 Abstract ( 6 )   HTML ( 0 )   PDF (947KB) ( 9 )   In this research, we studied the effect of lime dosages on algae control as well as the dynamic changes in nitrogen and phosphorus nutrients in urban landscape water based on the growth and decline of algae blooms at Guhua Park in Shanghai. The results showed clear seasonal variations in algae biomass in Guhua Park. The growth of algae could be inhibited by the addition of lime, and the inhibition performance improved with increases in lime dosage. Specifically, the algal inhibition rate ranged from 20% to 46% when the applied lime dosage increased from 0.02 g/L to 0.2 g/L. When the lime dosage increased from 0.2 g/L to 0.5 g/L, however, there was no significant increase in inhibition efficiency observed. Therefore, considering both algal inhibition efficiency and economic cost, the optimum dosage of lime is 0.2 g/L. Meanwhile, nitrogen and phosphorus nutrients in water initially increased and then decreased, reaching a final dynamic equilibrium. This study offers a new approach for algae control of urban landscape water.
 Health assessment of transboundary rivers based on the PSR and matter-element extension models: A case study of Taipu River XIE Yihan, LI Gen, YANG Mengjie, CHU Xiaoye 2020, 2020 (1):  110-122.  doi: 10.3969/j.issn.1000-5641.201831013 Abstract ( 8 )   HTML ( 0 )   PDF (734KB) ( 7 )   Taking Taipu River as an example, a multi-index assessment system for the water body and riparian zone is constructed based on the PSR model. Index weights are calculated with the entropy weight method, and the Taipu River is evaluated using the PSR and matter-element extension models. The results show that the Wujiang segment is classified as “high pressure-good state-low response ability”, the Jiashan segment is classified as “low pressure-medium state-low response ability”, and Qingpu segment is classified as “low pressure-medium state-high response ability”. The result of the health assessment of Wujiang is Grade Ⅲ (poor). Meanwhile, Jiashan and Qingpu are both Grade Ⅱ (medium), but leaning towards Grade I (good); this indicates that although the current health status of the river is medium, the health status of the water source area could be gradually restored by further increasing protection of the water source given that the policy is to some extent already effective. The results can provide decision support for river management and ecological construction of the riparian zone in Taipu River.
Estuary and Coastal Research