The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider Euler for incompressible flow an ideal whose Lagrangian transport velocity possesses additional rough-in-time, divergence-free vector field. recent work, have demonstrated that this system can be derived from Clebsch and Hamilton-Pontryagin variational pri...

The Minimal Residual (MR) is modified for adaptive filtering application. Three forms of MR based algorithm are presented: i) the low complexity SPCG, ii) MREDSI, and iii) MREDSII. The low complexity is a reduced complexity version of a previously proposed SPCG algorithm. Approximations introduced reduce the algorithm to an LMS type algorithm, but, maintain the superior convergence of the SPCG ...

The Beale-Powell restart algorithm is highly useful for large-scale unconstrained optimization. In this paper, we use an example to show that the algorithm may fail to converge. The global convergence of a slightly modiied algorithm is proved.

Semidefinite Programming (SDP) provides strong bounds for many NP-hard combinatorial problems. Arguably the most popular/efficient search direction for solving SDPs using a primal-dual interior point (p-d i-p) framework is the HKM direction. This direction is a Newton direction found from the linearization of a symmetrized version of the optimality conditions. For many of the SDP relaxations of...

Variations in anatomy of the tendons and ligaments are not uncommon cause a diagnostic dilemma. We describe novel ligament encountered ankle extending from posterior inferior tibiofibular to calcaneum. Awareness normal variant is essential during evaluation study.

Retrieval tasks provide learners with an opportunity to focus both on meaning and on form. There are four different retrieval directions. The present study aimed to identify the optimal direction of recall type retrievals during reading and to investigate the outcomes of each one. Forty-eight intermediate EFL learners took part in the study. One of the experimental groups was provided with the ...

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters.  Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.

Academic essays entail taking a stance on the truth value of propositions. Epistemic adverbs deal with the speaker's assessment of the truth value of propositions. Employing a corpus-based approach with descriptive statistics and qualitative description, this study explored the use of epistemic stance adverbs in academic essays written by native English speakers and Iranian EFL learners. Follow...