On the orientable regular embeddings of complete multipartite graphs

AbstractLet Km[n] be the complete multipartite graph with m parts, while each part contains n vertices. The regular embeddings of complete graphs Km[1] have been determined by Biggs (1971) [1], James and Jones (1985) [12] and Wilson (1989) [23]. During the past twenty years, several papers such as Du et al. (2007, 2010) [6,7], Jones et al. (2007, 2008) [14,15], Kwak and Kwon (2005, 2008) [16,17] and Nedela et al. (2002) [20] contributed to the regular embeddings of complete bipartite graphs K2[n] and the final classification was given by Jones [13] in 2010. Since then, the classification for general cases m≥3 and n≥2 has become an attractive topic in this area. In this paper, we deal with the orientable regular embeddings of Km[n] for m≥3. We in fact give a reduction theorem for the general classification, namely, we show that if Km[n] has an orientable regular embedding M, then either m=p and n=pe for some prime p≥5 or m=3 and the normal subgroup Aut0+(M) of Aut+(M) preserving each part setwise is a direct product of a 3-subgroup Q and an abelian 3′-subgroup, where Q may be trivial. Moreover, we classify all the embeddings when m=3 and Aut0+(M) is abelian. We hope that our reduction theorem might be the first necessary approach leading to the general classification

Thermal Conductivity Performance of Polypropylene Composites Filled with Polydopamine-Functionalized Hexagonal Boron Nitride

Mussel-inspired approach was attempted to non-covalently functionalize the surfaces of boron nitride (BN) with self-polymerized dopamine coatings in order to reduce the interfacial thermal barrier and enhance the thermal conductivity of BN-containing composites. Compared to the polypropylene (PP) composites filled with pristine BN at the same filler content, thermal conductivity was much higher for those filled with both functionalized BN (f-BN) and maleic anhydride grafted PP (PP-g-ma) due to the improved filler dispersion and better interfacial filler-matrix compatibility, which facilitated the development of more thermal paths. Theoretical models were also applied to predict the composite thermal conductivity in which the Nielsen model was found to fit well with the experimental results, and the estimated effective aspect ratio of fillers well corresponded to the degree of filler aggregation as observed in the morphological study

Atomistic Conversion Reaction Mechanism of WO3 in Secondary Ion Batteries of Li, Na, and Ca

Intercalation and conversion are two fundamental chemical processes for battery materials in response to ion insertion. The interplay between these two chemical processes has never been directly seen and understood at atomic scale. Here, using in situ HRTEM, we captured the atomistic conversion reaction processes during Li, Na, Ca insertion into a WO3 single crystal model electrode. An intercalation step prior to conversion is explicitly revealed at atomic scale for the first time for Li, Na, Ca. Nanoscale diffraction and ab initio molecular dynamic simulations revealed that after intercalation, the inserted ion–oxygen bond formation destabilizes the transition‐metal framework which gradually shrinks, distorts and finally collapses to an amorphous W and MxO (M=Li, Na, Ca) composite structure. This study provides a full atomistic picture of the transition from intercalation to conversion, which is of essential importance for both secondary ion batteries and electrochromic devices.Das Wechselspiel zwischen Ioneninterkalation und Umwandlung des WO3‐Elektrodenmaterials wurde durch In‐situ‐TEM auf atomarer Ebene untersucht. Die Bildung von Ion‐Sauerstoff‐Bindungen destabilisiert das WO3‐Gerüst: Es schrumpft, wird verzerrt und fällt schließlich zu einer amorphen W‐ und MxO‐Verbundstruktur (M=Li, Na, Ca) zusammen.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134843/1/ange201601542_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134843/2/ange201601542.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134843/3/ange201601542-sup-0001-misc_information.pd

Atomistic Conversion Reaction Mechanism of WO3 in Secondary Ion Batteries of Li, Na, and Ca

Intercalation and conversion are two fundamental chemical processes for battery materials in response to ion insertion. The interplay between these two chemical processes has never been directly seen and understood at atomic scale. Here, using in situ HRTEM, we captured the atomistic conversion reaction processes during Li, Na, Ca insertion into a WO3 single crystal model electrode. An intercalation step prior to conversion is explicitly revealed at atomic scale for the first time for Li, Na, Ca. Nanoscale diffraction and ab initio molecular dynamic simulations revealed that after intercalation, the inserted ion–oxygen bond formation destabilizes the transition‐metal framework which gradually shrinks, distorts and finally collapses to an amorphous W and MxO (M=Li, Na, Ca) composite structure. This study provides a full atomistic picture of the transition from intercalation to conversion, which is of essential importance for both secondary ion batteries and electrochromic devices.The interplay between ion intercalation and WO3 battery electrode conversion was investigated at atomic scale by using in situ HRTEM. The ion–oxygen bond formation destabilizes the WO3 framework which gradually shrinks, distorts and finally collapses to an amorphous W and MxO (M=Li, Na, Ca) composite structure.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135051/1/anie201601542.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135051/2/anie201601542-sup-0001-misc_information.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135051/3/anie201601542_am.pd

Prevalence and Factors Associated with Hepatitis B Immunization and Infection among Men Who Have Sex with Men in Beijing, China

Background: Among the Chinese population of 1.3 billion, there are an estimated 93 million carriers of hepatitis B virus (HBV). Men who have sex with men (MSM) are at increased risk for HBV infection; however, the prevalence of HBV immunization and infection among Chinese MSM remains undetermined. Methods: A cross-sectional survey of 1,114 eligible participants was conducted in Beijing, China. Multiple methods were used to recruit study participants. Demographic information and potential correlated factors were collected by questionnaire. Additionally, blood specimens were collected and tested for sexually transmitted infections and serologic markers of hepatitis B immunization and infection. Results: Laboratory data were available for 1,111 participants (99.7%), the prevalence of hepatitis B immunization was 38.9%, and 26.5% had serologic markers of HBV infection. Multivariate analyses indicated that higher education level, smaller number of male sex partners in the past 12 months, reported diagnosis of sexually transmitted disease (STD), and history of blood donation were independently associated with HBV immunization. Absence of steady male sex partner(s) in the past 12 months, and reported diagnosis of STD were shown to be independently associated with HBV infection. MSM positive for HBV infection were more likely to have past or current syphilis infection. Conclusions: Low prevalence of HBV immunization and high prevalence of HBV infection among Chinese MSM and a correlation between sexual risk factors and hepatitis B infection indicate that comprehensive preventative measures for HBV among MSM, including blood donor and HIV-STD clinic vaccination programs as well as targeted health education campaigns should be developed in China