best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

G./Endriss, 2011: Automated theorem search (through a universal reduction step) for ranking sets of objects B./G./Seedig, 2014: Finding preference profiles for k-majority digraphs G., 2014: Finding preference profiles of given Condorcet dimension • In this paper Method: more evolved technique to also treat strategyproofness for irresolute social choice functions Results: e.g., efficiency and st...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

A previous paper [2] presented a model (UCPF-HC) of the hippocampus as a unitary coherent particle filter, which combines the classical hippocampal roles of associative memory and spatial navigation, using a Bayesian filter framework. The present paper extends this model to include online learning of connections to and from the CA3 region. Learning in the extended neural network is equivalent t...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

The arithmetic complexity counts the number of algebraically independent entries in periodic continued fraction $\theta=[b_1,\dots, b_N, \overline{a_1,\dots,a_k}]$. If $\mathscr{A}_{\theta}$ is a noncommutative torus corresponding to rational elliptic curve $\mathscr{E}(K)$, then rank $\mathscr{E}(K)$ given by simple formula $r(\mathscr{E}(K))= c(\mathscr{A}_{\theta})-1$, where $c(\mathscr{A}_{...