Additive results for the group inverse in an algebra with applications to block operators

We derive a very short expression for the group inverse of a(1) + ... + a(n) when a(1), ... , a(n) are elements in an algebra having group inverse and satisfying a(i)a(j) = 0 for i C∗-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062Benítez, J, Liu, X and Zhu, T.Nonsingularity and group invertibility of linear combinations of two k-potent matrices, Linear Multilinear Algebra (accepted)Castro-González, N., Dopazo, E., & Martínez-Serrano, M. F. (2009). On the Drazin inverse of the sum of two operators and its application to operator matrices. Journal of Mathematical Analysis and Applications, 350(1), 207-215. doi:10.1016/j.jmaa.2008.09.035González, N. C., & Koliha, J. J. (2004). New additive results for the g-Drazin inverse. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 134(6), 1085-1097. doi:10.1017/s0308210500003632Cvetković-Ilić, D. S., Djordjević, D. S., & Wei, Y. (2006). Additive results for the generalized Drazin inverse in a Banach algebra. Linear Algebra and its Applications, 418(1), 53-61. doi:10.1016/j.laa.2006.01.015Deng, C. Y. (2009). The Drazin inverses of sum and difference of idempotents. Linear Algebra and its Applications, 430(4), 1282-1291. doi:10.1016/j.laa.2008.10.017Deng, C, Cvetković-Ilić, DS and Wei, Y.Some results on the generalized Drazin inverse of operator matrices, Linear Multilinear Algebra (2009). DOI: 10.1080/03081080902722642Djordjević, D. S., & Wei, Y. (2002). Additive results for the generalized Drazin inverse. Journal of the Australian Mathematical Society, 73(1), 115-126. doi:10.1017/s1446788700008508Hartwig, R. E., Wang, G., & Wei, Y. (2001). Some additive results on Drazin inverse. Linear Algebra and its Applications, 322(1-3), 207-217. doi:10.1016/s0024-3795(00)00257-3Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-9

Impacts of biochar amendment and straw incorporation on soil heterotrophic respiration and desorption of soil organic carbon

Abstract While biochar amendment and straw incorporation in soil have received great attention due to the potential of carbon sequestration and improvements in soil physicochemical properties, there were limited studies addressing their impacts on soil heterotrophic respiration over a seasonal cycle. Here, we conducted a field experiment to evaluate the effects of biochar amendment and straw incorporation on the temporal variations of soil heterotrophic respiration and desorption of soil organic carbon (SOC) in the North China Plain. We measured CO2 efflux over 1-year period in the field, together with water extractable organic carbon (WEOC) and soil microbial biomass carbon (SMBC). Our study showed a significant exponential relationship (P < 0.001) between CO2 efflux and temperature, with Q 10 values in a range of 2.6–3. CO2 efflux was significantly higher in summer under straw incorporation (5.66 μmol m−2 s−1) than under biochar amendments (3.54–3.92 μmol m−2 s−1) and without amendment (3.76 μmol m−2 s−1). We found significantly lower WEOC:SOC ratio and SMBC:SOC ratio under biochar amendments than with straw incorporation and without amendment. Our study indicated that biochar amendment had a greater potential for reducing SOC desorption and CO2 efflux in the cropland of North China Plain

Folic Acid-Modified Fluorescent-Magnetic Nanoparticles for Efficient Isolation and Identification of Circulating Tumor Cells in Ovarian Cancer

Ovarian cancer (OC) is a lethal disease occurring in women worldwide. Due to the lack of obvious clinical symptoms and sensitivity biomarkers, OC patients are often diagnosed in advanced stages and suffer a poor prognosis. Circulating tumor cells (CTCs), released from tumor sites into the peripheral blood, have been recognized as promising biomarkers in cancer prognosis, treatment monitoring, and metastasis diagnosis. However, the number of CTCs in peripheral blood is low, and it is a technical challenge to isolate, enrich, and identify CTCs from the blood samples of patients. This work develops a simple, effective, and inexpensive strategy to capture and identify CTCs from OC blood samples using the folic acid (FA) and antifouling-hydrogel-modified fluorescent-magnetic nanoparticles. The hydrogel showed a good antifouling property against peripheral blood mononuclear cells (PBMCs). The FA was coupled to the hydrogel surface as the targeting molecule for the CTC isolation, held a good capture efficiency for SK-OV-3 cells (95.58%), and successfully isolated 2&ndash;12 CTCs from 10 OC patients&rsquo; blood samples. The FA-modified fluorescent-magnetic nanoparticles were successfully used for the capture and direct identification of CTCs from the blood samples of OC patients