Hopf heap and Hopf heap module

In this paper, we firstly give some results and properties of Hopf heaps. In addition, we get a equivalent definition of a Hopf truess by a Hopf heap. Using this equivalence definition, we construct some examples of Hopf trusses by Hopf heaps. Finally, we introduce the conception of Hopf heap modules, and give the structure theorem of Hopf heap modules.Comment: 16page

Effects of Cryogenic Treatment after Annealing of Ti-6Al-4V Alloy Sheet on Its Formability at Room Temperature

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This is an Open Access article made available under the terms of the Creative Commons Attribution licence CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.In this article, the effects of cryogenic treatment after annealing on the formability of Ti-6Al-4V alloy sheet were experimentally studied. The Ti-6Al-4V titanium alloy was treated by cryogenic treatment after annealing (ACT). Tensile tests were carried out using a universal machine at room temperature. The microstructure evolution of Ti-6Al-4V subjected to ACT was also investigated using an optical microscope (OM). Both the shearing performance and drawing formability were analyzed by punch shearing tests and deep drawing tests, respectively. Results showed that after ACT, the tendency of the β phase can be apparently changing into stable β’ and α’ phases. The elastic modulus is lower than that of the untreated material. It was found that both the yield strength and tensile strength are declined slightly, whereas the ductility is increased significantly. The shear strength in punch shearing is decreased at room temperature and cryogenic temperature. The ratio of smooth zone on the section after ACT3 is much larger than the others. The rollover diameters are not obviously greater than those of the untreated. Additionally, the height of the burr shows a decreasing trend after ACT. During deep drawing, drawing depth is deeper than that of the untreated material, the drawing load after ACT is reduced, and the decreasing tendency of the drawing load slows down. It is noted that the micro-cracks occur at the bottom of the sample.Peer reviewe

IL-8 Produced Via Bidirectional Communication Between Prostate Cancer and M2 Macrophages as a Potential Diagnostic and Prognostic Biomarker

PURPOSE: Owing to the mortality associated with metastatic prostate cancer and the shortcomings of the current parameters in predicting the disease prognosis, we require the identification of viable biomarkers, which would help in the diagnosis and prognosis of the disease. We aimed to determine whether the interleukin-8 level in the tumor microenvironment could serve as a potential clinical diagnostic marker and prognostic factor for prostate cancer. METHODS: The migration assay of prostate cancer cells was performed in an in vitro co-culture model. Cell lines PC3 and DU145 were divided into two groups and co-cultured with M0 and M2 macrophages, respectively. We used reverse transcription-quantitative polymerase chain reaction to detect M2 macrophage marker expression levels. Immunohistochemistry analyses of tissue microarrays were performed to analyze the correlation between the increased expression of interleukin-8 and the prognosis of prostate cancer. A retrospective analysis based on 142 residual serum specimens was performed to analyze the level of interleukin-8. RESULTS: We observed that M2 macrophages promoted the migration of prostate cancer cells and significantly increased the concentrations of interleukin-8 in the co-culture supernatants. We observed increased expression of CD163 and interleukin-8 in prostate cancer tissues. Furthermore, the levels of interleukin-8 in the serum of prostate cancer patients were higher than those in healthy controls. Untreated patients had higher levels of interleukin-8, which could be a predictor of a higher metastasis rate. CONCLUSION: These results suggest that interleukin-8 produced via bidirectional communication between prostate cancer cells and M2 macrophages is a putative biomarker for prostate cancer diagnosis and treatment

Estimation of the hydraulic parameters of leaky aquifers based on pumping tests and coupled simulation/optimization: verification using a layered aquifer in Tianjin, China

Accurate estimates of aquifer parameters are necessary for effective groundwater management and for geotechnical engineering applications. Pumping tests may be employed to estimate the hydraulic conductivity in leaky aquifer/aquitard systems. This work introduces a hybrid algorithm with global search capacity (the Genetic algorithm, GA) and local search capacity—the Levenberg-Marquardt (LM) algorithm—coupled with a modified Neuman-Witherspoon solution for leaky aquifers to estimate the aquifer’s hydraulic parameters from pumping-test data. The GA is employed to determine the initial guesses of the aquifer parameter values. The optimal parameter values are then obtained with the LM algorithm, yielding a mixed GA/LM algorithm, herein named GALMA. Results show that the drawdown trends based on the estimated parameters agree well with measured drawdown. The proposed estimation algorithm identifies aquifer parameters with greater reliability than previous approaches. Verification of the GALMA is carried out based on three pumping tests in a layered aquifer in Tianjin, China, and on four historical case studies involving diverse hydrogeological settings. The excellent match between observed drawdown and GALMA-estimated parameters demonstrates the estimation accuracy and superior performance relative to previously reported estimation methods

Equivalent crossed products of monoidal Hom-Hopf algebras

In this paper, we give a Maschke-type theorem for a Hom-crossed product on a finite dimensional monoidal Hom-Hopf algebra, and investigate a sufficient and necessary condition for two Hom-crossed products to be equivalent. Furthermore, we construct an equivalent Hom-crossed system based on a same Hom-crossed product by using lazy Hom-2-cocyle