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排序方式: 共有206条查询结果,搜索用时 15 毫秒
1.
In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions. 相似文献
2.
We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant. 相似文献
3.
Frictionless indentation responses of transversely isotropic piezoelectric film/rigid substrate systems under circular cylindrical indenter (i.e., punch), conical indenter (i.e., cone), and spherical indenter (i.e., sphere) are investigated. Both insulating and conducting indenters are considered. The technique of Hankel transformation is employed to derive the corresponding dual integral equations for the mixed boundary value indentation problems. For the two limiting cases of infinitely thick and infinitely thin piezoelectric films, closed-form solutions are obtained. For piezoelectric films of finite thickness, a numerical method is constructed to solve the dual integral equations and semi-empirical models having only two unknown parameters are proposed for the responses of indentation force, electric charge and electric potential, and contact radius. With the two parameters inferred from the numerical results, the semi-empirical formulae are found to provide good estimates of the indentation responses for the two limiting cases of infinitely thick and thin piezoelectric films, as well as those in between. The inferred parameters in the proposed semi-empirical formulae for normalized indentation force and electric charge are checked against four different piezoelectric materials and are found to be insensitive to the selection of piezoelectric materials. It is believed that the proposed semi-empirical indentation formulae are useful in developing experimental indentation techniques to extract the material properties of piezoelectric films. 相似文献
4.
T. Wanjun L. Yuwen Y. Xil W. Zhiyong W. Cunxin 《Journal of Thermal Analysis and Calorimetry》2005,81(2):347-349
Summary In this paper two approximate formulae have been developed for calculation of the integral òT0Tmexp(-E/RT)dT by using integration-by-parts approaches. They are in the following forms: I(m,T) = (RTm+2)/(E+(m+2)RT)exp(-E/RT) I(m,T) = (RTm+2)/(E+(m+2)(0.00099441E+0.93695599RT)exp(-E/RT) The validity of the two formulae has been confirmed and their accuracies have been tested with data from numerical calculating. In contrast to existing other integral methods, both the present approaches are simply used, accurate, and can be used for arbitrary values of m. 相似文献
5.
Analysis of mono- and disaccharides in milk-based formulae by high-performance liquid chromatography with refractive index detection 总被引:1,自引:0,他引:1
A simple and reproducible method for the qualitative and quantitative analysis of free mono- and disaccharides (fructose, glucose, galactose, sucrose, lactulose and lactose) in milk-based formulae by high-performance liquid chromatography (HPLC) with refractive index (RI) detection was developed and validated. The method showed good linearity with determination coefficients exceeding 0.99. The limits of detection (DL) in these sugars were 0.17, 0.13, 0.06, 0.16, 0.05 and 0.25 mg/ml, respectively; and the limits of quantification (QL), 0.27, 0.24, 0.20, 0.26, 0.22 and 0.38 mg/ml. The relative standard deviations (R.S.D.s) for repeatability in fructose, sucrose, lactulose and lactose were 0.78, 0.99, 2.91 and 0.46 and the R.S.D.s for reproducibility were 4.8, 6.15, 7.04 and 2.49, respectively. Recoveries in all sugars were between 93 and 113%. 相似文献
6.
董艳 《数学的实践与认识》2016,(9):40-46
在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性. 相似文献
7.
8.
J. Morais M. A. Pérez‐de la Rosa 《Mathematical Methods in the Applied Sciences》2015,38(17):4365-4387
Over the past few years, considerable attention has been given to the role played by the Lamé's Wave Functions (LWFs) in various problems of mathematical physics and mechanics. The LWFs arise via the method of separation of variables for the wave equation in ellipsoidal coordinates. The present paper introduces the Lamé's Quaternionic Wave Functions (LQWFs), which extend the LWFs to a non‐commutative framework. We show that the theory of the LQWFs is determined by the Moisil‐Theodorescu type operator with quaternionic variable coefficients. As a result, we explain the connections between the solutions of the Lamé's wave equation, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions on the other. We establish analogues of the basic integral formulas of complex analysis such as Borel‐Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. We further obtain analogues of the boundary value properties of the LQWFs such as Sokhotski‐Plemelj formulae, the ‐hyperholomorphic extension of a given Hölder function and on the square of the singular integral operator. We address all the text mentioned earlier and explore some basic facts of the arising quaternionic function theory. We conclude the paper showing that the spherical, prolate, and oblate spheroidal quaternionic wave functions can be generated as particular cases of the LQWFs. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
9.
Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume. 相似文献
10.