摘要：
In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.
摘要：
Radon in the household water (especially groundwater) which is an important source of indoor radon, has become a potential health hazard to residents. In this study, radon concentrations in groundwater sampled from five villages near Dongpo W-polymetallic metallogenic region were measured using RAD-7 detector with RAD H2O accessory, and the effect of regional geology and mineralization on radon concentration in groundwater was studied. In addition, we also estimated the radiation doses received by people via ingestion of radon in water and inhalation of the radon from the indoor air while using water. The results show that the radon concentration in groundwater samples varies from 1.29 Bq L(-1) to 31.31 Bq L(-1) with 10.47 Bq L(-1) on average, and about 31.3% of the groundwater samples analyzed have a higher radon concentration than the maximum contaminant level of 11.1 Bq L(-1) recommended by United States Environmental Protection Agency (USEPA). The relatively high radon level in groundwater can be attributed to a relatively high uranium background produced by the magmatic activity and magmatic-hydrothermal system. The values of annual effective dose (AEDing) due to ingestion of radon in groundwater range from 0.002mSv y(-1) to 0.055mSv y(-1), 0.005mSv y(-1) to 0.11mSv y(-1) and 0.008mSv y(-1) to 0.188mSv y(-1) for adult, child and infant respectively. The values of annual effective dose due to the inhalation of radon released from water are 63.6, 15.4 and 3.8 times of those through the ingestion of radon in groundwater by the adults, children and infants, respectively. In addition, the values of estimated total annual effective doses are 0.020-0.480mSv y(-1), 0.017-0.406mSv y(-1) and 0.020-0.484mSv y(-1) for adult, child and infant, respectively. These values are much lower than the reference dose level of 1mSv y(-1) recommended by World Health Organization (WHO) and United Nations Scientific Committee on the Effect of Atomic Radiation (UNSCEAR).
摘要：
In contrast to the Wiener index, the detour index considers the length of the longest path between each pair of vertices. We give the explicit expressions for the expected values of the detour index and the hyper-detour index of the random polyphenylene chain.
摘要：
Let G = (V, E) be a connected simple graph with vertical bar V vertical bar = n and vertical bar E vertical bar m. The first and the second multiplicative Zagreb eccentricity index are defined as Z(1)(G) = Pi(u is an element of v(G)) e(u)(2) and Z(2)(G) = Pi(uv is an element of E(G)) e(u)e(v) respectively, where e(u) is the eccentricity of a vertex u of G. The multiplicative eccentric connectivity index is defined by Z(3)(G) Pi(uv is an element of E(G)) (e(u) + e(v)). In this paper, the comparisions between these indices are investigated in detail. As a result, an inequality for the index Z(3)(G), which is similar to the Zagreb indices inequality, is proved.
关键词：
Bifurcation control;Competitive web site model;Internet;Stability;Hopf bifurcation;Fractional order;Delay
摘要：
In today's society, the Internet has become an important tool of our life due to its potential applications in various areas such as economics, industry, agriculture, medical and health care, and information processing. To understand and grasp the law of the Internet, many competitive web site models of the Internet and some phenomena related to World Wide Web have been investigated systematically. However, many scholars only study the integer-order competitive web site models of the Internet. Up to now, there are few papers that focus on the dynamics of fractional-order competitive web site models of Internet, which possess memory property. In this paper, we are concerned with the stability and the existence of Hopf bifurcation of a fractional-order competitive web site model of Internet. By choosing the time delay as parameter and applying the Routh-Hurwitz criteria, we will establish a new sufficient condition guaranteeing the stability and the existence of Hopf bifurcation for fractional-order competitive web site model of Internet. The research reveals that fractional order and the delay play a key role in describing the stability and Hopf bifurcation of the considered system. Computer simulations are implemented to support the analytic results. Finally, a simple conclusion is presented. The theoretical findings of this article have a great significance in handling the competition dynamics among different web sites.
期刊：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION,2019年9(4):1393-1406 ISSN：2156-907X
通讯作者：
Xiao, Qizhen
作者机构：
[Xiao, Qizhen; Liu, Hongliang; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Shi, Hongxia] Hunan First Normal Univ, Sch Math & Computat Sci, Changsha 410205, Hunan, Peoples R China.;[Chen, Haibo] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Xiao, Qizhen] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Biharmonic equation;ground state and nodal solution;variational methods;Hessian matric;energy doubling
作者机构：
[Cassani, Daniele; Zhang, Jianjun] Univ Insubria, Dip Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy.;[Cassani, Daniele] RISM, Via GB Vico 46, I-21100 Varese, Italy.;[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Tarsi, Cristina] Univ Milan, Dip Matemat, Via C Saldini 50, I-20133 Milan, Italy.;[Zhang, Jianjun] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.
通讯机构：
[Tarsi, Cristina] U;Univ Milan, Dip Matemat, Via C Saldini 50, I-20133 Milan, Italy.
关键词：
Kirchhoff equations;Sign-changing solutions;Invariant sets of descending flow
摘要：
We are concerned with sign-changing solutions to nonlocal perturbation of the nonlinear Schrodinger equation in the whole R-3. By using the method of invariant sets of descending flow, we prove the existence of multiple sign-changing solutions provided the perturbation is sufficiently small. (C) 2019 Elsevier Ltd. All rights reserved.
摘要：
We derive a more generally parameterized post-post-Newtonian solution for the light propagation in the gravitational field of one spherically-symmetric body. Based on the solution for the light velocity, we give the formula of the light deflection when both the emitter and receiver are located in the regions far away from the body, which is the most important scenario in the real applications. Our results can be applied to more metric theories of gravitation.
期刊：
Mechanics Based Design of Structures and Machines,2019年47(4):479-496 ISSN：1539-7734
通讯作者：
Rao, Qiuhua
作者机构：
[Xu, Feng] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.;[Xu, Feng; Rao, Qiuhua] Univ South China, Sch Civil Engn, Changsha 410075, Hunan, Peoples R China.;[Ma, Wenbo] Xiangtan Univ, Coll Civil Engn & Mech, Xiangtan, Peoples R China.
通讯机构：
[Rao, Qiuhua] U;Univ South China, Sch Civil Engn, Changsha 410075, Hunan, Peoples R China.
关键词：
Traction force;compressive and shearing rheological model;structure optimization;track shoe;sinkage
摘要：
Based on compressive and shearing rheological models of the deep-sea sediment simulant, new rheological calculation formulae of traction forces for actual track shoe structures were deduced and the multi-objective structural optimization models were established in order to determine optimal track shoe structural parameters. RecurDyn software with introduction of programed rheological models was used to simulate the moving performances of the tracked mining vehicle before and after optimization. Research results show that the maximum traction force calculated by the new rheological calculation formula is much smaller than that by the Bekker theory and more close to the actual situation. The optimized tracked mining vehicle has larger traction force and smaller sinkage than the original tracked mining vehicle, which verifies the validity of the multi-objective optimization model based on the new rheological calculation formula of track force. It is better to choose the thick-triangle track shoe or the sharp-triangle track shoe when the sinkage or the traction force is considered as a dominant factor, respectively. The new rheological calculation formula of traction force and the multi-objective structural optimization model could provide a theoretical basis for safe operation and optimal design of a tracked mining vehicle.
作者机构：
[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Zhang, Jianjun] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.;[Zhang, Jianjun] Univ Insubria, Dipartimento Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy.
通讯机构：
[Zhang, Jianjun] C;[Zhang, Jianjun] U;Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.;Univ Insubria, Dipartimento Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy.
关键词：
gauged Schrodinger equations;sign-changing solutions;invariant sets of descending flow
摘要：
We are concerned with sign-changing solutions of the following gauged nonlinear Schrodinger equation in dimension two including the so-called Chern-Simons term {-Delta u + omega u + (h2(vertical bar x vertical bar)/vertical bar x vertical bar(2) + integral(+infinity)(vertical bar x vertical bar) h(s)/s u(2)(s) ds) u = u = lambda vertical bar u vertical bar(p-2) u in R-2, u(x) = u(vertical bar x vertical bar) is an element of H-1(R-2), where omega, lambda > 0, p is an element of (4, 6) and h(s) = 1/2 integral(s)(0) tau u(2)(tau)d tau. Via a novel perturbation approach and the method of invariant sets of descending flow, we investigate the existence and multiplicity of sign-changing solutions. Moreover, energy doubling is established, i.e. the energy of sign-changing solution w(lambda) is strictly larger than twice that of the ground state energy for lambda > 0 large. Finally, for any sequence lambda(n) -> infinity as n -> infinity, up to a subsequence, lambda(1/p-2)(n) w(lambda n) -> w strongly in H-rad(1)(R-2) as n -> infinity, where w is a sign-changing solution of -Delta u + omega u = vertical bar u vertical bar(p-2)u, u is an element of H-rad(1) (R-2).
