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Das, Lovejoy,Nivas, Ram,Singh, Abhishek Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.4
The differentiable manifold with f - structure were studied by many authors, for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial $F_{a(j){\times}(j)$-structure satisfying $$\prod\limits_{j=1}^{k}\;[F^2+a(j)F+\lambda^2(j)I]\;=\;0$$ However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1, 2,$\ldots$,$K\;\in\;N$, and obtain integrability conditions of the distributions $\pi_m^j$ and ${\pi\limits^{\sim}}_m^j$.
Heiber, Michael C.,Okubo, Takashi,Ko, Seo-Jin,Luginbuhl, Benjamin R.,Ran, Niva A.,Wang, Ming,Wang, Hengbin,Uddin, Mohammad Afsar,Woo, Han Young,Bazan, Guillermo C.,Nguyen, Thuc-Quyen The Royal Society of Chemistry 2018 ENERGY AND ENVIRONMENTAL SCIENCE Vol.11 No.10
<P>The rational design of new high performance materials for organic photovoltaic (OPV) applications is largely inhibited by a lack of design rules for materials that have slow bimolecular charge recombination. Due to the complex device physics present in OPVs, rigorous and reliable measurement techniques for charge transport and charge recombination are needed to construct improved physical models that can guide materials development and discovery. Here, we develop a new technique called impedance-photocurrent device analysis (IPDA) to quantitatively characterize the competition between charge extraction and charge recombination under steady state operational conditions. The measurements are performed on actual lab scale solar cells, have mild equipment requirements, and can be integrated into normal device fabrication and testing workflows. We perform IPDA tests on a broad set of devices with varying polymer:fullerene blend chemistry and processing conditions. Results from the IPDA technique exhibit significantly improved reliability and self-consistency compared to the open-circuit voltage decay technique (OCVD). IPDA measurements also reveal a significant negative electric field dependence of the bimolecular recombination coefficient in high fill factor devices, a finding which is inaccessible to most other common techniques and indicates that many of these techniques may overestimate the value that is most relevant for describing device performance. Future work utilizing IPDA to build structure-property relationships for bimolecular recombination will lead to enhanced design rules for creating efficient OPVs that are suitable for commercialization.</P>