1 
The Mean IntegralSpear, Donald W. 12 1900 (has links)
The purpose of this paper is to examine properties of the mean integral. The mean integral is compared with the regular integral. If [a;b] is an interval, f is quasicontinuous on [a;b] and g has bounded variation on [a;b], then the man integral of f with respect to g exists on [a;b]. The following theorem is proved. If [a*;b*] and [a;b] each is an interval and h is a function from [a*;b*] into R, then the following two statements are equivalent: 1) If f is a function from [a;b] into [a*;b*], gi is a function from [a;b] into R with bounded variation and (m)∫^b_afdg exists then (m)∫^b_ah(f)dg exists. 2) h is continuous.

2 
On Bounded VariationLewis, Paul Weldon 08 1900 (has links)
This paper is primarily concerned with developing the theory of realvalued functions of bounded variation and those ideas which are closely related to this main topic. In addition to this, some emphasis has been placed on the relationship of the theory of functions of bounded variation to specific areas of analysis. In particular, integration theory has been chosen as the vehicle to demonstrate this connection.

3 
On the boundedness character of thirdorder rational difference equations /Quinn, Eugene P. January 2006 (has links)
Thesis (Ph. D.)University of Rhode Island, 2006. / Includes bibliographical references (leaves 175178).

4 
Functions of bounded variationLind, Martin January 2006 (has links)
<p>The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.</p>

5 
Functions of bounded variationLind, Martin January 2006 (has links)
The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.

6 
Long term behavior or the positive solutions of the nonautonomous difference equation : x [subscript] n+1 = A [subscript] n [superscript] x [subscript] n1 [divided by] 1+x [subscript] n, n=0,1,2... /Bellavia, Mark R. January 2005 (has links)
Thesis (M.S.)Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaf 41).

7 
Functions of bounded variation and the isoperimetric inequality. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
Lin, Jessey. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 7980). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

8 
Minimizing the mass of the codimensiontwo skeleton of a convex, volumeone polyhedral regionJanuary 2011 (has links)
In this paper we establish the existence and partial regularity of a (d2)dimensional edgelength minimizing polyhedron in [Special characters omitted.] . The minimizer is a generalized convex polytope of volume one which is the limit of a minimizing sequence of polytopes converging in the Hausdorff metric. We show that the (d2)dimensional edgelength ζ d 2 is lowersemicontinuous under this sequential convergence. Here the edge set of the limit generalized polytope is a closed subset of the boundary whose complement in the boundary consists of countably many relatively open planar regions.

9 
Comparison of BV Norms in Weighted Euclidean Spaces and Metric Measure SpacesCAMFIELD, CHRISTOPHER SCOTT 25 August 2008 (has links)
No description available.

10 
Diferencovatelnost inverzního zobrazení / Differentiability of the inverse mappingKonopecký, František January 2011 (has links)
Primary objective of the thesis is proof of the statement that if for ∈ ℕ a ≥ 1 a bilipschitz mapping belongs to +1, loc ∩ ,∞ loc then also its inverse −1 belongs to +1, loc . We prove a similar statement also for spaces loc . For this purpose we construct a new ordering of th partial derivatives to generalized Jacobian matrix. Thanks to this matrix we are able to differentiate matrices in an applicable way. Generalized Jacobian matrix is projected so that there still holds the Chain rule and, in some way, also rules for matrices product differentiation. 1

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