Uniqueness of meromorphic solutions of a certain type of difference equations

Jun-Fan Chen,Shu-Qing Lin 대한수학회 2022 대한수학회보 Vol.59 No.4

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

Expressions of meromorphic solutions of a certain type of nonlinear complex differential equations

Jun-Fan Chen,Gui Lian 대한수학회 2020 대한수학회보 Vol.57 No.4

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^{n}+Q_{d}(z,f)=\sum_{i=1}^{3}p_{i}(z)e^{\alpha_{i}(z)}$$ are studied by using Nevanlinna theory, where $n\geq5$ is an integer, $Q_{d}(z,f)$ is a differential polynomial in $f$ of degree $d\leq n-4$~with rational functions as its coefficients, $p_{1}(z)$, $p_{2}(z)$, $p_{3}(z)$~are non-vanishing rational functions, and $\alpha_{1}(z)$, $\alpha_{2}(z)$, $\alpha_{3}(z)$ are nonconstant polynomials such that $\alpha_{1}'(z)$, $\alpha_{2}'(z)$, $\alpha_{3}'(z)$ are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.

EXPRESSIONS OF MEROMORPHIC SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR COMPLEX DIFFERENTIAL EQUATIONS

Chen, Jun-Fan,Lian, Gui Korean Mathematical Society 2020 대한수학회보 Vol.57 No.4

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Q_d(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p₁(z), p₂(z), p₃(z) are non-vanishing rational functions, and α₁(z), α₂(z), α₃(z) are nonconstant polynomials such that α'₁(z), α'₂(z), α'₃(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.

ON THE EXISTENCE OF SOLUTIONS OF FERMAT-TYPE DIFFERENTIAL-DIFFERENCE EQUATIONS

Chen, Jun-Fan,Lin, Shu-Qing Korean Mathematical Society 2021 대한수학회보 Vol.58 No.4

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

Compressive behavior of concrete under high strain rates after freeze-thaw cycles

Xudong Chen,Chen Chen,Zhiheng Liu,Jun Lu,Xiangqian Fan 사단법인 한국계산역학회 2018 Computers and Concrete, An International Journal Vol.21 No.2

The dynamic compressive behavior of concrete after freezing and thawing tests are investigated by using the split Hopkinson pressure bar (SHPB) technique. The stress-strain curves of concrete under dynamic loading are measured and analyzed. The setting numbers of freeze-thaw cycles are 0, 25, 50, and 75 cycles. Test results show that the dynamic strength decreases and peak strain increases with the increasing of freeze-thaw cycles. Based on theWeibull distribution model, statistical damage constitutive model for dynamic stress-strain response of concrete after freeze-thaw cycles was proposed. At last, the fragmentation test of concrete subjected to dynamic loading and freeze-thaw cycles is carried out using sieving statistics. The distributions of the fragment sizes are analyzed based on fractal theory. The fractal dimensions of concrete increase with the increasing of both freeze-thaw cycle and strain rate. The relations among the fractal dimension, strain rates and freeze-thawing cycles are developed.

Family History, Tobacco Smoking, and Risk of Ischemic Stroke

Mengyu Fan,Jun Lv,Canqing Yu,Yu Guo,Zheng Bian,Songchun Yang,Ling Yang,Yiping Chen,Feifei Li,Yaoming Zhai,Ping Wang,Junshi Chen,Zhengming Chen,Lu Qi,Liming Li 대한뇌졸중학회 2019 Journal of stroke Vol.21 No.2

Background and Purpose Both genetic factors and smoking are associated with ischemic stroke (IS) risk. However, little is known about the potential interaction of these factors. We aimed to assess whether smoking and a positive family history interact to increase the risk of IS. Methods The nationwide prospective study recruited 210,000 men and 300,000 women in 2004 to 2008 at ages 30 to 79 years. During 9.7 years of follow-up, we documented 16,923 and 20,656 incident IS cases in men and women without major chronic diseases at baseline, respectively. Multivariable Cox regression models were used to examine associations between family history and IS. Likelihood ratio tests were used to test the smoking-family history interactions on IS. Results About 67.8% (n=135,168) of men ever smoked regularly compared with 2.7% (n=7,775) of women. Among men, a significant interaction between family history and smoking on IS was observed (P for interaction=0.03), with more pronounced association between family history and IS among ever-regular smokers (hazard ratio [HR], 1.21; 95% confidence interval [CI], 1.16 to 1.27) than among never-smokers (HR, 1.11; 95% CI, 1.01 to 1.23). The association between family history and IS among ex-smokers after more than 10 years of cessation (HR, 1.01; 95% CI, 0.85 to 1.20) appeared similar to that among never-smokers. Among women, a similar but not significant interaction between family history and smoking on IS was observed. Ever-regular smokers who had a family history of stroke had the highest risk of IS. Conclusions Among Chinese men, the association of family history with IS was accentuated by smoking, and such accentuation tended to be lowered by cessation.

Structural Characterization and Optical Properties of Sol-gel-derived Polycrystalline Pb(Zr0.35Ti0.65)O3 Thin Films

Fan Zhang,Rong-Jun Zhang,Zi YiWang,Yu-Xiang Zheng,Song-You Wang,Hai-Bin Zhao,Liang-Yao Chen,Xiao Bin Liu,An Quan Jiang 한국물리학회 2013 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.63 No.1

Polycrystalline Pb(Zr0.35Ti0.65)O3 thin films prepared on Pt/Ti/SiO2/Si substrate by using solgel technique were characterized by using X-ray diffraction (XRD) and atomic force microscopy (AFM). The optical properties of the films were investigated by using spectroscopic ellipsometry (SE) with a four-phase optical model, air/roughness layer/PZT layer/Pt layer in the spectral range of 300 - 800 nm. The optical band gap of the films calculated following the Tauc’s Law was smaller than that of an amorphous PZT thin film with some microcrystals existing on the surface. The result indicates that the quantum-size effect leads to an increase in band gap when the crystalline dimensions become very small.

Silica Nano-particle Anneal Treatment and Its Effect on Chemical Mechanical Polishing

Junning Chen,Shibin Lu,Haibo Wang,Ying Meng,Feifei Wang,Min Fan 대한전기학회 2019 Journal of Electrical Engineering & Technology Vol.14 No.1

Introduction: Chemical mechanical polishing is the only one technology to obtain global planarization, which is widely applied to polish silicon, copper dual damascene structure, high/low K dielectric materials, tungsten plugs, poly-silicon gates and shallow trench isolation structure. SiO2 is widely used as abrasive for its superior properties like stability, suspension property and low viscosity There are lots of studies on silica properties. However, the detailed silica surface, inner characteristic and its effect on polishing performance are still unclear. we must also explore the silica nano-particle tiny structure difference, so we designed an experiment that we anneal the colloid silica and re-dispersed it to analyze the variety of particles properties and its influences on CMP performance. Materials: The water glass was purchased from the market. KOH (90%) and H2SO4 (98%) were purchased commercially from Shanghai Aladdin Bio-Chem technology Co., Ltd. All reagents were of analytical grade and used without further purification. Method: Diluted KOH or H2SO4 were added to 1 wt% annealed silica slurry to adjust pH value to 11.0. The slurry was milled in the polishing process. Arsenic doped 4 inch (100) silicon wafer was used to polish. The structural and morphological evolution of silica nano-particles induced by heat treatment are studied by scanning electron microscopy (SEM), X-Ray diffraction (XRD), Fourier transform infrared spectrum (FTIR), differential thermal (DTA) and thermal gravimetric analysis (TGA), which disclose the external and internal structure.

Viscosity methods of approximation for a common solution of a finite family of accretive operators

Jun-Min Chen,Li-Juan Zhang,Tie-Gang Fan 영남수학회 2011 East Asian mathematical journal Vol.27 No.1

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

Sampling-based Event-triggered and Self-triggered Control for Linear Systems

Jun Chen,Yuan Fan,Chengxiao Zhang,Cheng Song 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.3

This work considers the event-triggered and self-triggered control for linear systems with periodic sampling schemes. An event-triggered control using sampled states is proposed. The asymptotic stability of the closedloop system is guaranteed by a condition in terms of a linear matrix inequality. Moreover, a self-triggered control with sampling is presented and the next control task release time is predicted based on the current sampled data. It is noted that by introducing the periodic sampling scheme, Zeno behaviors can be naturally avoided in both of the algorithms. Finally, simulation results are provided to illustrate the theoretical effectiveness.