Sic transit...: South Eastern Europe-Japan University Cooperation Network Student Forum

"Sic transit..." documents the proceedings of ‘South Eastern Europe-Japan University Cooperation Network Student Forum’ held at the University of Tsukuba in 2010. The proceedings comprise individual research papers as well as reports of the two discussion sessions and overall Forum evaluation. While the individual papers discuss issues from each researcher’s specific field of expertise under the Forum umbrella theme, the discussion sessions address a wide range of issues and problems concerning language and society from an essentially trans-disciplinary perspective. 要旨 "Sic transit..."（かくして...は過ぎ去る）は、2010年に筑波大学において開催された「南東欧・日本学生知的交流会議」の報告書です。本報告書は、個々の論文ならびに２つのディスカッション・セッション報告と学生会議に対する総評を収めています。各論文においては、統一テーマの枠内で、研究者が各自の専門領域から問題を論じているのに対して、２つのディスカッション・セッションにおいては、本質的に領域横断的な視点から、言語と社会に関する広範な論点と課題を取り上げています

Invariant Geometric Curvilinear Optimization with Restricted Evolution Dynamics

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is a curvilinear functional defined by a given differential one-form, while the optimal state to be determined is a differential curve connecting two given points, among all the curves satisfying some given primal feasibility conditions. The resulting outcome is an invariant curvilinear Fritz–John maximum principle. Afterward, this result is approached by means of parametric equations. The classical single-time Pontryagin maximum principle for curvilinear cost functionals is revealed as a consequence

Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs

Partially Projective Algorithm for the Split Feasibility Problem with Visualization of the Solution Set

This paper introduces a new three-step algorithm to solve the split feasibility problem. The main advantage is that one of the projective operators interferes only in the final step, resulting in less computations at each iteration. An example is provided to support the theoretical approach. The numerical simulation reveals that the newly introduced procedure has increased performance compared to other existing methods, including the classic CQ algorithm. An interesting outcome of the numerical modeling is an approximate visual image of the solution set

Common Fixed Points of Operators with Property (E) in CAT(0) Spaces

This paper features the search for common fixed points of two operators in the nonlinear metric setting provided by CAT(0) spaces. The analysis is performed for the generalized nonexpansivity condition known as condition (E), Garcia-Falset et al., and relies on the three step iteration procedure Sn by Sintunavarat and Pitea. The convergence analysis reveals the approximate solutions as limit points for an iteration sequence, where both the nonexpansive mappings to be analyzed and the specific curved structure of the framework interfere. To point out properly the meaning of this approach, we provide also examples accompanied by numerical simulations. The Poincaré half-plane is one of the non-positively curved setting to be used

New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process

Split variational inclusions are revealed as a large class of problems that includes several other pre-existing split-type issues: split feasibility, split zeroes problems, split variational inequalities and so on. This makes them not only a rich direction of theoretical study but also one with important and varied practical applications: large dimensional linear systems, optimization, signal reconstruction, boundary value problems and others. In this paper, the existing algorithmic tools are complemented by a new procedure based on a three-step iterative process. The resulting approximating sequence is proved to be weakly convergent toward a solution. The operation mode of the new algorithm is tracked in connection with mixed optimization–feasibility and mixed linear–feasibility systems. Standard polynomiographic techniques are applied for a comparative visual analysis of the convergence behavior

On Suzuki Mappings in Modular Spaces

Inspired by Suzuki’s generalization for nonexpansive mappings, we define the ( C ) -property on modular spaces, and provide conditions concerning the fixed points of newly introduced class of mappings in this new framework. In addition, Kirk’s Lemma is extended to modular spaces. The main outcomes extend the classical results on Banach spaces. The major contribution consists of providing inspired arguments to compensate the absence of subadditivity in the case of modulars. The results herein are supported by illustrative examples

Common Fixed Points of Operators with Property (E) in CAT(0) Spaces

This paper features the search for common fixed points of two operators in the nonlinear metric setting provided by CAT(0) spaces. The analysis is performed for the generalized nonexpansivity condition known as condition (E), Garcia-Falset et al., and relies on the three step iteration procedure Sn by Sintunavarat and Pitea. The convergence analysis reveals the approximate solutions as limit points for an iteration sequence, where both the nonexpansive mappings to be analyzed and the specific curved structure of the framework interfere. To point out properly the meaning of this approach, we provide also examples accompanied by numerical simulations. The Poincaré half-plane is one of the non-positively curved setting to be used