Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.     

Focusing properties of a bounded cylindrical field

Numerical solution of motion equations has been used in the non-relativistic limit in order to determine the focussing properties of the cylindrical field between concentric cylinders of radii R₁, R₂ with two boundaries along the Z-axis, for charged particles entering the field parallel to the symmetry axis. The field is a solution of the Laplace equation ²U(R, Z)=0, with the boundary conditions as follows: U(R₁, Z)=U(R, 0)=U(R, L)=0, U(R₂, Z)=V. It was shown that this field can be used for the energy analysis with second order focussing.     

Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives, when emergencies occur, rumors will spread widely on the internet. However, it is quite difficult for the netizens to distinguish the truth of the information. The main reasons are the uncertainty of netizens' behavior and attitude, which make the transmission rates of these information among social network groups be not fixed. In this paper, we propose a stochastic rumor propagation model with general incidence function. The model can be described by a stochastic differential equation. Applying the Khasminskii method via a suitable construction of Lyapunov function, we first prove the existence of a unique solution for the stochastic model with probability one. Then we show the existence of a unique ergodic stationary distribution of the rumor model, which exhibits the ergodicity. We also provide some numerical simulations to support our theoretical results. The numerical results give us some possible methods to control rumor propagation. Firstly, increasing noise intensity can effectively reduce rumor propagation when $\widehat{\mathcal{R}}$₀>1. That is, after rumors spread widely on social network platforms, government intervention and authoritative media coverage will interfere with netizens' opinions, thus reducing the degree of rumor propagation. Secondly, speed up the rumor refutation, intensify efforts to refute rumors, and improve the scientific quality of netizen (i.e., increase the value of β and decrease the value of α and γ), which can effectively curb the rumor propagation.     

Towards a realistic Einstein-Gauge cosmology

We present the cosmological solutions in the six-dimensional Einstein-gauge theory to which is added a matter term. The general behavior of the scale factors of the ordinary (R₃) and extra (R₂) dimensions can be depicted in four stages. Stage 1: Both R₃ and R₂ expand. Stage 2: R₂ is a constant and R₃ is an inflationary solution. Stage 3: R₂ recollapses towards its minimum value, R₃ will continue to increase monotonically. Stage 4: R₂ stabilizes at R_KK and R₃ expands in the usual FRW way, while the four-dimensional cosmological constant becomes zero.     

Shape coexistence in 76Se within the neutron–proton interacting boson model

We have investigated the low-lying energy spectrum and electromagnetic transition strengths in even–even ⁷⁶Se using the proton–neutron interacting boson model (IBM-2). The theoretical calculation for the energy levels and E2 and M1 transition strengths is in good agreement with the experimental data. Specifically, the excitation energy and E2 transition of ${0}_{2}^{+}$ state, which is intimately associated with shape coexistence, can be accurately reproduced. The analysis on low-lying states and the key structure indicators R₁, R₂, R₃ and R₄ and M1 transitions indicates that there is a coexistence between spherical shape and γ-soft shape in ⁷⁶Se.     

级联式平面抛物面型X射线组合折射透镜的设计与制作

X射线组合折射透镜(CRL)已逐步成为同步辐射光源下X射线聚焦光学器件的标准配件之一,它具有结构紧凑、易调节校准、适用光子能量范围大等优点.本文设计了一种级联式平面抛物面型CRL,它将N1个具有较大抛物面几何孔径(R0)的折射单元I与N2个具有较小抛物面顶点曲率半径(R)的折射单元II级联,以解决常规CRL设计过程中焦斑尺寸与透过率的矛盾.采用PMMA材料,利用LIGA技术制作了一组级联式平面抛物面型CRL,其中折射单元I的主要结构参数为N1=15,R1=200μm,2R01=564μm;折射单元II的主要结构参数为N2=20,R2=50μm,2R02=140μm.在上海光源同步辐射线束上,所制作的级联式平面抛物面型CRL实现了对初始光斑尺寸为200μm×100μm的入射X射线的一维聚焦,测试得到的焦距为1.052 m,横向焦斑尺寸为24.9μm@8 keV,透过率为2.19%.     

Multilayer relaxation of Rh(311)

The multilayer relaxation of the Rh(311) surface was investigated by means of LEED structure determination both for vertical and surface parallel (registry) relaxations. Excellent agreement between experimental and calculated spectra could be achieved mirrored by a minimum Pendry R-factor R = 0.174. The first three layer spacings are oscillatorily relaxed by Δd₁₂/d₀ = −14.5 ± 1.8%, Δd₂₃/d₀ = +4.9 ±2.0% and Δd₃₄/d₀ = −1.0 ±2.0%. There seems to be a coherent registry shift of the fir Δs = 0.03 ± 0.07 Å which, however, is within the error limits of the structure determination. Moreover, an energy dependent inner potential is detected. The results are discussed in comparison to equivalent surfaces of other materials as well as for the less open surfaces of rhodium.     

Etching mask optimization of InAs/GaSb superlattice mid-wavelength infared 640×512 focal plane array

In this paper we focused on the mask technology of inductively coupled plasma(ICP) etching for the mesa fabrication of infrared focal plane arrays(FPA).By using the SiO_2 mask,the mesa has higher graphics transfer accuracy and creates less micro-ripples in sidewalls.Comparing the IV characterization of detectors by using two different masks,the detector using the SiO_2 hard mask has the R_0A of 9.7×10~6 Ω·cm~2,while the detector using the photoresist mask has the R_0A of3.2 × 10~2 Ω·cm~2 in 77 K.After that we focused on the method of removing the remaining SiO_2 after mesa etching.The dry ICP etching and chemical buffer oxide etcher(BOE) based on HF and NH4 F are used in this part.Detectors using BOE only have closer R_0A to that using the combining method,but it leads to gaps on mesas because of the corrosion on AlSb layer by BOE.We finally choose the combining method and fabricated the 640×512 FPA.The FPA with cutoff wavelength of 4.8 μm has the average R_0A of 6.13 × 10~9 Ω·cm~2 and the average detectivity of 4.51 × 10~9 cm·Hz~(1/2).W~(-1)at 77 K.The FPA has good uniformity with the bad dots rate of 1.21%and the noise equivalent temperature difference(NEDT) of 22.9 mK operating at 77 K.     

白光发光二级管用红色荧光粉LiSrBO3: Eu3+的制备与发光性能研究

采用高温固相法制备了LiSrBO₃:xEu³⁺ 荧光粉, 并通过XRD, 红外(FITR) 和荧光光谱(PL) 等对其表征. 结果表明, LiSrBO₃: Eu³⁺ 荧光粉可被波长为395 nm 的紫外线和466 nm 的蓝光有效激发, 且发射主波长为612 nm (Eu³⁺的电偶极跃迁⁵D₀ →⁷F₂) 的红光. 研究了Eu³⁺ 掺杂浓度对LiSrBO₃: Eu³⁺ 材料发光强度的影响, Eu³⁺ 掺杂浓度为6% 时样品的发射强度最大, 并且证实Eu³⁺ 之间的能量传递机制为电偶极子- 电偶极子相互作用. Li⁺, Na⁺, K⁺ 作为电荷补偿剂的引入全部导致LiSrBO₃: Eu³⁺ 材料发射强度增强, 其中, Li⁺ 的引入要优于Na⁺ 和K⁺. 少量Al³⁺的掺杂降低了Eu³⁺ 所处格位的对称性, 增强了Eu³⁺ 的612 nm 的电偶极发射, 改善了LiSrBO₃: Eu³⁺ 红色材料的色纯度. 关键词： 白光发光二级管 光致发光 浓度猝灭 电荷补偿剂     

The thermodynamics of purely elastic scattering theories and conformal perturbation theory

We discuss the thermodynamic Bethe ansatz, and explain how it allows one to reduce the infinite-volume thermodynamics of a (1 + 1)-dimensional purely elastic scattering theory to the solution of a set of integral equations for the one-particle excitation energies. The free energy at zero chemical potential(s) and temperature T is related to the ground state energy E₀(R) of the theory on a cylinder of circumference R = 1/T. E₀(R) determines properties of the CFT describing the UV limit of the given massive theory. These include the central charge (which we investigated in earlier work), the scaling dimension d of the conformal field whose perturbation leads to the massive theory, the coefficients in the conformal perturbation theory (CPT) expansion of E₀(R) in powers of R^2−d, and the bulk term in the CPT calculation of the ground-state energy. We determine the bulk term analytically, and obtain numerically the first six coefficients in the expansion of E₀(R) for many purely elastic scattering theories, including the scaling limit of the T = T_c Ising model in a magnetic field. The perfect agreement with (more limited) direct CPT results provides further strong support for the identification of these theories as specific perturbed CFTs. We suggest that the singularities of E₀(R), the first of which is responsible for the finite radius of convergence of CPT, are square-root branch points and related to the zeros of the partition function of the corresponding lattice model.     

(2+1)维Korteweg-de Vries方程的复合波解及局域激发

借助Maple符号计算软件,利用Pdccati方程(ζ′=a_0+a_1ζ+a_2ζ~2)展开法和变量分离法,得到了(2+1)维Korteweg-de Vries方程(KdV)包含q=C_1x+C_2y+C_3t+R(x,y,t)的复合波解,根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。     

H3正三角形和H4正四面体结构的变分计算

采用改进排列通道量子力学(Modified Arrangement Channel Quantum Mechanics,简称MACQM)方法和变分法,计算了H₃体系正三角形和H₄体系的正四面体结构的能量曲线.当H₃体系原子核的间距R=1.74a₀,波函数变分参数α=1.03时,体系能量有最低值-1.58161 a.u.;当H₄体系原子核的间距R=1.60a₀,波函数变分参数α=1.07时,体系能量有最低值-2.28097 a.u.,这表明H₃体系的正三角形构型和H₄的正四面体结构是可以稳定存在的.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Comparative analysis of the 1H NMR relaxation enhancement produced by iron oxide and core-shell iron-iron oxide nanoparticles

Physicochemical and magnetorelaxometric characterization of the colloidal suspensions consisting of Fe-based nanoparticles coated with dextran have been carried out. Iron oxide and iron core/iron oxide shell nanoparticles were obtained by laser-induced pyrolysis of Fe(CO)₅ vapours. Under different magnetic field strengths, the colloidal suspension formed by iron oxide nanoparticles showed longitudinal (R₁) and transverse (R₂) nuclear magnetic relaxation suspension (NMRD) profiles, similar to those previously reported for other commercial magnetic resonance imaging (MRI) contrast agents. However, colloidal suspension formed by ferromagnetic iron-core nanoparticles showed a strong increase of the R₁ values at low applied magnetic fields and a strong increase of the R₂ measured at high applied magnetic field. This behaviour was explained considering the larger magnetic aggregate size and saturation magnetization values measured for this sample, 92 nm and 31 emu/g Fe, respectively, with respect to those measured for the colloidal suspensions of iron oxide nanoparticles (61 nm and 23 emu/g Fe). This suspension can be used both as T₁ and T₂ contrast agent.     

Identification of patients with hereditary haemochromatosis by magnetic resonance imaging and spectroscopic relaxation time measurements

A total of 4302 healthy blood donors were screened for elevated serum ferritin and transferrin saturation. Fifteen had increased serum ferritin at a follow-up examination. Five relatives of these donors also entered the study. Eleven patients had elevated liver iron concentrations, while five had normal liver iron concentrations. The R₂ relaxation rate in the liver was first measured with a conventional multi-spin-echo imaging sequence, and then by a volume-selective spectroscopic multi-spin-echo sequence, in order to achieve a minimum echo time of 4 msec. No correlation was found between the relaxation rate R₂ and the liver iron concentration, when R₂ was calculated from the imaging data. Multi-exponential transverse relaxation could be resolved when the spectroscopic sequence was used. A strong correlation between the initial slope of the relaxation curve and the liver iron concentration was found (r = 0.90, p < 0.001). Signal intensity ratios between liver and muscle were calculated from the first three echoes in the multi-echo imaging sequence, and from a gradient echo sequence. A strong correlation between the logarithm of the signal intensity ratios and the liver iron concentration was found. Although both spectroscopic T₂ relaxation time measurements and signal intensity ratios could be used to quantify liver iron concentration, the gradient echo imaging seemed to be the best choice. Gradient echo imaging could be performed during a single breath hold, so motion artifacts could be avoided. The accuracy of liver iron concentration estimates from signal intensity ratios in the gradient echo images was about 35%.     

Computer modeling of carrier transport in PbSnSe photodiodes

A numerical technique has been used to solve the carrier transport equations for n⁺−p Pb_0.935Sn_0.065Se photodiode configuration. The model computes the spatial distribution of the electric field, electron and hole concentrations and the generation-recombination mechanisms. Also the effect of doping profiles on the photodiode parameters (R₀A product, quantum efficiency) is analysed. Results of calculations indicate the potential possibilities of constructing higher quality PbSnSe photodiodes. The R₀A product of experimentally measured PbSnSe photodiodes is controlled by Shockley-Read generation-recombination mechanisms.     

Two-loop renormalization of tanβ and its gauge dependence

Renormalization of two-loop divergent corrections to the vacuum expectation values (v₁,v₂) of the two Higgs doublets in the minimal supersymmetric standard model, and their ratio tanβ=v₂/v₁, is discussed for general R_ξ gauge fixings. When the renormalized (v₁,v₂) are defined to give the minimum of the loop-corrected effective potential, it is shown that, beyond the one-loop level, the dimensionful parameters in the R_ξ gauge fixing term generate gauge dependence of the renormalized tanβ. Additional shifts of the Higgs fields are necessary to realize the gauge-independent renormalization of tanβ.     

Fluctuation-induced attraction of vortices in anisotropic superconductors

We study the fluctuation-induced attraction of vortices for continuous anisotropic superconductors by using quantum statistical physics. In the low temperature or quantum limit, only the low-lying modes are relevant, the induced short-range attractive potential is proportional to (k_BT)³K₁(ΓR/λ), while in high temperature or classical limit, the induced attractive potential reduced to long-range van der Waals type k_BT/R⁴ for two vortices separated by a distance R.     

Magnetic properties of novel superparamagnetic MRI contrast agents based on colloidal nanocrystals

Novel systems based on colloidal magnetic nanocrystals (NCs), potentially useful as superparamagnetic (SP) contrast agents for magnetic resonance imaging (MRI) have been investigated. The NCs we have studied comprise organic-capped single-crystalline maghemite (γ-Fe₂O₃) cores possessing controlled sizes and shapes. We have comparatively examined spherical and tetrapod-like NCs, the latter being branched particles possessing four arms which depart out at tetrahedral angles from a central point. The as-synthesized NCs are passivated by hydrophobic surfactant molecules and thus are fully dispersible in nonpolar media only. The NCs have been made soluble in aqueous solution by applying a procedure based on the surface intercalation and coating with an amphiphilic polymer shell. NMR relaxivities R₁ and R₂ were compared with ENDOREM^®, one of the standard commercial SP-MRI contrast agent. We found that the spherical NCs exhibit R₁ and R₂ relaxivities slightly lower than those of ENDOREM^®, over the whole frequency range; on the contrary, tetrapods show relaxivities about one order of magnitude lower. The physical origin of such difference in relaxivities between tetrapod- and spheres-based nanostructures is under investigation and it is possibly related to different sources of the magnetic anisotropy.