Idempotents, nilpotents, rank and order in finite transformation semigroups

Let E, E₁ denote, respectively, the set of singular idempotents in T[sub]n (the semigroup of all full transformations on a finite set X[sub]n = {1,..., n}) and the set of idempotents of defect 1. For a singular element in Tn, let k(),k₁ () be defined by the properties ∈ Eᵏ⁽ᵃ⁾, ∉ Eᵏ⁽ᵃ⁾⁻¹, ∈ E₁ᵏ¹⁽ᵃ⁾, ∉ E₁ᵏ¹⁽ᵃ⁾⁻¹. In this Thesis, we obtain results analogous to those of Iwahori (1977), Howie (1980), Saito (1989) and Howie, Lusk and McFadden (1990) concerning the values of k() and k₁() for the partial transformation semigroup P[sub]n. The analogue of Howie and McFadden's (1990) result on the rank of the semigroup K(n,r) = { ∈ T [sub]n: |im | ≤ r,2 ≤ r ≤ n-1} is also obtained. The nilpotent-generated subsemigroup of P[sub]n was characterised by Sullivan in 1987. In this work, we have obtained its depth and rank. Nilpotents in IO[sub]n and PO[sub]n (the semigroup of all partial one-one order-preserving maps, and all partial order-preserving maps) are studied. A characterisation of their nilpotent-generated subsemigroups is obtained. So also are their depth and rank. We have also characterised their nilpotent-generated subsemigroup for the infinite set X = {1,2,...}. The rank of the semigroup L(n,r) = {a ∈ S : |im | ≤r, 1 ≤ r ≤ n - 2} is investigated for S = O[sub]n,PO[sub]n,SPO[sub]n and I[sub]n (where O[sub]n is the semigroup of all order-preserving full transformations, SPO[sub]n the semigroup of all strictly partial order- preserving maps, and In the semigroup of one-one partial transformation)

Rice husk as Biosorbent for the adsorption of methylene blue

The ability of rice husk (RH) to adsorb methylene blue (MB) from aqueous solutions has been studied at different initial dye concentrations (10, 20, 30, 40, and 50 mg/L), contact time (10 to 120 mins), pH (2–10) and adsorbent dosage (0.05, 0.1, 0.15, 0.20 and 0.25 g). The MB percentage removal was found to increase with increase in three adsorption parameters studied. Adsorption data were modeled using Langmuir and Freundlich adsorption isotherms with the Freundlich model being the best fit and pseudo-second-order model was the best order that described the kinetics of the MB adsorption process

Prediction of cumulative death cases in Brazil due to Covid-19 using mathematical models

The novel corona virus (2019-nCoV) infection has spread rapidly to other provinces and neighbouring countries since the emergence of the first cases at Wuhan, China. Estimation of the death cases by mathematical modelling can help to determine the potential and severity of the outbreak and to provide critical information on the type and intensity of disease response. In this paper, we present different growth models such as Von Bertalanffy, Baranyi-Roberts, Morgan-Mercer-Flodin (MMF), modified Richards, modified Gompertz, modified Logistics and Huang in fitting and analyzing the epidemic trend of COVID-19 in the form of total number of death cases of SARS-CoV-2 in Brazil as of 15th of July 2020. The MMF model was found to be the best model with the highest adjusted R2 value with the lowest RMSE value. The Accuracy and Bias Factors values were close to unity (1.0). The parameters obtained from the MMF model include maximum growth of death rate (log) of 0.03 (95% CI from 0.02 to 0.028), curve constant (δ) that affects the inflection point of 0.7057 (95% CI from 0.68 to 0.73) and maximal total number of death (ymax) of 17,619,760 (95% CI from 9,705,100 to 34,994,517). The MMF model predicted that the total number of death cases for Brazil on the coming 15th of August and 15th of September 2020 will be 132,787 (95% CI of 123,422 to 142,863) and 212,166 (95% CI of 192,578 to 233,746), respectively. The predictive ability of the model utilized in this study is a powerful tool for epidemiologist to monitor and assess the severity of COVID-19 in Brazil in months to come. However, as with any other model, these values need to be taken with caution due to the unpredictability of the COVID-19 situation locally and globally

Women's health: seminars on antenatal and primary healthcare

Primary health care (PHC) is the first level of contact for individuals, the family and the community with the national health system and “address the main health problem in the community, providing health promotion, preventive, curative and rehabilitative services accordingly.” This study aimed to determine the factors affecting utilization of healthcare services in the rural area of Bauchi State, fifteen years retrospective study on pregnancy-induced diabetes progresses to types-2-diabetes mellitus (DM) in Gombe South senatorial district of Gombe State and the impact of Nigeria State health investment project (Nship) on quality maternal and child health services among women of child bearing age (15-49 years) and children under 5 years in Bauchi State, Nigeria. The study was a sequential mixed methods approach including: (a) descriptive cross-sectional hospital-based research design (b) retrospective review ‘questionnaire survey’ on pre-post field interventions survey and (c) In-depth interview of the respondents. Factors that affect utilization of PHC includes; inexpensive cost and easy access to health facility 26.7%), treatment satisfaction 18.8% and nearness to place of residence 26.7%. The 1.1% of the women had gestational DM (GDM). Nship sharply increased the level of delivery of pregnant women. Improved living conditions increased utilization of health facilities. DM progressing to types 2 DM was not a public health problem in Gombe South senatorial district. Nship positively impacted the quality of maternal and child’s health in Bauchi State from 2016 to 2020

Montmorillonite for Adsorption and Catalytic Elimination of Pollutants from Wastewater: A State-of-the-Arts Review

Clay minerals have been recognized as one of the cheap and effective materials for wastewater remediation. Among the various clay minerals, montmorillonite (MMT) has received much attention due to its wide availability, low-cost and promising properties such as high porosity, mechanical strength, and cation exchange capacity. Additionally, MMT has high swelling properties. These features make it an ideal material for wastewater remediation applications. In addition, it possessed good cationic exchange capacity, making it easier to interact with various molecules. MMT and its composites exhibited good selectivity and catalytic activity for contaminants elimination from wastewater. Surface modification and functionalization have been identified as a way to improve the MMT’s adsorptive performance and endow it with light and light-harnessing properties. Thus, MMT composites, especially metal and metal-oxide nanoparticles, have shown good adsorption and photocatalytic activity toward the elimination/mineralization of various contaminants such as dyes, pharmaceuticals, heavy metals, and other organic and inorganic species. As such, MMT and its composites can be adopted as potential materials for wastewater remediation

Runs test for the residuals of the Morgan-Mercer-Flodin MMF model used for modelling the total number of Covid-19 cases for Brazil

Numerous papers fail to conduct statistical diagnostics of the nonlinear model that was used, and the data may be nonrandom, which is a need for all parametric statistical evaluation procedures that rely on random data. Whenever the diagnostic tests find that the residuals reflect a pattern, there are a range of treatments available, such as nonparametric analysis or transferring to a different model, which should resolve the issue. Organisms’ growth including viral infection cases over time usually exhibit a sigmoidal growth profile that exhibits lag time, acceleration to a maximal value and a final phase where the rate decreases and eventually reaches zero or an asymptote (A) is observed. For the analysis of the COVID-19 pandemic, the total infection case of SARS-CoV-2 in Brazil as of 15th of July 2020 to the 20thof December 2020 was modelled using several primary growth models with the Morgan-Mercer-Flodin (MMF) model found to be the best. We were the first to note on the high suitability of the MMF model to fit total death and infection cases for COVID-19. The least-squares technique used in normal nonlinear regression including in the MMF model must be subjected to the notion that the residual values must be random. In order to satisfy this requirement, we conduct the Wald–Wolfowitz runs test statistical diagnosis tests. The maximum number of runs counting was 5, and the predicted number of runs under the premise of randomness was 25.96. The z-value indicates how many normal errors the number of runs discovered exceeds the anticipated number of runs, and the p-value indicates how severe this z-value is. The significance is the same as with the other data on p-values. The null hypothesis that the residuals are really random can be rejected if the p-value is less than 0.05. Because the p-value was smaller than 0.05, the null hypothesis was dismissed, implying that there is strong evidence of non-randomness of the residues and further remedy is needed

Hepato-curative effects of crude phenol root extract of soddom of apple (C. Procera) on CCL4 induced hepatotoxicity in albino rats

The effects of phenol root extracts of C. procera and livolin on liver function indices of CCl4 induced hepatotoxicity was evaluated on forty (40) albino rats. The animals were grouped into four (I, II, III and IV) of 10 rats each, 120mg/kg of CCl4 was administered to rats in group II, III, and IV intramuscularly followed by oral administration of 10mg/kg livolin and phenol root extract of C. procera to group III and IV respectively. Analysis of variance (ANOVA) for multiple comparisms test were used to compare the result of the liver and kidney biochemical parameters from the test and control groups at 10 days interval for 20 days. The hepatic biochemical markers Alanine Aminotransferase (ALT), Aspartate Amino Transferases (AST), Alkaline Phosphatases (ALP) of the toxicant group (Gp II) were significantly higher (P<0.001), while group III (treated with livolin) statistically decreased (P<0.05) when compared with control (Gp I), this confirms the toxicity and treatment with livolin respectively. Oral administrations of the extracts at 10 days exposure lower all the liver function markers and increase the concentration of urea and albumin. This is an indication of the hepatocurative effect of the extract against CCl4 induced rats. However, at 20 days exposure the activities of the liver markers were raised. The Histopathological photomicrograph showed moderate cytolysis and karyolysis.Keywords: Hepatocurative, Calotropis Procera, hepatotoxicity, cytolysis, Carbontetrachloride

Central composite design-based optimization of Staphylococcus sp. strain Amr-15 growth on acrylamide as a nitrogen source

As an approach for bioremediation, the decomposition of acrylamide by microorganisms has received gradual but persistent worldwide interest. Prior to this study, a molybdenum-reducing bacteria had been identified and exhibited the ability to breakdown amides. Its key growth parameters on acrylamide were further investigated. A Central Composite Design (CCD) was employed to optimize the two previously identified key factors (incubation time and acrylamide concentration). For the examination of the significant factors or parameters, ANOVA, the perturbation plot, and numerous other diagnostic plots were employed. Using the "Numerical Optimisation" toolbox of Design Expert software, predicted ideal conditions were calculated. There were two ideal conditions investigated. The first was to determine the optimal growth under the employed range of variables, while the second was to forecast the optimal growth at the greatest acceptable acrylamide concentration of 1 g/L. The solution for the first predicted model predicted a maximum growth of 8.96 Log CFU/mL (95 percent confidence interval from 8.19 to 9.73), which was confirmed by experimental results with a growth of 9.88 Log CFU/mL (95 percent confidence interval from 9.79 to 9.97), which was close to the predicted values but significantly greater than the predicted values. The second numerical optimization for maximum growth with the highest acrylamide content. The solution had a predicted maximum growth of 7.81 Log CFU/mL (95 percent C.I. from 7.06 to 8.57) and was experimentally confirmed to have a growth of 8.74 Log CFU/mL (95 percent C.I. from 8.56 to 8.92), with the difference not being statistically significant (p0.05) indicating close agreement between predicted and experimental values. The findings of the RSM exercise demonstrated that growth on acrylamide may be optimized more efficiently with RSM than with OFAT, indicating that RSM is more useful in this regard than OFAT

Isolation and Characterization of Di-(2-ethylhexyl) Phthalate from the Leaves of Combretum micranthum (Altum) Combretaceae

Combretum micranthum is a medicinal plant used in traditional medicine for treatment of wounds, sores, diarrhoea, pain, fever and skin infections. This study was aimed at isolation and characterization of compounds from the leaves of Combretum micranthum. The pulverized leaves of the plant were gradiently extracted with hexane, ethyl acetate and methanol using soxhlet apparatus. The isolation of the compound was done using silica gel gravity column chromatography and preparative thin layer chromatography which yielded yellow compound ‘A’. The characterization of the isolated compound was carried out using 13C-NMR, 1H-NMR and GC-MS. Data obtained from the spectral analyses, suggested the compound to be di-(2-ethylhexyl) phthalate