We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. The cartoon component u is modeled by a function of bounded variation, while v, usually represented by a square integrable function, is now being modeled by a more refined and weaker texture norm, as ...

Variational problems for Sobolev maps with bounded total variation that take values into the 1-dimensional projective space are studied. We focus on the different features from the case of Sobolev maps with bounded conformal p-energy that take values into the p-dimensional projective space, for p ≥ 2 integer, recently studied in [18]. In the last decades there has been a growing interest in the...

This note is devoted to obtain an approximation result for BV-functions by means of a quasipolyhedral sequence of BV-functions. This approximation could have interesting applications in some problems of the Calculus of Variations.

The choice calculus provides a language for representing and transforming variation in software and other structured documents. Variability is captured in localized choices between alternatives. The space of all variations is organized by dimensions, which provide scoping and structure to choices. The variation space can be reduced through a process of selection, which eliminates a dimension an...

the effect of a distributed patch mass on the natural frequency of vibration of a laminated rectangular plate with simply supported boundaries is investigated. the third order displacement field of a composite laminated rectangular plate is defined using the two variable refined plate theory. equations of motion of the plate are obtained with the help of calculus of variation. parametric study ...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...