On Wiener regularity at a boundary point for a polyharmonic operator

1987 ◽  
pp. 53-55
Author(s):  
V. G. Maz′ya ◽  
T. Donchev
Keyword(s):  
Boundary Point ◽  
Polyharmonic Operator

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.

Orthogonal spherical wave source boundary point method and its application to acoustic holography

2004 ◽  
Vol 49 (16) ◽  
pp. 1758-1767 ◽  
Author(s):  
Chuanxing Bi ◽  
Xinzhao Chen ◽  
Jian Chen ◽  
Weibing Li
Keyword(s):  
Boundary Point ◽  
Spherical Wave ◽  
Point Method ◽  
Acoustic Holography ◽  
Wave Source ◽  
Boundary Point Method

Conodonts as biostratigraphic tools for redefinition and correlation of the Cambrian–Ordovician Boundary

1988 ◽  
Vol 125 (4) ◽  
pp. 349-362 ◽  
Author(s):  
J. F. Miller
Keyword(s):  
North America ◽  
Boundary Point ◽  
Outer Part ◽  
Head Group ◽  
Eastern Canada ◽  
Green Point ◽  
Hierarchical Arrangement ◽  
Stratotype Section ◽  
Evolutionary Lineages ◽  
Zones And Subzones

AbstractThe Cambrian–Ordovician Boundary is recognized at different horizons on various continents by utilizing several fossil groups. Conodonts are abundant, diverse, and less provincial and facies-controlled than other fossils in this interval; many species are widespread and some are cosmopolitan. Strata representing the Cambrian–Ordovician Boundary interval from Asia, Australia, and North America can be correlated easily when those strata are from cratonal or shelf environments. Strata from slope facies have fewer conodonts, fewer taxa, and taxa may have different ranges compared with cratonal and shelf facies. It may be easier to correlate intercontinentally within cratonal/shelf facies than to correlate intracontinentally from cratonal/shelf facies to slope facies.A new hierarchical arrangement of conodont interval zones and subzones is proposed for western North America. These include the Proconodontus tenuiserratus Zone, the P. posterocostatus Zone (new), the P. muelleri Zone (new), the Eoconodontus Zone (new, with Eoconodontus notchpeakensis and Cambrooistodus minutus Subzones), the Cordylodus proavus Zone (emended, with Hirsutodontus hirsutus, Fryxellodontus inornatus, and Clavohamulus elongatus Subzones), the Cordylodus intermedius Zone (new, with Hirsutodontus simplex and Clavohamulus hintzei Subzones), the Cordylodus lindstromi Zone (new), and Cordylodus angulatus Zone (new).The boundary point for the base of the Ordovician System will be chosen so as to coincide with a correlatable conodont zonal boundary; other fossil groups will support correlation of this boundary point. Three alternative horizons are being considered. The base of the Cordylodus proavus Zone is the most distinctive but is regarded by some as older than is appropriate for the base of the Ordovician. The base of the Cordylodus intermedius Zone is recognizable by faunal changes in several evolutionary lineages at a level that is slightly younger than the presently recognized boundary in Australia, North America, and parts of Asia but slightly older than the base of the Tremadoc Series of Europe. The base of the C. lindstromi Zone can be recognized in most areas by the lowest occurrence of the nominate species, which is of questioned taxonomic validity and uncertain biostratigraphic utility; this horizon is closest to the base of the Tremadoc Series of Europe.Choice of a stratotype section has been narrowed to the Cow Head Group in Newfoundland, eastern Canada; and to the Fengshan and Yehli formations in Jilin Province, northeastern China. The Cow Head Group was deposited on and near the base of the continental slope. Erosion by debrisslide breccias resulted in a significant hiatus near the boundary interval in the Broom Point sections, a condition contrary to guidelines for choice of boundary sections. This may be less of a problem in other sections, such as Green Point. The Dayangcha section in China was deposited on the outer part of a continental shelf and has acritarchs, conodonts, graptolites and trilobites. Additional study of the China section is needed to document fully the ranges of critical conodont taxa.

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