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In this paper, we study the Raǐkov completion of invariant fuzzy metric groups and complete fuzzy metric semigroups (in the sense of Kramosil and Michael). We establish that: (1) if $ (G, M,\ast) $ is a fuzzy metric group such that $ (M,\ast) $ is invariant, then the Raǐkov completion $ \varrho G $ of $ (G,\tau_{M}) $ is a fuzzy metric group $ (\varrho G, \widetilde{M},\ast) $ such that $ (\widetilde{M},\ast) $ is invariant on $ \varrho G $ and $ \widetilde{M}_{|G\times G\times [0,\infty)} = M $; (2) if $ (G, M, \ast) $ is a fuzzy metric semigroup such that $ (M, \ast) $ is invariant, then a fuzzy metric completion $ (\widetilde{G}, \widetilde{M}, \ast) $ of $ (G, M, \ast) $ is a fuzzy metric semigroup and $ (\widetilde{M}, \ast) $ is invariant.

Let us call a (para)topological group \emph{strongly submetrizable} if it admits a coarser separable metrizable (para)topological group topology. We present a characterization of simply $sm$-factorizable (para)topo\-logical groups by means of continuous real-valued functions. We show that a (para)topo\-logical group $G$ is a simply $sm$-factorizable if and only if for each continuous function $f\colon G\to \mathbb{R}$, one can find a continuous homomorphism $\varphi$ of $G$ onto a strongly submetrizable (para)topological group $H$ and a continuous function $g\colon H\to \mathbb{R}$ such that $f=g\circ\varphi$. This characterization is applied for the study of completions of simply $sm$-factorizable topological groups. We prove that the equalities $\mu{G}=\varrho_\omega{G}=\upsilon{G}$ hold for each Hausdorff simply $sm$-factorizable topological group $G$. This result gives a positive answer to a question posed by Arhangel'skii and Tkachenko in 2018. Also, we consider realcompactifications of simply $sm$-factorizable paratopological groups. It is proved, among other results, that the realcompactification, $\upsilon{G}$, and the Dieudonn\'e completion, $\mu{G}$, of a regular simply $sm$-factorizable paratopological group $G$ coincide and that $\upsilon{G}$ admits the natural structure of paratopological group containing $G$ as a dense subgroup and, furthermore, $\upsilon{G}$ is also simply $sm$-factorizable. Some results in [\emph{Completions of paratopological groups, Monatsh. Math. \textbf{183} (2017), 699--721}] are improved or generalized., Comment: Some problems posed in the old version are answered

Taking以三江平原湿地代表植物小叶章为对象,通过对杂类草草甸、典型草甸、沼泽化草甸、沼泽生境中小叶章个体大小与生物量差异及繁殖构件与植株生物量之间相关关系的分析,研究不同生境中水位对小叶章个体生物量与繁殖分配的影响。结果表明: 小叶章个体大小、高度及有性繁殖特征随水位升高而显著降低;杂类草草甸、典型草甸、沼泽化草甸和沼泽中小叶章的繁殖阈值分别为0.245、0.149、0.148和0.157 g;除沼泽化草甸外,其他3种生境中小叶章植株个体大小与繁殖分配均呈显著负相关;相较于个体大小,土壤含水量对于小叶章有性繁殖分配影响更大,不同生境中小叶章对个体大小和繁殖分配的差异投资是其具有良好生态适应性的基础条件。.

In the recent years, a growing number of studies have shown that the occurrence of myocardial ischemia (MI) is closely related to the gut microbiota (GM). The Danshen-Honghua herb pair (DHHP), a classic combination in traditional Chinese herbal formulas, has been widely applied throughout history to cure cardiovascular disease, exhibiting remarkable clinical efficacy to treat ischemic heart disease (IHD). However, the intrinsic regulation mechanism of DHHP in treating MI remains unclear. This study aims to investigate the possible protective mechanism of DHHP in rats with acute myocardial ischemia (AMI) induced by isoproterenol (ISO) through 16S rRNA gene sequencing technique. Pharmacodynamic results showed that DHHP significantly ameliorated the pathological changes and improved the abnormal cardiac enzymes levels in the AMI rats. In addition, GM analysis demonstrated that DHHP effectively ameliorated the ISO-induced dysbiosis of the GM community, mainly by enhancing the GM diversity and increasing the relative abundance of Bacteroides, Roseburia, unclassified_f__Lachnospiraceae, and Lachnospiraceae_NK4A136_group, the abundance ratio of Bacteroidetes to Firmicutes, and decreasing the relative abundance of Escherichia-Shigella and Enterococcus. In summary, this study revealed that DHHP could improve ischemic myocardial injury in rats, and that its regulation mechanism is associated with significantly ameliorating the composition of GM, thus contributing to further our understanding of the anti-MI mechanisms of DHHP.

In this paper, some three-space properties of semitopological and paratopological groups are considered. We show that: (1) if the closed invariant subgroup H of semitopological group G and the natural quotient group G / H have G δ -diagonals, then G has a G δ -diagonal; (2) if H is a compact invariant subgroup of paratopological group G, then the canonical quotient mapping from G to G / H is closed. An example is given to show that the result (2) can not be generalized to quasitopological groups.

The concept of gyrogroups is a generalization of groups which do not explicitly have associativity. Recently, Atiponrat extended the idea of topological (paratopological) groups to topological (paratopological) gyrogroups. In this paper, we prove that every regular (Hausdorff) locally gyroscopic invariant paratopological gyrogroup $G$ is completely regular (function Hausdorff). These results improve theorems of Banakh and Ravsky for paratopological groups. Also, we extend the Pontrjagin conditions of (para)topological groups to (para)topological gyrogroups., 15

Rice starch properties of apparent amylose content (AAC), amylose content (AC), and amylopectin content (AP) are considered as the most important factors influencing grain quality as they are highly correlated with eating quality. This report is the first effort of predicting AC and AP values in rice flours, and recognizing waxy rice from non-waxy rice using NIRS technique. Calibration models generated by different mathematical, preprocessing treatments and combinations of wavelengths and signals were compared and optimized. The model established by modified partial least squares (MPLS) with "2, 8, 8, 2"/ Inverse MSC and ∼138 wavelengths signals yielded high RSQ of 0.977, 0.928, and 0.912 for AAC, AC and AP, respectively, as simultaneous measurement. MPLS-DA (discriminant analysis) could classify waxy and non-waxy rice with 100% accuracy. This high-throughput technology is valuable for breeding programs, and for the purposes of quality control in the food industry.

We show that a regular (paratopological) semitopological group G admits a homeomorphic embedding as a subgroup into a product of strongly metrizable (paratopological) semitopological groups if and only if G is strictly ω-balanced with a countable index of regularity. Also, we prove that a topological group G admits a homeomorphic embedding as a subgroup into a product of strongly metrizable groups if and only if G is strictly ω-balanced. Using this fact we obtain a characterization of closed subgroups of a product of strongly metrizable groups.

In this paper, the concept of k-upper semi-continuous set-valued mappings is introduced. Using this concept, we give characterizations of k-semistratifiable and k-MCM spaces, which answers a question posed by Xie and Yan.

Let F ( X ) be the free topological group on a Tychonoff space X , and F n ( X ) the subspace of F ( X ) consisting of all words of reduced length at most n for each n ∈ N . In this paper conditions under which the subspace F 4 ( X ) of the free topological group F ( X ) on a generalized metric space X contains no closed copy of S ω are obtained and used to discuss countability axioms in free topological groups. It is proved that for a k -semistratifiable k -space X the subspace F 4 ( X ) is snf -countable if and only if X is compact or discrete; for a normal k - and ℵ-space X F 4 ( X ) is csf -countable if and only if X is an ℵ 0 -space or discrete; and for a k ⁎ -metrizable space X F 5 ( X ) is a k -space and F 4 ( X ) is csf -countable if and only if X is a k ω -space or discrete. Some results of K. Yamada, and F. Lin, C. Liu and J. Cao are improved.

In this paper, we mainly discuss the o-tightness in paratopological groups. The following results are obtained: (1) Every paratopological group H satisfying S m ( H ) ⋅ g e t ( H ) ≤ ω is G δ -preserving. (2) The o-tightness of the product space X × H is countable for every Hausdorff feathered paratopological group H and every space X with o t ( X ) ≤ ω . As an application, we deduce that every Hausdorff feathered paratopological group H has countable o-tightness; in particular, H is a Moscow space, which gives a positive answer to [2, Open problem 6.4.8] .

In this paper, we consider topological properties of free topological groups in terms of Arens' space S 2 and covering properties of free topological groups. We show that F 4 ( X ) contains no copy of S 2 when the set of all non-isolated points of a metrizable X being compact. We also establish that X n is submetrizable and subparacompact for each n ∈ ω if and only if F ( X ) is submetrizable and subparacompact which implies that the free topological group F ( S ) on Sorgenfrey line S is subparacompact. Moreover, suppose that X is a σ-discrete space if and only if F ( X ) σ-discrete which answers Open problem 7.6.16 in Arhangel'skii and Tkachenko (2008) [2] .

The metrizability conditions and cardinal invariants for compactly-fibered coset spaces in paratopological groups in terms of their remainders are considered. It mainly shows that: (1) Suppose that X is a quotient of a k-gentle paratopological group with respect to a compact subgroup; then the remainder Y of X is either pseudocompact or Lindelof; (2) Suppose that X is a quotient of paratopological group with respect to a compact subgroup with a remainder Y such that Y has a point-countable base; then X and Y are separable and metrizable; (3) Suppose that X is a quotient of paratopological group with respect to a compact subgroup with a remainder Y such that Y is weakly developable; then n w ( X ) = π w ( X ) = π w ( Y ) = ω . Many results on coset spaces of topological groups obtained by A.V. Arhangel'skii [5] are extended to coset spaces of paratopological groups.

In this paper, we consider the problem of inserting semi-continuous maps with values into some ordered topological vector spaces in a monotone fashion. We answer the questions of K. Yamazaki and provide a new characterization of stratifiable spaces, semi-stratifiable spaces, countably paracompact spaces, countably metacompact spaces, perfect spaces, and perfectly normal spaces during this process.

The concept of gyrogroups is a generalization of groups which do not explicitly have associativity. In this paper, the notion of fuzzy gyronorms on gyrogroups is introduced. The relations of fuzzy metrics (in the sense of George and Veeramani), fuzzy gyronorms and gyronorms on gyrogroups are studied. Also, the fuzzy metric structures on fuzzy normed gyrogroups are discussed. In the last, the fuzzy metric completion of a gyrogroup with an invariant metric are studied. We mainly show that let $d$ be an invariant metric on a gyrogroup $G$ and $(\widehat{G},\widehat{d})$ is the metric completion of the metric space $(G,d)$; then for any continuous $t$-norm $\ast$, the standard fuzzy metric space $(\widehat{G},M_{\widehat{d}},\ast)$ of $(\widehat{G},\widehat{d})$ is the (up to isometry) unique fuzzy metric completion of the standard fuzzy metric space $(G,M_d,\ast)$ of $(G,d)$; furthermore, $(\widehat{G},M_{\widehat{d}},\ast)$ is a fuzzy metric gyrogroup containing $(G,M_d,\ast)$ as a dense fuzzy metric subgyrogroup and $M_{\widehat{d}}$ is invariant on $\widehat{G}$. Applying this result, we obtain that every gyrogroup $G$ with an invariant metric $d$ admits an (up to isometric) unique complete metric space $(\widehat{G},\widehat{d})$ of $(G,d)$ such that $\widehat{G}$ with the topology introduced by $\widehat{d}$ is a topology gyrogroup containing $G$ as a dense subgyrogroup and $\widehat{d}$ is invariant on $\widehat{G}$., Comment: 19

This paper is dedicated to Professor Jinjin Li on the occasion of his 60th anniversary. In this paper, a new cardinal function called the strong Hausdorff number in semitopological groups is introduced. We mainly show that every paratopological group with countable strong Hausdorff number is ω-admissible. Applying this result, we prove that every bounded set in a paratopological group with countable strong Hausdorff number is strongly bounded, which partially answers to a question posed by Sanchez and Tkachenko.

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact (or monotonically countably metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally bounded functions., Comment: 15 pages

We say that a (para)topological group G is strongly submetrizable if it admits a coarser separable metrizable (para)topological group topology and is projectively strongly submetrizable if for each open neighborhood U of the identity in G, there is a closed invariant subgroup N contained in U such that the quotient (para)topological group G / N is strongly submetrizable. We show that a quotient group of a simply sm-factorizable ω-narrow topological abelian group can fail to be simply sm-factorizable. This answers a question posed by Arhangel'skii and the first listed author in 2018. If, however, the kernel of a quotient homomorphism is a bounded subgroup, then the homomorphism preserves simple sm-factorizability in the classes of topological and paratopological groups. We also prove that a regular (para)topological group G is simply sm-factorizable if and only if G is projectively strongly submetrizable and every continuous real-valued function on G is uniformly continuous on G ω , the P-modification of G. Making use of this fact we show that all weakly Lindelof projectively strongly submetrizable paratopological groups and all weakly Lindelof paratopological abelian groups are simply sm-factorizable. It is also established that every precompact paratopological group is simply sm-factorizable.

In this paper, we prove the following results: (1) Let f : G → H be a continuous d-open surjective homomorphism; if G is an R -factorizable paratopological group, then so is H. This improves a result by Peng and Zhang [4, Theorem 1.7] , and (2) let G be a regular (so G is completely regular by a theorem of Banakh and Ravsky) R -factorizable paratopological group; then every subgroup H of G is R -factorizable if and only if H is z-embedded in G. This result gives a partial answer to a question of M. Sanchis and M. Tkachenko [8, Problem 5.3] .

In this paper, we consider the problem of inserting semi-continuous function above the (generalized) real-valued function in a monotone fashion. We provide some characterizations of stratifiable spaces, semi-stratifiable spaces, and $k$-monotonically countably metacompact spaces ($k$-MCM) and so on. It is established that: \begin{enumerate} \item A space $X$ is $k$-MCM if and only if for each locally bounded real-valued function $h: X\rightarrow \mathbb{R}$, there exists a lower semi-continuous and $k$-upper semi-continuous function $h': X \rightarrow \mathbb{R}$ such that (i) $ | h| \leq h' $; (ii) $h'_1 \leq h'_2$ whenever $| h_1| \leq | h_2|$. \item A space $X$ is stratifiable if and only if for each function $h: X\rightarrow \mathbb{R}^*$ ($\mathbb{R}^*$ is the generalized real number set), there is a lower semi-continuous function $h': X\rightarrow \mathbb{R}^*$ such that (i) $ h'$ is locally bounded at each $x\in U_h$ with respect to $\mathbb{R}$, where $U_h=\{x\in X: h \text{~is locally bounded at ~}x \text{~with respect to~} \mathbb{R}\}$; (ii) $|h| \leq h'$; (iii) $h'_1\leq h'_2$ whenever $| h_1|\leq | h_2|$. \end{enumerate} We give a negative answer to the problem posed by K.D. Li \cite{12}.

In this paper, the countable tightness and the k-space property in free topological groups over generalized metrizable spaces are considered. The following main results are obtained: (1) A space X is separable or discrete if and only if the free topological group F ( X ) is of countable tightness for a paracompact σ-, k-space X; (2) A space X is an ℵ 0 -space or discrete if and only if F ( X ) is of countable tightness for a normal k ⁎ -metrizable k-space X; (3) A space X is a k ω -space or discrete if and only if F ( X ) is a k-space for a k ⁎ -metrizable space X. Some results on the countable tightness and the k-property of free topological groups over metric spaces are improved.

The following general question is considered by A.V. Arhangel’skii [Perfect mappings in topological groups, cross-complementary subsets and quotients, Comment. Math. Univ. Carolin. 2003]. Suppose that $G$ is a topological group, and $F , M$ are subspaces of $G$ such that $G = MF$. Under these general assumptions, how are the properties of $F$ and $M$ related to the properties of $G$? Also, A.V. Arhangel’skii and M. Tkachenko [Topological Groups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about the above question in paratopological groups [Open problem 4.6.9, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008]. In this paper, we mainly consider this question and some positive answers to this question are given. In particular, we find many A.V. Arhangel’skii's results hold for $k$-gentle paratopological groups.

Given an increasing sequence $(X_{n})_{n\in\omega}$ of quasi-uniform spaces and paratopological groups, we study the topology of the direct limits $\mathrm{qu}$ - ${\mathop{\lim}\limits_{\longrightarrow}}X_{n}$ and $\mathrm{pg}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ of the sequence $(X_{n})_{n\in\omega}$ in the categories of quasi-uniform spaces and paratopological groups, respectively. First, we prove that the quasi-uniformity of the quasi-uniform direct limit $\mathrm{qu}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ is generated by some special family of quasi-pseudometrics. Then we discuss some properties of the direct limits $\mathrm{pg}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ . Finally, we give an explicit description of the topology of the direct limit $\mathrm{pg}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ under certain conditions on the sequence of paratopological groups $(X_{n})_{n\in\omega}$ . Moreover, some questions about direct limits of $\mathrm{qu}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ and $\mathrm{pg}$ - $\mathop{\lim}\limits_{\longrightarrow}X_{n}$ are posed.

In this paper sequentially compact sets, weakly first-countable sets and generalized metric sets in extensions of topological groups are studied. Some three space properties on convergence phenomena are obtained. It is shown that (1) if H is a closed subgroup of a topological group G such that all sequentially compact subsets of both the group H and the quotient space G / H are sequential, then all sequentially compact subsets of G are sequential; (2) let H be a closed and second-countable subgroup of a topological group G , then G is a topological sum of ℵ 0 -subspaces if the quotient space G / H is a local ℵ 0 -space; (3) let H be a locally compact and metrizable subgroup of a topological group G , then G is sequential if the quotient space G / H is sequential.

In this paper, we attempt to extend some three space properties in topological groups to paratopological groups. The following results are established: (1) metrizability of compact (resp., sequentially compact, countably compact) subsets is a three space property in the class of k -gentle paratopological groups; (2) let N be a second-countable topological subgroup of an Abelian paratopological group G ; if the quotient paratopological group G / N has a countable network, then so does G ; (3) let G be an Abelian paratopological group and N a topological subgroup of G ; if both N and G / N are first-countable, then so is G .

In this paper, we give a unified internal description of T i -reflection T i ( G ) for a semitopological group G with the concepts of T i - quotient subgroups ( i ∈ { 0 , 1 , 2 } ). We also give internal descriptions for the T 3 -reflection T 3 ( G ) and regular reflection Reg ( G ) of a semitopological group G , which solves some problems of M. Tkachenko.

In this paper, the remainders of semitopological and paratopological groups are investigated. We mainly establish that if G is a non-locally compact semitopological group and bG is a compactification of G such that Y = b G ∖ G has locally a point-countable base, then bG is separable and metrizable. This gives a positive answer to a question posed in Wang and He (2014) [25] . We also show that if G is a non-locally compact R 1 -factorizable paratopological group and Y = b G ∖ G is a local ℵ-space, then bG is separable and metrizable. Some questions in [14] are answered.

We mainly discuss the remainders of Hausdorff compactifications of paratopological groups or semitopological groups. Thus, we show that if a nonlocally compact semitopological group G has a compactification bG such that the remainder Y = bG \ G possesses a locally countable network, then G has a countable π -character and is also first-countable, that if G is a nonlocally compact semitopological group with locally metrizable remainder, then G and bG are separable and metrizable, that if a nonlocally compact paratopological group has a remainder with sharp base, then G and bG are separable and metrizable, and that if a nonlocally compact ℝ1-factorizable paratopological group has a remainder which is a k -semistratifiable space, then G and bG are separable and metrizable. These results improve some results obtained by C. Liu (Topology Appl., 159, 1415–1420 (2012)) and A.V. Arhangel’skїǐ and M. M. Choban (Topology Proc., 37, 33–60 (2011)). Moreover, some open questions are formulated. У даній статті, в основному, розглядаються залишковi члени хаусдорфових компактифiкацiй паратопологічних груп або напівтопологічних груп. Tак, показано, що у випадку, коли нелокально компактна напівтопологічна група G має компактифікацію bG таку, що залишковий член Y=bG∖G має локально злічєнну мережу, група G має злічєнний π-характер, а також є першозліченною. Також доведено, що для нелокально компактної напівтопологічної групи з локально метризовним залишковим членом групи G i bG є сепарабельними i метризовними. Крім того, якщо нелокально компактна паратопологічна група має залишковий член з точною базою, то групи G i bG є сепарабельними і метризовними, а якщо нелокально компактна R1 -факторизовна паратопологічна група має залишковий член, який є простором, що допускає k-напівспрямлення, то групи G i bG є також сепарабельними i метризовними. Наведені результати покращують деякі результати, отримані C. Liu (Topology and Appl. - 2012. - 159. - P. 1415-1420) i A. V. Arhangel'skii, M. M. Choban (Topology Proc. - 2011. - 37. - P. 33 - 60). Крім того, сформульовано деякі відкриті питання.

The problem when a paratopolgical group (or semitopological group) is a topological group is interesting and important. In this paper, we continue to study this problem. It mainly shows that: (1) Let G be a paratopological group and put τ = ωHs(G); then G is a topological group if G is a Pτ-space; (2) every co-locally countably compact paratopological group G with ωHs(G) ≦ ω is a topological group; (3) every co-locally compact paratopological group is a topological group; (4) each 2-pseudocompact paratopological group G with ωHs(G) ≦ ω is a topological group. These results improve some results in [11, 13].

In this paper, the class of weakly ω-admissible paratopological groups is introduced. We mainly show that: (1) Every bounded set in a weakly ω-admissible paratopological group is p-bounded for each free ultrafilter p on ω; (2) every C-compact set in a weakly ω-admissible paratopological group is strongly r-pseudocompact. The class of weakly ω-admissible paratopological groups contains all totally ω-narrow, precompact, locally feebly compact, weakly Lindelof and saturated, and ω-admissible paratopological groups. It is worth mentioning that all the aforementioned spaces are not to satisfy any separation axiom. Some Sanchis, Sanchez and Tkachenko's results are improved.

In this article we continue the study of R -factorizability in paratopological groups. It is shown that: (1) all concepts of R -factorizability in paratopological groups coincide; (2) a Tychonoff paratopological group G is R -factorizable if and only if it is totally ω -narrow and has property ω - QU ; (3) every subgroup of a T 1 paratopological group G is R -factorizable provided that the topological group G ⁎ associated to G is a Lindelof Σ -space, i.e., G is a totally Lindelof Σ-space ; (4) if Π = ∏ i ∈ I G i is a product of T 1 paratopological groups which are totally Lindelof Σ -spaces, then each dense subgroup of Π is R -factorizable. These results answer in the affirmative several questions posed earlier by M. Sanchis and M. Tkachenko and by S. Lin and L.-H. Xie.

In this paper, cardinal invariants and R -factorizability in paratopological groups are studied. The main results are that (1) w ( G ) = ib ( G ⁎ ) × χ ( G ) holds for every paratopological group G; (2) every paratopological group G satisfies | G | ⩽ 2 i b ( G ⁎ ) ψ ( G ) ; (3) nw ( G ) = Nag ( G ) × ψ ( G ) is valid for every completely regular paratopological group G; (4) a completely regular paratopological group G is R 2 -factorizable (resp. R 3 -factorizable) if and only if it is a totally ω-narrow paratopological group with property ω-QU and Hs ( G ) ⩽ ω (resp. Ir ( G ) ⩽ ω ); (5) if G is a completely regular R 2 -factorizable (resp. R 3 -factorizable) paratopological group and p : G → K an open homomorphism onto a paratopological group K such that p − 1 ( e ) is countably compact, then K is R 2 -factorizable (resp. R 3 -factorizable), which gives a partial answer to the question posed by M. Sanchis and M.G. Tkachenko (2010) [17] .

In this paper, the remainders of topological and paratopological groups are discussed. Some conditions are given for a topological group G such that G or its compactification bG is separable and metrizable by the properties of the remainder b G ∖ G . Some properties are obtained for a paratopological group G such that the remainder b G ∖ G is a p-space or a Lindelof space. They improve some results of A.V. Arhangelʼskii (2005) [1] and F. Lin (2011) [14] , respectively, and also give partial answers to some questions posed by F. Lin (2011) [14] and C. Liu (2009) [16] .

It is proved that every remainder of a nonlocally compact semitopological group $G$ is a Baire space if and only if $G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space $G$ every remainder of $G$ is either Baire, or meagre and Lindelöf.

In this paper the concept of property ω - U is introduced in topological groups. The main results are that (1) every Lindelof topological group and every totally bounded topological group have property ω - U ; (2) a topological group is R -factorizable if and only if it is an ω-narrow group with property ω - U ; (3) M -factorizable groups are preserved by open continuous homomorphisms, which gives a positive answer to a problem posed by A.V. Arhangelʼskii and M. Tkachenko.

Some characterizations of semi-stratifiable and k-semi-stratifiable spaces in terms of semi-continuous functions, analogous to Urysohn Lemma, were established in this paper. Some applications of them in the insertion of functions are given as well.

In this paper, we introduce a monotone version of cb-spaces, monotone cb-spaces (mcb-spaces). This property is shown to relate closely to insertion of continuous functions. We give some characterizations of mcb-spaces and investigate the relations among mcb-spaces and cb-spaces, countably compact spaces, stratifiable spaces, MCP and MCM.

To explore the protective effects of N-acetylcysteine (NAC) on cochlear damage occurring in irradiated guinea pigs.Seventy-two guinea pigs were randomly divided into 4 groups (n = 18 each). Control group received neither NAC nor irradiation, irradiation group received total cranium irradiation of 70 Gy, irradiationsaline group cranium irradiation of 70 Gy and saline solution through a round window and NAC group cranium irradiation of 70 Gy and NAC through a round window. The right ear received radiation. The animals were sacrificed at Day 14 post-irradiation. The specimens were dehydrated, embeded in paraffin and serially cut into 5-µm slices. Sections were stained with immunohistochemistry and terminal deoxynucleotidyl transferase-mediated dUTP-biotin nick end labeling (TUNEL). The cochlear basal membranes were observed for malondialdehyde (MDA) and superoxide dismutase (SOD) with scanning electron microscope.The cilium of hair cells had no clear loss and apoptotic number of spiral ganglion cells decreased in NAC group. The average optical density value of Caspase 3 in spiral ganglion in NAC group significantly decreased versus the irradiation group (0.08 ± 0.02 vs 0.10 ± 0.01, P0.01). The level of MDA of NAC group also decreased versus the irradiation group (0.33 ± 0.05 vs 0.84 ± 0.13, P0.05). The level of SOD in the NAC group increased versus the irradiation group (10.7 ± 3.0 vs 8.7 ± 1.3, P0.05). The ratio of apoptotic cell in SGC in the NAC group at Day 14 (7.8% ± 1.8%) decreased versus the irradiation group (32.0% ± 8.7%) at Day 14.MDA and SOD may be involved in the pathogenesis of cochlear cell damage. And NAC protects the irradiated cochlear cell.

To study the differences of regulation of sodium salicylate on the auditory brain stem response (ABR) threshold and expression of glutamic acid decarboxylase (GAD) protein in spiral ganglion of juvenile and adult guinea pigs.Fourty juvenile guinea pigs which were born just four days and fourty adult guinea pigs which were born thirty days were selected. They were divided four groups (group A; group B; group C; group D). ABR threshold was detected before administration, after administration for 15 days and after administration stopped for 30 days. The protein expression of GAD were measured after administration for 15 days and after administration stopped for 30 days by the method of immunohistochemistry.ABR threshold of juvenile sodium salicylate groups (group C) was increased remarkably than that of before administration and the control after administration for 15 days (P0.001). ABR threshold of group C was returned to the level of that of before administration and after administration stopped for 30 days. ABR threshold of adult sodium salicylate groups (group D) was increased remarkably than that of before administration and the control after administration for 15 days (P0.001). ABR threshold of group D was kept the high level after administration stopped for 30 days. The protein expression of GAD of sodium salicylate groups (group C and D) was decreased than that of the control after administration for 15 days. The protein expression of group C was more visible regression than that of group D (t = 4.7, P0.001). The protein expression of group C was returned the level of before administration after administration stopped for 30 days, but the protein expression of group D was kept the high level.The results suggest that sodium salicylate can regulate differently ABR threshold and expression of GAD protein in spiral ganglion of juvenile and adult guinea pigs. The effects of sodium salicylate on ABR threshold and expression of GAD protein in spiral ganglion of juvenile pigs are more noticeable than that of adult guinea pigs, but these changes are easier to return the normal than that of adult guinea pigs.