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一类变时滞泛函微分方程的解
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作者 林壮鹏 林瀚 陈雯雯 《高等数学研究》 2012年第1期35-39,共5页
用皮卡(Picard)逐步逼近法证明一类变时滞泛函微分方程初值问题解的存在唯一性,它是常时滞泛函微分方程相应结论的推广.利用该结论可构造出一个新实例.
关键词 变时滞泛函微分方程 解的存在唯一性 皮卡方法
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非线性抛物方程初值问题解的存在性及其Picard逼近
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作者 杨金林 《包头钢铁学院学报》 1992年第1期5-10,共6页
本文应用Picard逼近方法证明了一类非线性抛物型方程初值问题解的存在性。
关键词 非线性 抛物型方程 皮卡逼近方法 初值问题
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一类非线性抛物方程初值问题解的存在性
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作者 杨勤荣 杨金林 《阴山学刊(自然科学版)》 1997年第1期1-4,共4页
本文应用皮卡逼近方法证明了一类非线性抛物型方程初值问题解的存在性.
关键词 皮卡方法 抛物型方程 非线性 初值问题
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Numerical Investigation of the Thermal Response to Skin Tissue during Laser Lipolysis 被引量:2
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作者 CHEN Bin ZHANG Yue LI Dong 《Journal of Thermal Science》 SCIE EI CAS CSCD 2018年第5期470-478,共9页
Laser lipolysis can effectively treat obesity and its associated diseases, such as hypertension, fatty liver, and hyperlipidemia. However, currently available invasive laser lipolysis, which transmits laser to a fiber... Laser lipolysis can effectively treat obesity and its associated diseases, such as hypertension, fatty liver, and hyperlipidemia. However, currently available invasive laser lipolysis, which transmits laser to a fiber-optic catheter inserted into the subcutaneous tissue for irradiation through an incision, may cause hematomas, infections, and empyrosis. The current study presents a novel, noninvasive approach for laser lipolysis, which directly irradiates the intact skin surface without an incision and preferentially targets adipose tissue at the near-infrared band. High laser energy is necessary to damage adipocytes; however, this may carbonate and burn the dermis. Therefore, the introduction of skin cooling is essential to avoid unwanted hyperthermal injury and improve the threshold of radiant exposure. In the current study, we investigated a novel noninvasive approach assisted with skin cooling by establishing a homogeneous multi-layer skin model. In this method, light propagation in the skin was simulated by using the Monte Carlo method. Skin cooling was employed before laser irradiation to protect the epidermis from thermal damage, which was treated as a boundary condition based on Newton's law. The numerical results showed that the photons were deposited in the adipose layer more than in the other layers. Laser can effectively destroy adipose tissue at an energy density of >200 J/cm^2 at 1210 nm wavelength, whereas at least 300 J/cm^2 is required at 1064 nm to achieve the same effect. In this experiment, at >5 s pulse width, the selectivity of adipose was not obvious. Moreover, the results indicated that 60 ms R134a or R404a spray can effectively reduce the temperature of the epidermis. R404a exhibited a stronger cooling effect than R134a. Cold air cooling at -10 °C for 10 s could effectively decrease the skin temperature, and deeper cooling could be achieved by cold air cooling compared with cryogen spray cooling. 展开更多
关键词 laser lipolysis Nd:YAG laser multi-layer skin model skin cooling
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