Motivated by the work initiated by Chapman [‘Determinants of Legendre symbol matrices’, Acta Arith. 115 (2004), 231–244], we investigate some arithmetical properties of generalised Legendre matrices over finite fields. For example, letting $a_1,\ldots ,a_{(q-1)/2}$ be all the nonzero squares in the finite field $\mathbb {F}_q$ containing q elements with $2\nmid q$, we give the explicit value of the determinant $D_{(q-1)/2}=\det [(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$. In particular, if $q=p$ is a prime greater than $3$, then

$$ \begin{align*}\bigg(\frac{\det D_{(p-1)/2}}{p}\bigg)= \begin{cases} 1 & \mbox{if}\ p\equiv1\pmod4,\\ (-1)^{(h(-p)+1)/2} & \mbox{if}\ p\equiv 3\pmod4\ \text{and}\ p>3, \end{cases}\end{align*} $$

where $(\frac {\cdot }{p})$ is the Legendre symbol and $h(-p)$ is the class number of $\mathbb {Q}(\sqrt {-p})$.

In this paper, the generation of relativistic electron mirrors (REMs) and the reflection of an ultra-short laser off this mirrors are discussed, applying two-dimensional particle-in-cell (2D-PIC) simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapidly expanding. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads the resonance between laser and REM. The reflected radiation near this interval and the corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, certain part of the reflected field could be selectively amplified or depressed, leading to the selectively adjusting of the corresponding spectra.

Since 2010, Jankowski’s Bunting Emberiza jankowskii has been listed as ‘Endangered’ on the IUCN Red List of Threatened Species. However, because no comprehensive surveys had been conducted, it was not known whether undiscovered populations existed elsewhere, so the population status of the species could not be assessed accurately. The aim of this study was to assess the breeding distribution and population size of Jankowski’s Bunting in China. Fifty sites in Inner Mongolia, and Jilin, Heilongjiang, Liaoning and Hebei Provinces were surveyed to locate suitable habitat and breeding populations of Jankowski’s Bunting. The surveyed sites included historical breeding distribution areas, wintering sites, and regions adjacent to historical breeding distribution areas. We confirmed that Jankowski’s Bunting has disappeared from most of its former breeding distributions, with the exceptions of Dagang, Xiergen and Tumiji. Additionally, 13 new breeding sites were discovered in Inner Mongolia. All currently known populations breed in Mongolian steppe-vegetation zones, with shrubs dominated by the natural Siberian apricot Prunus sibirica, indicating that this type of habitat is crucial for the survival of the species. Based on remote sensing, the suitable breeding habitat for Jankowski’s Bunting is estimated to be approximately 280 km2. The population size of Jankowski’s Bunting could range between 9,800 and 12,500 individuals, which is much higher than the numbers estimated in previous reports that were based on partial surveys. The suitable habitat remaining in Inner Mongolia would highly benefit from the implementation of the National Key Public Forest Protection Project. The population size of Jankowski’s Bunting is larger than previously estimated, but it is still threatened by habitat degradation and fragmentation, and our survey results reinforce the need for more research. The status of Jankowski’s Bunting in China still meets the IUCN criteria B2ab for an ‘Endangered’ species.

Four isonitrogenous and isoenergetic purified diets containing free arachidonic acid (ARA) or EPA (control group), 0·30 % ARA, 0·30 % EPA and 0·30 % ARA+EPA (equivalent) were designed to feed juvenile grass carp (10·21 (sd 0·10) g) for 10 weeks. Only the EPA group presented better growth performance compared with the control group (P<0·05). Dietary ARA and EPA were incorporated into polar lipids more than non-polar lipids in hepatopancreas but not intraperitoneal fat (IPF) tissue. Fish fed ARA and EPA showed an increase of serum superoxide dismutase and catalase activities, and decrease of glutathione peroxidase activity and malondialdehyde contents (P<0·05). The hepatopancreatic TAG levels decreased both in ARA and EPA groups (P<0·05), accompanied by the decrease of lipoprotein lipase (LPL) activity in the ARA group (P<0·05). Fatty acid synthase (FAS), diacylglycerol O-acyltransferase and apoE gene expression in the hepatopancreas decreased in fish fed ARA and EPA, but only the ARA group exhibited increased mRNA level of adipose TAG lipase (ATGL) (P<0·05). Decreased IPF index and adipocyte sizes were found in the ARA group (P<0·05). Meanwhile, the ARA group showed decreased expression levels of adipogenic genes CCAAT enhancer-binding protein α, LPL and FAS, and increased levels of the lipid catabolic genes PPARα, ATGL, hormone-sensitive lipase and carnitine palmitoyltransferase 1 (CPT-1) in IPF, whereas the EPA group only increased PPARα and CPT-1 mRNA expression and showed less levels than the ARA group. Overall, dietary EPA is beneficial to the growth performance, whereas ARA is more potent in inducing lipolysis and inhibiting adipogenesis, especially in IPF. Meanwhile, dietary ARA and EPA showed the similar preference in esterification and the improvement in antioxidant response.

We examined the in vitro developmental competence of parthenogenetic activation (PA) oocytes activated by an electric pulse (EP) and treated with various concentrations of AZD5438 for 4 h. Treatment with 10 µM AZD5438 for 4 h significantly improved the blastocyst formation rate of PA oocytes in comparison with 0, 20, or 50 µM AZD5438 treatment (46.4% vs. 34.5%, 32.3%, and 24.0%, respectively; P < 0.05). The blastocyst formation rate was higher in the group treated with AZD5438 for 4 h than in the groups treated with AZD5438 for 2 or 6 h (42.8% vs. 38.6% and 37.2%, respectively; P > 0.05). Furthermore, 66.67% of blastocysts derived from these AZD5438-treated PA oocytes had a diploid karyotype. The blastocyst formation rate of PA and somatic cell nuclear transfer (SCNT) embryos was similar between oocytes activated by an EP and treated with 2 mM 6-dimethylaminopurine for 4 h and those activated by an EP and treated with 10 µM AZD5438 for 4 h (11.11% vs. 13.40%, P > 0.05). In addition, the level of maturation-promoting factor (MPF) was significantly decreased in oocytes activated by an EP and treated with 10 µM AZD5438 for 4 h. Finally, the mRNA expression levels of apoptosis-related genes (Bax and Bcl-2) and pluripotency-related genes (Oct4, Nanog, and Sox2) were checked by RT-PCR; however, there were no differences between the AZD5438-treated and non-treated control groups. Our results demonstrate that porcine oocyte activation via an EP in combination with AZD5438 treatment can lead to a high blastocyst formation rate in PA and SCNT experiments.

Most species of the genus Eulecanium Cockerell (Hemiptera: Coccidae) are important economic pests for ornamental plants and fruit trees. Two morphologically similar species, Eulecanium giganteum Shinji and E. kuwanai Kanda, are distributed mainly in China and are quite difficult to identify because of the paucity of distinguishing characteristics, which can only be observed in slide-mounted young, adult females. Furthermore, we demonstrate here that the species occur in sympatry and on many of the same host plants. Mitochondrial cytochrome c oxidase I (COI) and the D2–D3 expansion segments of 28S rDNA were used for accurate identification of these two Eulecanium species from 19 different locations in China. The average K2P distances of COI sequences were 0.47% in E. kuwanai and 0.32% in E. giganteum, and the interspecific divergences varied from 7.23% to 8.34%. Neighbour-joining (NJ) trees of COI and 28S rDNA revealed two distinct non-overlapping clusters, respectively. Meanwhile, “best close match” analysis also showed that 100% of individuals were classified successfully using COI and 28 S sequences. Differentiating between E. giganteum and E. kuwanai is challenging when using ecological and morphological traits. In contrast, identification using DNA diagnostics appears to be very effective, especially when slide-mounted specimens are difficult to obtain.

0.7(0.1BiYbO3-0.9PbTiO3)-0.3 Pb(Mg1/3Nb2/3)O3 (0.7BYPT-0.3PMN) ternary piezoelectric ceramics were prepared by a columbite precursor method. The effects of sintering temperature on the crystalline phase, microstructure, and electrical properties of the ceramics were systematically investigated. There were two phases coexisting in the 0.7BYPT-0.3PMN ceramics sintered at 1100–1250 °C, one is the perovskite host phase with tetragonal symmetry and the other is Yb2Ti2O7 impurity phase. It was observed that, with increasing sintering temperature, the piezoelectric constant d33, dielectric constant εr, planar electromechanical coupling coefficient kp, and Curie temperature TC increased initially and then decreased. An apparent structure distortion could also be observed in samples synthesized at high sintering temperature due to the severe volatilization of Pb and Bi. The optimum performances of the material were obtained for samples sintered at 1150 °C with d33 = 100 pC/N, εr = 494, kp = 25.4%, and TC = 380 °C, respectively. It can be ascribed to the combined effect of a higher density, structural homogeneity with decreased tetragonality as well as a small amount of pyrochlore phase.

Motivated by various applications in queuing theory, this article is devoted to the monotonicity and convexity of some functions associated with discrete-time or continuous-time denumerable Markov chains. For the discrete-time case, conditions for the monotonicity and convexity of the functions are obtained by using the properties of stochastic dominance and monotone matrix. For the continuous-time case, by using the uniformization technique, similar results are obtained. As an application, the results are applied to analyze the monotonicity and convexity of functions associated with the queue length of some queuing systems.