The Improper Integral

2015 ◽  
pp. 417-437
Author(s):  
Miklós Laczkovich ◽  
Vera T. Sós
Keyword(s):  
Improper Integral

70.25 An Improper Integral Evaluated

1986 ◽  
Vol 70 (452) ◽  
pp. 144
Author(s):  
A. Sackfield ◽  
D. A. Hills
Keyword(s):  
Improper Integral

Rotational λ – hypersurfaces in Euclidean spaces

2021 ◽  
Vol 30 (1) ◽  
pp. 29-40
Author(s):  
KADRI ARSLAN ◽  
ALIM SUTVEREN ◽  
BETUL BULCA
Keyword(s):  
Present Article ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Special Solution ◽  
Euclidean Spaces ◽  
Self Similar ◽  
The Mean ◽  
Similar Flows

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational \lambda -hypersurfaces in \mathbb{R}^{4}.

Study on Static Assembly Interference Pressure between a Thin-Wall Flexible Cup and a Hollow Flexible Shaft

2011 ◽  
Vol 179-180 ◽  
pp. 212-219
Author(s):  
Guo Ping Wang ◽  
Hua Ling Chen ◽  
She Miao Qi ◽  
Jiu Hui Wu ◽  
Lie Yu
Keyword(s):  
Cylindrical Shell ◽  
Pressure Distribution ◽  
Superposition Principle ◽  
Special Solution ◽  
Thin Wall ◽  
Thin Cylindrical Shell ◽  
Bending Deformation ◽  
Flexible Shaft ◽  
First Time ◽  
Thin Shell Theory

Distribution of static interference pressure between a thin-wall flexible cup and a flexible shaft fluctuates heavily along the axis of the cup and is quite different from pressure distribution of common interference styles. In this article, aiming at solving distribution of static interference pressure between a thin-wall flexible cup with much thicker bottom and a hollow flexible shaft, mechanical model and mathematical model of solving the problem were built based on classic thin shell theory. Special difference is that precise special solution of bending equation of thin cylindrical shell was used to substitute the special solution which is original from bending deformation of thin cylindrical shell in no moment status. And a brand new general solution, the relational expression between bending deformation of thin wall of the cup and distribution of the static interference pressure, was obtained. Then, a method used to solve the pressure distribution was presented by solving integral equation and applying superposition principle for the first time. Through using the method to solve an example and comparing calculated results with FEM results, it was proved that the method is correct and effective.

Spectral Moments Calculation of Linear System Output

1983 ◽  
Vol 50 (4a) ◽  
pp. 901-903 ◽  
Author(s):  
P-T. D. Spanos
Keyword(s):  
Dynamic Systems ◽  
Random Vibration ◽  
Linear Equations ◽  
Spectral Moments ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Improper Integral ◽  
System Output ◽  
Noise Input ◽  
Stable Linear

The stationary output of a stable linear dynamic system to white noise input is considered. It is shown that the spectral moments of the output can be determined as the solution of a set of linear equations. The corresponding solutions are utilized for determining an improper integral which can be quite useful in random vibration analyses of linear dynamic systems.

Teaching Electromagnetics through Finite Elements. Part I: The Rationale

1988 ◽  
Vol 25 (1) ◽  
pp. 33-49 ◽  
Author(s):  
S. Ratnajeevan H. Hoole
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Special Solution ◽  
The Finite Element Method ◽  
Solution Methods ◽  
Element Method

The rationale for teaching undergraduate electromagnetics partly through the finite element method, is put forward. Properly presented, the finite element method, easily within the ken of the engineering undergraduate, promotes clarity and helps to replace large portions of syllabi devoted to special solution methods, with problems of industrial magnitude and character.

scholarly journals Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Zhongyu Jiang ◽  
Guoqing Zhou
Keyword(s):  
Homogeneous Equation ◽  
Pressure Coefficient ◽  
Circumferential Stress ◽  
Surrounding Rock ◽  
Special Solution ◽  
Operator Matrix ◽  
Specific Expression ◽  
Symplectic Algorithm ◽  
Ground Stress ◽  
The Relationship

The stress analysis of the wellhole surrounding rock and the regular failure of the wellhole has always been a concern for the well builders. Firstly, the Hamilton canonical equations are obtained by using the Hamiltonian variational principle in the sector domain, and the zero eigensolution and nonzero eigensolutions of the homogeneous equation are solved. According to the Hamiltonian operator matrix with the orthogonal eigenfunction system, the special solution form of the nonhomogeneous boundary condition equation is obtained. Then, according to the principle of the same coefficient being equal, the relationship equation between the direction eigenvalue and the angle coefficient is obtained, from which the specific expression of the special solution of the equation can be determined. Furthermore, the analytical solution of the wellhole surrounding rock problem under nonuniform ground stress is obtained by using the linear elastic accumulative principle. Finally, a concrete example is given to compare the finite element method and the symplectic algorithm. The results are consistent, which ensures the accuracy and the reliability of the symplectic algorithm. The relationship between the circumferential stress distribution around the hole and the lateral pressure coefficient is further analyzed.

scholarly journals Zur Kaskadentheorie der Trennung polynärer Isotopengemische

1965 ◽  
Vol 20 (5) ◽  
pp. 663-666 ◽  
Author(s):  
Alfred Narten
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Isotope Separation ◽  
Special Solution ◽  
Ternary Mixtures ◽  
Important Case ◽  
Reflux Ratio ◽  
Maximum Production

The theory of isotope separation in cascades is extended to polynary mixtures. Conditions for minimum reflux (maximum production) are derived. For square cascades, the general solution of the differential equations is indicated; a special solution is given for the important case of large reflux ratio. The enrichment of middle components in ternary mixtures is discussed, it is shown to be impractical in a single square cascade.

scholarly journals Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Elhassan Eljaoui ◽  
Said Melliani ◽  
L. Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Fuzzy Mapping ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Improper Integral ◽  
Convolution Formula

We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

Sign in / Sign up

Export Citation Format

Share Document