Conditional mean dimension

We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.

THE LEVEL OF PRINCIPAL’S INSTRUCTIONAL LEADERSHIP PRACTICES AND ITS RELATIONSHIP WITH SCHOOL-BASED MANAGEMENT IN SECONDARY SCHOOL IN TUMPAT DISTRICT, KELANTAN, MALAYSIA

This study aims to identify the level of principals’ instructional leadership practices and their relationship with the school-based management in secondary schools in Tumpat district, Kelantan. This study was conducted in the form of survey using a quantitative method with a total of 286 respondents using a questionnaire as a research instrument. Quantitative data were analyzed descriptively and inferentially using SPSS software version 25.0. The result of this study showed that the level of principal's instructional leadership practices was high (mean=4.25, s.d.=0.444) where the dimension of forming a positive school environment scored the highest mean (mean=4.30, s.d.=0.459). The level of school-based management was also high (mean=4.24, s.d.=0.427) with the highest score mean dimension was the dimension of planning and evaluation (mean=4.29, s.d.=0.450). The Pearson correlation test showed a significant relationship between the level of principals’ instructional leadership practices and school-based management which was at a high correlation level (r=0.895). Therefore, the implication of this study is able to provide an exposure to the Ministry of Education Malaysia who can take initiatives to make improvements in the basic aspects of education and also leadership programs in order to strengthen the leadership practices of principals in schools. This study also has implications to school principals in re-evaluating all their practices and actions in managing schools to further improve the effectiveness and the quality of their administration. In conclusion, this study gives the impression that principals’ instructional leadership practices have impacts on school-based management which to some extent can affect the performance of teachers and students as well as the results of the effectiveness of school functions.

Antiulcerogenic Activity of Vitamin E on Gastric Ulcers produced by Indomethacin

Objective: To study the morphological and histological effects of vitamin E on gastric lesions produced by indomethacin.Materials and Methods: This was an animal interventional study, 48 adult healthy albino mice were selected and were split into four groups A, B, C and D. Number of animals in each group was 12. Group A was categorized as control. Evion 400mg/kg was administered to Group B. Indocid 25mg/kg was given to group C. Indocid and Evion both (25mg/kg &400 mg/kg respectively) were administered to Group D. In all group, six animals were selected and treated for three days and rest for eight days with calculated doses of drugs. Mice were sacrificed and dissection was done 24 hours after the last dose. The stomach was identified, washed, and observed under dissecting microscope to study the number and shape of ulcers. The dimension of ulcers was measured under a compound microscope.Results: No ulcers were seen in groups A and B. 35 and 10 ulcers were observed in groups C and D respectively. The mean number of ulcers in groups C and D was statistically significant (p-value=0.000). In comparison to group D, Pindot, linear, Irregular, and punched-out ulcers were more prevalent in group C and were statistically significant (p-value < 0.05). The mean linear dimension of ulcers in group C was much greater than in group D. The mean dimension of ulcers in group C1 and C2 was 262.50µm and 232.5µm respectively. Whereas in group D1 and D2 given both Indocid and vitamin E the dimensions were 56.5µm and 50µm.Conclusion: Vitamin E has an anti-ulcerogenic effect on stomach mucosa by reducing the number and dimension of ulcers.

Particulate bound mercury pollution in the Central Italian Herbarium (Firenze, Italy)

&lt;p&gt;The attention devoted to air quality is particularly important in workplaces, such as museums, where the health of visitors and workers must couple with the safeguard of collections. This especially holds for herbaria where, until the middle of the last century, the collections were protected using a solution of mercury dichloride (HgCl&lt;sub&gt;2&lt;/sub&gt;) to prevent cryptogamic or animal infestations. The decomposition of HgCl&lt;sub&gt;2&lt;/sub&gt; causes the Hg reduction through a reaction pathway that is still poorly known, and the consequent release of Hg&lt;sup&gt;0&lt;/sup&gt; in the indoor atmosphere. Besides Hg&lt;sup&gt;0&lt;/sup&gt;, Hg in air exists also as bound to particulate (PBM). In the museums&amp;#8217; atmosphere, this fraction may represent a non-negligible proportion of total atmospheric Hg and should be monitored.&lt;/p&gt;&lt;p&gt;This study aims to characterize the PBM in the &lt;em&gt;Central Italian Herbarium&lt;/em&gt; of Firenze (University of Firenze, Italy), one of the largest herbaria worldwide. Here recent studies proved high levels of Hg&lt;sup&gt;0&lt;/sup&gt;.&lt;/p&gt;&lt;p&gt;PBM sampling has been carried twice (2018 and 2020 soon after the lockdown period caused by the Covid-19), collecting the dust on a SEM-EDS stub from different surfaces (furniture, wall cornice, sample cabinet). Samples were roughly divided according to their deposition time between old (&lt;em&gt;OD&lt;/em&gt;), almost-new (&lt;em&gt;AD&lt;/em&gt;) and new dust (&lt;em&gt;ND&lt;/em&gt;). The samples were analyzed using SEM-EDS to characterize the dimension and the chemical speciation of Hg particulate.&lt;/p&gt;&lt;p&gt;Hg-particles were detected in all the three types of dust collected in both the years: the mean dimension is 0.80&amp;#177;0.01 &amp;#181;m (3&amp;#963;). The highest number of Hg-particles has been always reached in the &lt;em&gt;AD&lt;/em&gt;, i.e. the dust collected directly on the packages containing herbarium specimens, with a strong increase in the 2020 sample. Additionally, the EDS microanalysis revealed that Hg-particles are now mainly associated with S (sometimes with O), suggesting the presence of sulphate or sulphide.&lt;/p&gt;&lt;p&gt;The above evidences show that PBM constitutes a fraction of Hg pollution in the &lt;em&gt;Herbarium&lt;/em&gt; that cannot be ignored. The number of particles strongly increased in a period of low attendance of the &lt;em&gt;Herbarium&lt;/em&gt; rooms and consequently cleaning, due to the COVID-19 pandemic: despite this, almost all are still classifiable as fine particulate (i.e. ECD&lt; 2.5 &amp;#181;m) particularly harmful for human health. The presence of sulphate/sulphide indicated the change of Hg speciation with time and its reaction with S and O. These compounds, although less bioavailable than Hg&lt;sup&gt;0&lt;/sup&gt;, still represent a risk for both herbarium workers and visitors.&lt;/p&gt;&lt;p&gt;The results of the present study offer preliminary information on the abatement system to be installed in the museum halls, which should be supplied with filters to retain very fine particles (&lt; 1 &amp;#181;m).&lt;/p&gt;

A variational principle for the metric mean dimension of free semigroup actions

We consider continuous free semigroup actions generated by a family $(g_y)_{y \,\in \, Y}$ of continuous endomorphisms of a compact metric space $(X,d)$ , subject to a random walk $\mathbb P_\nu =\nu ^{\mathbb N}$ defined on a shift space $Y^{\mathbb N}$ , where $(Y, d_Y)$ is a compact metric space with finite upper box dimension and $\nu $ is a Borel probability measure on Y. With the aim of elucidating the impact of the random walk on the metric mean dimension, we prove a variational principle which relates the metric mean dimension of the semigroup action with the corresponding notions for the associated skew product and the shift map $\sigma $ on $Y^{\mathbb {N}}$ , and compare them with the upper box dimension of Y. In particular, we obtain exact formulas whenever $\nu $ is homogeneous and has full support. We also discuss several examples to enlighten the roles of the homogeneity, of the support and of the upper box dimension of the measure $\nu $ , and to test the scope of our results.