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PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES
Bruce C. Berndt,Roberta R. Zhou 대한수학회 2014 대한수학회지 Vol.51 No.5
In a recent systematic study, C. Sandon and F. Zanello of- fered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan’s formulas for mul- tipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ra- manujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan’s catalogue of theta function formulas.
PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES
Berndt, Bruce C.,Zhou, Roberta R. Korean Mathematical Society 2014 대한수학회지 Vol.51 No.5
In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.
Effect of Annealing Temperature on Binary TiO2:SiO2 Nanocrystalline Thin Films
F. Mei,C. Liu,J. B. Wang,L. Zhou,W. K. Zhao,Y. L. Fang,Y. Y. Ren 한국물리학회 2006 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.48 No.6
Binary TiO2:SiO2 nanocrystalline thin films were prepared using liquid phase deposition at 35 C and annealed in air at temperatures ranging from 100 C to 500 C. The microstructural and the optical properties of the thin films were characterized by using an ultraviolet-visible spectrophotometer, a Fourier transform infrared spectrophotometer, a scanning electron microscope, and a transmission electron microscope. The photocatalytic performance of the thin films was evaluated by using photocatalytic degradation of methylene blue. The results showed that most TiO2 nanocrystallites were uniformly dispersed onto an amorphous SiO2 matrix and that nanopores had been formed on top of the TiO2 nanoparticles, resulting in an improved photocatalytic efficiency due to an increase number of effective adsorption sites. As we increased the annealing temperature, the small crystallites progressively aggregated into larger clusters, reducing the specific surface area of the TiO2 nanocrystallites. Moreover, SiO2 nanopowders moved towards the surface and covered the TiO2, resulting in a decreased photocatalytic activity.e
Hui, K.S.,Hui, K.N.,Dinh, D.A.,Tsang, C.H.,Cho, Y.R.,Zhou, W.,Hong, X.,Chun, H.H. Elsevier Science 2014 Acta materialia Vol.64 No.-
A green chemical approach to control the dimensions of Ag nanoparticle-decorated graphene oxide (AgNP-GO) composites was proposed by in situ ultrasonication of a mixture of AgNO<SUB>3</SUB> and GO solution with the assistance of vitamin C acting as an environmentally friendly reducing agent at room temperature. The AgNP-GO composites were characterized by X-ray diffraction, transmission electron microscopy, energy-dispersive spectroscopy, Fourier transform infrared spectroscopy, Raman spectra and ultraviolet-visible absorption spectra. The results demonstrated that Ag nanoparticles with an average diameter of ~15nm were uniformly dispersed on the surface of GO nanosheets by in situ ultrasonication of 1min with vitamin C. Increasing the ultrasonication times resulted in Ag nanoparticles with tunable dimensions ranging from 15 to 55nm being formed on the surface of GO nanosheets. The amount of silver nitrate and the ultrasonication time play a key role in the control of the dimension of Ag nanoparticles on GO, and a formation mechanism of the as-prepared AgNP-GO composites is proposed. This study provides a guide to controlling the dimensions of AgNP-GO composites, which may hold promise as advanced materials for various analytical applications such as catalysis, sensors and microchips.
Hur, S.,Chung, J. W.,Zhou, C. G.,Lee, J. H.,Cho, S.,Kim, M.,Lee, M.,Kim, H. C.,Jae, H. J. Springer Science + Business Media 2017 European radiology Vol.27 No.4
<P>aEuro cent The existence of Sappey's superior artery was proved with a radiological method.</P>
Le-Le Shao,Jia-Min Zhou,Qing Zhu,Xiao-Ling Wang,Robert C. Hider,Tao Zhou 한국식품과학회 2019 Food Science and Biotechnology Vol.28 No.4
Melanosis developed in shrimp (Penaeus vannamei)is mainly initiated by polyphenoloxidase (PPO),thus understanding of the characteristics of PPO in shrimpis important for controlling the melanosis of shrimp. Theshrimp cephalothorax turns black most rapidly amongst allthe tissues during the chilled storage. Crude PPO extractedfrom this cephalothorax has an optimal pH of 6.0 and anoptimal temperature of 50 C. PPO is relatively stable underneutral and weak alkaline conditions (pH 5.5–9.0) andthe temperature range of 25–35 C. The kinetic parametersKm and Vmax were recorded as 3.02 mM and 54.3 U/mg ofprotein, respectively, using L-Dopa as a substrate. Themolecular weight of PPO was estimated as 200–220 kDaby an activity staining test. A hydroxypyridinone derivative,5-hydroxy-1-octyl-4-oxo-1,4-dihydropyridine-2-carbaldehydeO-ethyl oxime, was demonstrated to efficientlyinhibit the PPO, indicating that this compound might findapplication as a shrimp preservative.
Deletion of the Lmna Gene Induces Growth Delay and Serum Biochemical Changes in C57BL/6 Mice
Ruan, J.,Liu, X.G.,Zheng, H.L.,Li, J.B.,Xiong, X.D.,Zhang, C.L.,Luo, C.Y.,Zhou, Z.J.,Shi, Q.,Weng, Y.G. Asian Australasian Association of Animal Productio 2014 Animal Bioscience Vol.27 No.1
The A-type lamin deficient mouse line ($Lmna^{-/-}$) has become one of the most frequently used models for providing insights into many different aspects of A-type lamin function. To elucidate the function of Lmna in the growth and metabolism of mice, tissue growth and blood biochemistry were monitored in Lmna-deficient mice, heterozygous ($Lmna^{+/-}$) and wide-type ($Lmna^{+/+}$) backcrossed to C57BL/6 background. At 4 weeks after birth, the weight of various organs of the $Lmna^{-/-}$, $Lmna^{+/-}$ and $Lmna^{+/+}$ mice was measured. A panel of biochemical analyses consisting of 15 serological tests was examined. The results showed that Lmna deficient mice had significantly decreased body weight and increased the ratio of organ to body weight in most of tissues. Compared with $Lmna^{+/+}$ and $Lmna^{+/-}$ mice, $Lmna^{-/-}$ mice exhibited lower levels of ALP (alkaline phosphatase), Chol (cholesterol), CR (creatinine), GLU (glucose), HDL (high-density lipoprotein cholesterol) and higher levels of ALT (alanine aminotransferase) (p<0.05). $Lmna^{-/-}$ mice displayed higher AST (aspartate aminotransferase) values and lower LDL (lowdensity lipoprotein cholesterol), CK-MB (creatine kinase-MB) levels than $Lmna^{+/+}$ mice (p<0.05). There were no significant differences among the three groups of mice with respect to BUN (blood urea nitrogen), CK (creatine kinase), Cyc C (cystatin C), TP (total protein), TG (triacylglycerols) and UA (uric acid) levels (p>0.05). These changes of serological parameters may provide an experimental basis for the elucidation of Lmna gene functions.
Redditt, Thomas J.,Chung, Eui-Hwan,Karimi, Hana Zand,Rodibaugh, Natalie,Zhang, Yixiang,Trinidad, Jonathan C.,Kim, Jin Hee,Zhou, Qian,Shen, Mingzhe,Dangl, Jeffery L.,Mackey, David,Innes, Roger W. American Society of Plant Biologists 2019 The Plant cell Vol.31 No.11
<P>The <I>Pseudomonas syringae</I> effector protein AvrRpm1 ADP ribosylates RIN4 proteins from Arabidopsis and soybean, which promotes association of RIN4 with EXO70E2 and suppression of callose deposition.</P><P>The <I>Pseudomonas syringae</I> effector protein AvrRpm1 activates the Arabidopsis (<I>Arabidopsis thaliana</I>) intracellular innate immune receptor protein RESISTANCE TO PSEUDOMONAS MACULICOLA1 (RPM1) via modification of a second Arabidopsis protein, RPM1-INTERACTING PROTEIN4 (<I>At</I>RIN4). Prior work has shown that AvrRpm1 induces phosphorylation of <I>At</I>RIN4, but homology modeling indicated that AvrRpm1 may be an ADP-ribosyl transferase. Here, we show that AvrRpm1 induces ADP-ribosylation of RIN4 proteins from both Arabidopsis and soybean (<I>Glycine max</I>) within two highly conserved nitrate-induced (NOI) domains. It also ADP ribosylates at least 10 additional Arabidopsis NOI domain-containing proteins. The ADP-ribosylation activity of AvrRpm1 is required for subsequent phosphorylation on Thr-166 of <I>At</I>RIN4, an event that is necessary and sufficient for RPM1 activation. We also show that the C-terminal NOI domain of AtRIN4 interacts with the exocyst subunits EXO70B1, EXO70E1, EXO70E2, and EXO70F1. Mutation of either EXO70B1 or EXO70E2 inhibited secretion of callose induced by the bacterial flagellin-derived peptide flg22. Substitution of RIN4 Thr-166 with Asp enhanced the association of <I>At</I>RIN4 with EXO70E2, which we posit inhibits its callose deposition function. Collectively, these data indicate that AvrRpm1 ADP-ribosyl transferase activity contributes to virulence by promoting phosphorylation of RIN4 Thr-166, which inhibits the secretion of defense compounds by promoting the inhibitory association of RIN4 with EXO70 proteins.</P><P>[Figure]</P>
Effects of sintering atmosphere on the superconductivity of MgB<sub>2</sub>
Zhou, S,Zhang, Y,Pan, A V,Dou, S X,Chung, K C,Kim, Y K,Yoo, J M IOP Publishing Ltd 2009 Superconductor science & technology Vol.22 No.4
<P>Pure MgB<SUB>2</SUB> bulk samples were sintered in different atmospheres: high purity Ar, high purity Ar with 0.01<I>% </I>O<SUB>2</SUB>, high purity Ar with 0.03<I>% </I>O<SUB>2</SUB> and high purity Ar with 5<I>% </I>H<SUB>2</SUB>. The superconductivity and microstructure of these samples were studied. It was found that in the range of this study the impurity gas in Ar had strong effects on aspects of the superconductivity such as critical current density, <I>J</I><SUB>c</SUB>, the irreversibility field, <I>H</I><SUB>irr</SUB>, and the upper critical field <I>H</I><SUB>c2</SUB>. When the samples were sintered in Ar with O<SUB>2</SUB> impurity, their low field <I>J</I><SUB>c</SUB> decreased as the O<SUB>2</SUB> content increased. The high field <I>J</I><SUB>c</SUB>, in contrast, was improved as the concentration of the O<SUB>2</SUB> impurity increased. For the sample sintered in Ar with H<SUB>2</SUB> impurity, its <I>J</I><SUB>c</SUB> is significantly higher than that of the sample sintered in high purity Ar. The smaller grain size and crystallinity degradation caused by the impure atmosphere is proposed to be the reason for the <I>J</I><SUB>c</SUB> improvement in both the O<SUB>2</SUB> and the H<SUB>2</SUB> added to the Ar gas sintering cases. </P>
Transport and thermodynamic properties ofSr3Ru2O7near the quantum critical point
Zhou, Z. X.,McCall, S.,Alexander, C. S.,Crow, J. E.,Schlottmann, P.,Bianchi, A.,Capan, C.,Movshovich, R.,Kim, K. H.,Jaime, M.,Harrison, N.,Haas, M. K.,Cava, R. J.,Cao, G. American Physical Society 2004 Physical review. B, Condensed matter and materials Vol.69 No.14