scholarly journals The non-linear geometry of Banach spaces after Nigel Kalton

2014 ◽  
Vol 44 (5) ◽  
pp. 1529-1583 ◽  
Author(s):  
G. Godefroy ◽  
G. Lancien ◽  
V. Zizler
Keyword(s):  
Banach Spaces ◽  
Non Linear ◽  
Linear Geometry

On a Theorem of Beurling and Livingston

1965 ◽  
Vol 17 ◽  
pp. 367-372 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Banach Space ◽  
Fourier Series ◽  
Banach Spaces ◽  
General Result ◽  
Functional Equations ◽  
Linear Functional ◽  
Monotone Mappings ◽  
Conjugate Space ◽  
Non Linear ◽  
Duality Mappings

In their paper (1), Beurling and Livingston established a generalization of the Riesz-Fischer theorem for Fourier series in Lp using a theorem on duality mappings of a Banach space B into its conjugate space B*. It is our purpose in the present paper to give another proof of this theorem by deriving it from a more general result concerning monotone mappings related to recent results on non-linear functional equations in Banach spaces obtained by the writer (2, 3, 4, 5) and G. J. Minty (6).

scholarly journals Simple eigenvalues and bifurcation for a multiparameter problem

1988 ◽  
Vol 31 (1) ◽  
pp. 77-88 ◽  
Author(s):  
D. F. McGhee ◽  
M. H. Sallam
Keyword(s):  
Banach Spaces ◽  
Simple Eigenvalue ◽  
Linear Mapping ◽  
Spectral Parameters ◽  
Non Linear ◽  
Multiparameter Problem ◽  
Image Position ◽  
Bifurcation Of Solutions

We are concerned with the problem of bifurcation of solutions of a non-linear multiparameter problem at a simple eigenvalue of the linearised problem.Let X and Y be real Banach spaces, and let A, Bi, i = 1, …, n∈B(X, Y). Let : Rn × X → Y be a non-linear mapping. We consider the equationwhereand λ=(λ1, λ2,…,λn) ∈ Rn is an n-tuple of spectral parameters.

Quasi-Static Assessment of Response to Slamming Impact on Free Fall Lifeboats

2015 ◽  
Author(s):  
Svein Erling Heggelund ◽  
Zhiyuan Li ◽  
Beom-Seon Jang ◽  
Jonas W. Ringsberg
Keyword(s):  
Beam Theory ◽  
Free Fall ◽  
Calculation Model ◽  
Theory Approach ◽  
Design Assessment ◽  
Static Assessment ◽  
Non Linear ◽  
The Impact ◽  
Stiffened Steel ◽  
Linear Geometry

Design against impact loads (slamming) can be challenging and time consuming and can involve complex calculations. Application of simplified, quasi-static calculation approaches will make the design process much easier. In this paper, such simplified methods are discussed using free fall lifeboats as a case. Results from non-linear FE-analysis show that the response is non-linear due to large deformations. The impact pressure is then mainly carried by membrane stress and the dynamic response is small. A non-linear beam theory approach for hand calculation is established. As the non-linear calculation model is the most realistic, it is recommended that this is used in an initial design assessment. Although the results are on the conservative side, simple hand calculations including non-linear geometry can be used to predict the maximum strain. Linear methods are also investigated. However, these methods should be used with more rigid structures such as stiffened steel and aluminium panels.

Evaluation of Gun Support Structure Using Equivalent Dynamic Approach in Non Linear FEA

2013 ◽  
Vol 376 ◽  
pp. 331-335
Author(s):  
Sunil Shukla ◽  
H. S. Deshmukh ◽  
Patil Vinaay ◽  
B.A. Thite A.
Keyword(s):  
Standard Operating Procedure ◽  
Dynamic Loads ◽  
Robot Arm ◽  
Dynamic Approach ◽  
Contact Algorithm ◽  
Standard Operating ◽  
Non Linear ◽  
Single Structure ◽  
Cost Efficient ◽  
Linear Geometry

Robot Gun structure is an efficient way in which multiple welds can be done simultaneously. However mounting several weld guns on a single structure induces a variety of dynamic loads, especially during movement of the robot arm as it maneuvers to reach the weld locations.The primary idea employed in this paper, is to model those dynamic loads as equivalent G force loads in FEA. This approach will be on the conservative side, and will be saving time and subsequently cost efficient. The approach of the paper is towards creating a standard operating procedure (SOP) when it comes to analysis of such structures, with emphasis on deploying various technical aspects of FEA such as Non Linear Geometry, Multipoint Constraint Contact Algorithm, Multizone meshing .

scholarly journals On the Equation ax—xb = c

1968 ◽  
Vol 8 (2) ◽  
pp. 383-384 ◽  
Author(s):  
R. F. Berghout
Keyword(s):  
Division Ring ◽  
Tangent Plane ◽  
The Other ◽  
Three Dimensions ◽  
Memorial Lecture ◽  
Line Pair ◽  
Commutative Case ◽  
Non Linear ◽  
Point Of Intersection ◽  
Linear Geometry

Beniamino Segre, in his memorial lecture of 1958 [5], [6], inaugurated the study of non-linear geometry in three dimensions over a division ring. In his treatment of sections of quadrics by planes, he is naturally led to consider conics and the problem of tangency. Now in the commutative case the locus of intersection of a quadric and a plane containing a generator is the line-pair consisting of this generator and one from the other family. Such a plane is then the tangent plane of the point of intersection of the two generators. Segre extends this notion to the non-commutative case, where the locus of intersection is not always a line-pair. He joins up the remaining points of intersection in pairs, and calls the points where the lines so formed cut the base generator, the ‘points of contact’ of the plane (π) and the quadric (Q). A line in π is called a ‘tangent’ if it passes through a point of contact, but does not contain any of the points of intersection of Q and π.

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