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CN 34-1054/N

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2020 Vol. 50, No. 3

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Original Paper
Measuring energy efficiency incorporating regional heterogeneities: A meta-frontier method with log-linear technology
ANG Sheng, DENG Fang, YANG Feng
2020, 50(3): 245-260. doi: 10.3969/j.issn.0253-2778.2020.03.001
Article Views:131 Full article PDF
Abstract:
China’s provinces vary greatly in the economic development, resource endowments, and science and technology levels, which leads the heterogeneity of production technology. A data envelopment analysis model is proposed based on the log-linear energy technology and meta-frontier method, which considers the heterogeneity of production technology. Energy performances of China’s 30 provinces during the 2006-2015 period were measured and causes of energy inefficiency were analyzed with the model. Empirical results indicate that, most of the provinces in China have great potential for energy efficiency improvement. It is also shown that the eastern region has the highest average annual energy efficiency while that of the western region is the lowest, with the central region somewhere in between. It is suggested to enhance management capabilities for the eastern provinces should be enhanced, improve both technology and management efficiency for central and western provinces, to improve their energy performances.
On the multiplicatively weighted Harary index of composite graphs
TIAN Jing, PENG Guiqin, PEI Lidan, PAN Xiangfeng
2020, 50(3): 261-270. doi: 10.3969/j.issn.0253-2778.2020.03.002
Article Views:130 Full article PDF
Abstract:
Let HM(G) be the multiplicatively weighted Harary index of the molecular graph G, which is defined as HM(G)=∑{u,v}V(G)dG(u)dG(v)dG(u,v), where dG(u) is the degree of a vertex u∈V(G), and the dG(u,v) denotes the distance between u and v in G. We introduce four graph operations and obtain explicit formulas for the values of multiplicatively weighted Harary index of composite graphs generated by the four graph operations. Based on this, a lower and an upper bound is determined for the multiplicatively weighted Harary index among graphs in each of the four classes of composite graphs.
LMD-BPF method for modal parameter identification and its applications
BIAN Jie, ZHENG Jinni, CHEN Yanong, XU Youliang, CHEN Yunxi
2020, 50(3): 271-281. doi: 10.3969/j.issn.0253-2778.2020.03.003
Article Views:120 Full article PDF
Abstract:
In view of the difficulties existing in the accurate identification of structures’ modal parameters, a modal parameter identification method based on local mean decomposition (LMD) and band-pass filtering (BPF) was proposed. Firstly, the LMD method was used in the decomposition of a displacement simulation signal and a frequency measuring signal of a compressor guide vane, and modal aliasing phenomenon existed in the decomposed PF components; Then, the LMD-BPF method was utilized in the decomposition of the displacement simulation signal and frequency testing signal of the guide vane, and each modal frequency was accurately and successfully separated; Finally, the LMD-BPF modal parameter identification method was employed to identify the modal parameters of the displacement simulation signal and frequency testing signal of the guide vane. The maximum errors between the four modal frequencies and damping ratios of the identified displacement simulation signal and the corresponding theoretical values were 0.205% and 2.387%, respectively. The maximum difference between the three modal frequencies of the identified guide vane and the testing frequencies was less than 1.0%, and the maximum difference between the three modal damping ratios of the identified guide vane and those identified by half power bandwidth method was less than 0.65%. The simulation analysis and experimental study of modal parameter identification verified the validity of the proposed method.
Asymptotic analysis of an SIQS epidemic model with varying total population size and quarantine measures
FU Jingbo
2020, 50(3): 282-288. doi: 10.3969/j.issn.0253-2778.2020.03.004
Article Views:131 Full article PDF
Abstract:
A class of SIQS epidemic model with vertical infection and varying total population size and quarantine measures was established, by employing the epidemic dynamic theory, and considering both the input and output of the population. The threshold conditions which guarantee the global asymptotic stable disease-free equilibrium and endemic equilibrium of the SIQS epidemic model are obtained using methods including Routh-Hurwitz bounded, Lyapunov function and generalized Bendixson-Dulac function. The results show that the spread and prevalence of a disease can be controlled within a certain range, and that quarantine measures can accelerate the extinction of the disease.
The Erdo″s-So′s conjecture for 2-center spiders
WANG Shicheng, HOU Xinmin
2020, 50(3): 289-293. doi: 10.3969/j.issn.0253-2778.2020.03.005
Article Views:114 Full article PDF
Abstract:
The Erdo″s-So′s Conjecture states that if G is a graph with average degree more than k-2, then G contains every tree on k vertices. A spider can be seen as a tree with at most one vertex of degree more than two. Fan, Hong, and Liu proved that the conjecture holds for spiders.
L2-harmonic p-forms on submanifolds with finite total curvature
ZHOU Jundong, YIN Songting
2020, 50(3): 294-299. doi: 10.3969/j.issn.0253-2778.2020.03.006
Article Views:104 Full article PDF
Abstract:
Let M be an n-dimensional complete submanifold with flat normal bundle in an (n+l)-dimensional sphere Sn+l. Let Hp(L2(M)) be the space of all L2-harmonic p-forms (2≤p≤n-2) on M. Firstly, we show that Hp(L2(M)) is trivial if the total curvature of M is less than a positive constant depending only on n. Secondly, we show that the dimension of Hp(L2(M)) is finite provided the total curvature of M is finite.
Multiplicity of solutions to elliptic equations with exponential nonlinearities
XUE Yimin, CHEN Shouting
2020, 50(3): 300-311. doi: 10.3969/j.issn.0253-2778.2020.03.007
Article Views:134 Full article PDF
Abstract:
The multiplicity of positive solutions to quasi-linear elliptic equations with exponential nonlinearities is obtained through a singular Trudinger-Moser inequality, which is due to Ref.[21], the mountain-pass theorem without the Palais-Smale condition and the Ekeland’s variational principle. In particular, for the proof of our main results, we follow the lines of Refs.[11,15].
Biharmonic submanifolds with mean parallel curvature on Mm(c)×R
MI Rong
2020, 50(3): 312-316. doi: 10.3969/j.issn.0253-2778.2020.03.008
Article Views:115 Full article PDF
Abstract:
Let Mn be an n-dimensional submanifold with parallel mean curvature H of product space form Mm(c)×R, where Mm(c) is a space form with constant sectional curvature c. By using the method of Simons inequality, a series of results are obtained.
A robust joint modeling approach for longitudinal data
TAN Jiaxin, ZHANG Weiping
2020, 50(3): 317-327. doi: 10.3969/j.issn.0253-2778.2020.03.009
Article Views:105 Full article PDF
Abstract:
A robust method is proposed for analyzing longitudinal continuous responses
A note on the maximal degree in random k-trees
FENG Qunqiang, ZHOU Chun, LI Xing
2020, 50(3): 328-334. doi: 10.3969/j.issn.0253-2778.2020.03.010
Article Views:81 Full article PDF
Abstract:
The random variable Zn is investigated, the maximal node degree in a random k-tree at step n for k≥2.
Suitable for the construction of degenerate smooth interpolated surfaces patches in isogeometric analysis
WANG Xuhui, YAN Mingye, WU Meng
2020, 50(3): 335-342. doi: 10.3969/j.issn.0253-2778.2020.03.011
Article Views:91 Full article PDF
Abstract:
Different from constructing the degenerate smooth surface patches in the field of classical geometric modeling, the paper constructs an interpolation operator based on the singular H regularity parameterization in the isogeometric analysis. First, the definition of H regularity is introduced based on singular parameterization. Then, the definition of D-patch and interpolation operator is discussed. Finally, the Gsmoothness of the interpolation surface is verified and numerical examples are given.
On the number of edges not covered by monochromatic copies of a matching-critical graph
YUAN Longtu
2020, 50(3): 343-348. doi: 10.3969/j.issn.0253-2778.2020.03.012
Article Views:85 Full article PDF
Abstract:
Given a graph H, let f(n,H) denote the maximum number of edges not contained in any monochromatic copy of H in a 2-edge-coloring of Kn. The Turn number of a graph H, denoted by ex(n,H), is the maximum number of edges in an n-vertex graph which does not contain H as a subgraph. It is easy to see that f(n,H)≥ex(n,H) for any H and n. We show that this lower bound is tight for matching-critical graphs including Pertersen graph and vertex-disjoint union of copies of cliques with same order.
The ai-invariants of powers of ideals
TIAN Shixin, SHEN Yihuang
2020, 50(3): 349-359. doi: 10.3969/j.issn.0253-2778.2020.03.013
Article Views:91 Full article PDF
Abstract:
Inspired by the recent work of Lu and O’Rourke, we study the ai-invariants of (symbolic) powers of some graded ideals. When I and J are two graded ideals in two distinct polynomial rings R and S over a common field K. We study the ai-invariants of the powers of the fiber product via the corresponding conditions on I and J. When IΔ is the Stanley-Reisner ideal of a k-dimensional complex Δ with k≥2. We investigate the ai-invariants of the symbolic powers of IΔ.
On the quasi Gauss map for a compact sub-manifold in Euclidean space
WANG Qi, ZHOU Zhijin, FENG Linan
2020, 50(3): 360-362. doi: 10.3969/j.issn.0253-2778.2020.03.014
Article Views:51 Full article PDF
Abstract:
Let  σ be the quasi Gauss map of a compact and oriented  n-dimensional isometric immersion sub-manifold  Mn in the  (n+p)-dimensional Euclid space  Rn+p. Denote by ξ the unit mean curvature vector field to  Mn and denote by  Hi the  i-mean curvature along the direction  ξ.Assume that  Hi>0,  i=1,2,…,r for some integer  r  (1≤r≤n-1) and  Hr is a constant. By applying an integral formula recently given by themselves, it is proven that if the image σ(Mn) lies within an open  n-dimension unit semi sphere  Sn+ then  Mn must be totally quasi umbilical. This result generalizes a relevant theorem on hypersurfaces in Euclid space.
Dual-band filter design based on composite patch and substrate integrated waveguide structures
LI Anran
2020, 50(3): 363-368. doi: 10.3969/j.issn.0253-2778.2020.03.015
Article Views:87 Full article PDF
Abstract:
A new type of patch double band-pass filter based on circular substrate integrated waveguide is designed. By loading a circular metal patch, the circular SIW (circular substrate integrate waveguide, CSIW) cavity changes into the composite multilayer circular patch SIW filter. Compared to dual mode CSIW filter, composite multilayer circular patch SIW resonator not only reduces the resonant eigen mode frequency of its main mode, but also adds new modes to form a dual band. To prove its effectiveness, a simulation model is built in HFSS (high frequency structure simulator). Then through parameter optimization, the dual-band composite multilayer circular patch SIW filter is obtained. The results show that the dual-band frequency of the filter is from 1.88 GHz to 2.08 GHz and from 3.35 GHz to 3.60 GHz, and that the upper and lower sidebands of the two passbands have Transmission zeros, which shows good selectivity.
Research on multi-fractals of weighted hypernetworks
LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng
2020, 50(3): 369-381. doi: 10.3969/j.issn.0253-2778.2020.03.016
Article Views:113 Full article PDF
Abstract:
Hypernetwork is a kind of network that is more complex than ordinary complex networks, while hypernetwork dimension is a feasible tool for measuring it. For the case that both node weight and hyperedge weight in weighted hypernetworks can value among positive real number, negative real number, pure imaginary number and complex number, etc., fractal dimensions for various weighted hypernetworks is proposed and their multi-fractals are discussed. It is shown that among all types of weighted hypernetworks, except those with both node weight and hyperedge weight being positive or negative real numbers, other types of weighted hypernetworks share multi-fractals and can be divided into seven different categories that are all distributed in the entire complex plane. The analytic expressions of multi-fractal dimensions for all types of weighted hypernetworks are also presented. Finally, some important properties of the multi-fractal dimensions of these weighted hypernetworks are analyzed.
Analysis of anxiety and depression status and influencing factors in diabetic patients with or without retinopathy
YU Hua, LIU Huanzhong, LIU Qiang, YANG Kefei, SUN Yehuan
2020, 50(3): 382-388. doi: 10.3969/j.issn.0253-2778.2020.03.017
Article Views:100 Full article PDF
Abstract:
The aim of the present study was to explore the anxiety and depression status and influencing factors of diabetic patients with or without retinopathy. A total of 225 diabetic patients of Chaohu Hospital of Anhui Medical University were enrolled in the study, including 97 patients with retinopathy (diabetic retinopathy group, DR group) and 128 patients without retinopathy (non-diabetic retinopathy group, NDR group). The patient's general data were collected by questionnaire, and the Hamilton Anxiety Scale (HAMA) and Hamilton Depression Scale (HAMD) were used to assess the incidence and scores of anxiety and depression. The incidence and scores of anxiety and depression were compared between the two groups. The influencing factors of anxiety and depression status were evaluated. The results show that the incidence of anxiety and depression in DR group was higher than that in NDR group (anxiety: χ2=13.049, P<0.001; depression: χ2=13.049, P<0.001); and the scores of anxiety and depression in DR group were higher than those in NDR group (anxiety: t=-6.628, P<0.001; depression: t=-4.599, P<0.001). A univariate analysis reveals that gender, age, diabetes duration, monthly income, understanding of their own condition, understanding that diabetes can cause retinopathy, visual acuity, and ophthalmology were the influencing factors of anxiety scores in diabetic patients (t/F=-3.795, 4.364, -7.079, 5.213, 3.117, 4.702, 20.793, 5.087, P<0.05). Gender, diabets duration, monthly income, understanding that diabetes can cause retinopathy, visual acuity, and ophthalmology were the influencing factors of depression scores in diabetic patients (t/F=-2.363, -5.162, 3.844, -2.707, 12.638, -2.586, P<0.05). The results of multiple linear regression showed that gender, age, understanding of their condition, and visual acuity were the influencing factors of anxiety scores in diabetic patients. Gender and visual acuity were the influencing factors of depression score in diabetic patients. Patients with diabetic retinopathy have higher levels of anxiety and depression than those without retinopathy. Gender, age, time of diabetes, monthly income, understanding of their own condition, and visual acuity were the influencing factors of anxiety and depression scores in diabetic patients. It is necessary to give corresponding intervention to these factors so as to improve the quality of life of diabetic patients.

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