A Martin Compact with a Non-Negligible Irregular Boundary Point

1973 ◽  
Vol 17 (2) ◽  
pp. 351-355 ◽  
Author(s):  
M. G. Shur
Keyword(s):  
Boundary Point ◽  
Irregular Boundary

Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle

1983 ◽  
Vol 93 (3-4) ◽  
pp. 327-343 ◽  
Author(s):  
Y. A. Kondratiev ◽  
O. A. Oleinik
Keyword(s):  
Dirichlet Problem ◽  
Boundary Conditions ◽  
Boundary Point ◽  
Biharmonic Equation ◽  
Maximum Modulus ◽  
Integral Inequalities ◽  
Energy Estimates ◽  
Irregular Boundary ◽  
Continuity Of Solutions

SynopsisIn this paper energy estimates for solutions of the Dirichlet problem for the biharmonicequation, expressing Saint-Venant's principle in elasticity, are proved. From these integral inequalities, estimates for the maximum modulus of solutions and the gradient of solutions with homogeneous Diriehlet's boundary conditions in a neighbourhood of an irregular boundary point or in a neighbourhood of infinity are derived. These estimates characterize the continuity of solutions and their gradients at these points.

Dynamic Analysis of Cage Stress in Tapered Roller Bearings Using Component-Mode-Synthesis Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Tomoya Sakaguchi ◽  
Kazuyoshi Harada
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Boundary Point ◽  
Axial Load ◽  
Synthesis Method ◽  
Load Condition ◽  
Component Mode Synthesis ◽  
Analysis Model ◽  
Tapered Roller ◽  
Tapered Roller Bearings

In order to investigate cage stress in tapered roller bearings, a dynamic analysis tool considering both the six degrees of freedom of motion of the rollers and cage and the elastic deformation of the cage was developed. Cage elastic deformation is equipped using a component-mode-synthesis (CMS) method. Contact forces on the elastically deforming surfaces of the cage pocket are calculated at all node points of finite-elements on it. The location and pattern of the boundary points required for the component-mode-synthesis method were examined by comparing cage stresses in a static condition of pocket forces and constraints calculated by using the finite-element and the CMS methods. These results indicated that one boundary point lying at the center on each bar is appropriate for the effective dynamic analysis model focusing on the cage stress, especially at the pocket corners of the cages, which are actually broken. A behavior measurement of a polyamide cage in a tapered roller bearing was conducted for validating the analysis model. It was confirmed in both the experiment and analysis that the cage whirled under a large axial load condition and the cage center oscillated in a small amplitude under a small axial load condition. In the analysis, the authors discussed the four models including elastic bodies having a normal eigenmode of 0, 8 or 22, and rigid-body. There were small differences among the cage center loci of the four models. These two cages having normal eigenmodes of 0 and rigid-body whirled with imperceptible fluctuations. At least approximately 8 normal eigenmodes of cages should be introduced to conduct a more accurate dynamic analysis although the effect of the number of normal eigenmodes on the stresses at the pocket corners was insignificant. From the above, it was concluded to be appropriate to introduce one boundary point lying at the center on each pocket bar of cages and approximately 8 normal eigenmodes to effectively introduce the cage elastic deformations into a dynamic analysis model.

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

scholarly journals A Modified Mann Iteration by Boundary Point Method for Finding Minimum-Norm Fixed Point of Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Songnian He ◽  
Wenlong Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Boundary Point ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Method ◽  
Minimum Norm ◽  
Mann Iteration ◽  
Boundary Point Method

LetHbe a real Hilbert space andC⊂H a closed convex subset. LetT:C→Cbe a nonexpansive mapping with the nonempty set of fixed pointsFix(T). Kim and Xu (2005) introduced a modified Mann iterationx0=x∈C,yn=αnxn+(1−αn)Txn,xn+1=βnu+(1−βn)yn, whereu∈Cis an arbitrary (but fixed) element, and{αn}and{βn}are two sequences in(0,1). In the case where0∈C, the minimum-norm fixed point ofTcan be obtained by takingu=0. But in the case where0∉C, this iteration process becomes invalid becausexnmay not belong toC. In order to overcome this weakness, we introduce a new modified Mann iteration by boundary point method (see Section 3 for details) for finding the minimum norm fixed point of Tand prove its strong convergence under some assumptions. Since our algorithm does not involve the computation of the metric projectionPC, which is often used so that the strong convergence is guaranteed, it is easy implementable. Our results improve and extend the results of Kim, Xu, and some others.

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