Smoothing nilpotent actions on 1-manifolds

Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0, 1]$, or $S^1$, and let \Homeo_+(M) (resp. \Diff_+^1(M)) be the group of orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It is a classical result that if $N$ is a finitely-generated, torsion-free nilpotent group, then there exist 1-1 homomorphisms \phi\colon N \to \Homeo_+(M). Farb and Franks show that, in fact, there exists a 1-1 homomorphism N \to \Diff_+^1(M). In this paper we obtain a stronger result: every action \phi\colon N \to \Homeo_+(M) is topologically conjugate to an action \tilde{\phi}\colon N \to \Diff_+^1(M).Comment: 16 page

Extraction, Phytochemical Screening and Anti-Inflammatory Activity of Hydro-Ethanolic Extract of Roots of Dactylorhiza hatagirea

The present work showed phytochemical screening, anti-inflammatory activities and sub-acute toxicity of hydro-ethanolic extract of roots of Dactylorhiza hatagirea (D. hatagirea) and rhizomes of Curcuma angustifolia (C. angustifolia). The anti-inflammatory activity was evaluated by Carrageenan-Induced Rat Paw Edema method. Acute toxicity of the extract (2000 mg/kg) was examined in Swiss albino mice for 14 days. Qualitative analysis of various phytochemical constituents and quantitative analysis of total phenolics and flavonoids were determined by the well-known test protocol available in the literature. Quantitative analysis of phenolic and flavonoids was carried out by Folins Ciocalteau reagent method and aluminium chloride method respectively. Phytochemical analysis revealed the presence of phenols, flavonoids, tannins, saponins, alkaloids. The total phenolics content of roots of Dactylorhiza hatagirea and rhizomes of Curcuma angustifolia extract was (0.675, 0.456mg/100mg), followed by flavonoids (0.832, 1.091mg/100mg) respectively. Hydro-ethanolic extract up to 2000 mg/kg did not produce any toxic effects. The hydro-ethanolic extract of Dactylorhiza hatagirea and Curcuma angustifolia (100 and 200 mg/kg) inhibited the inflammation induced by carrageenan in rats in a dose dependent manner. After anti-inflammatory activity tablet formulation was prepared of the extract and evaluated as per IP.  The hydro-ethanolic extract of Dactylorhiza hatagirea and Curcuma angustifolia possesses a strong anti-inflammatory activity and may be considered an interesting source of effective anti-inflammatory compounds. Keywords:   Sub-acute toxicity, anti-inflammatory effect, Dactylorhiza hatagirea, Curcuma angustifolia, Herbal tablet formulatio

Quantitative Analysis on Awareness About NEP 2020 Policy In First Year Student

The National Education Policy (NEP) 2020 is a comprehensive agenda that goals to transform the Indian education system to meet the challenges of the 21st century. It introduces several innovative approaches to enhance the quality and inclusivity of education. This research article explores the awareness of first year students in India regarding the NEP 2020. This research article investigates the awareness of students in India belonging undergraduate regarding the National Education Policy 2020 (NEP). The study aims to understand the level of awareness, perception, and engagement of students, who are the stakeholders in these respective groups with the NEP 2020. Primary data was collected by using a structured research instrument through Google forms & analysis was done through basic percentage analysis, bivariate U test keeping in mind the results of data normality along with Association and Reversion analysis. The findings provide insights into the awareness gaps and varying levels of engagement across the different educational levels, offering valuable implications for policymakers and educators to effectively implement the NEP 2020 reforms at each stage of education. This article presents the exact structure of NEP2020 for degree student, awareness about the NEP2020 in first year students and difficulties faced by students while accepting NEP2020.   &nbsp

Formulation Development and Evaluation of Fast Dissolving Oral Film of Midodrine Hydrochloride

Oral fast dissolving midodrine hydrochloride films prepared by solvent casting method, PEG 400 was the selected plasticizers, incorporating superdisintegrants such as croscarmellose sodium (CCS) and sodium starch glycolate (SSG) to achieve the goal. Drug content, weight variability, film thickness, disintegration time, endurance, percentage of moisture content, and in vitro dissolution tests were analyzed for the prepared films. In all formulations, the tensile strength value was found from 0.965±0.045 and 1.256±0.032 and the folding capacity was over 100. The assay values ranged from 97.98±0.25 to 99.89±0.36 percent for all formulations. The disintegration time was ranging between 55±9 to 120±6 sec, the minimum time for disintegration was found in formulation F5 (55±9). The prepared F5 formulation shows greater release of the drug (99.25±0.41 percent) within 15 min relative to other formulations. As the drug having low solubility, fast disintegration may leads to more drug availability for dissolution, resulting in faster absorption in systemic circulation increased systemic availability of drug leads to quick onset of action which is prerequisite for hypertension. Keywords: Midodrine hydrochloride, Fast dissolving films, Solvent casting method, Superdisintegrants

Steady State Simulation of an Azeotropic Distillation System Using Aspen Plus

Ethanol-water forms homogeneous minimum boiling azeotrope and it has most common occurrence in many industrial processes. There are various techniques exist to separate azeotropic compositions. In this work we studied the basic features of azeotropic distillation using Aspen plus simulation. Since entrainers are indispensable in separating constant boiling mixtures, in this work, performances of three different entrainers were studied viz. benzene, n-pentane and cyclohexane. The effect of various process variables viz. reflux-ratio and distillate rate on the purity of the final products was studied in detail. RadFrac simulator was used to study the distillation process and NRTL method was used as the base thermodynamic method. It has been found out after simulation that cyclohexane performed best where maximum purity of ethanol (99.91%) was obtained closely followed by n-pentane (99.84%) and benzene (99.77%) as entrainers. The optimum number of stages were 25 (for n-pentane), 45 each for benzene and cyclohexane respectively

In Vitro Antioxidant Activity, Total Phenolic and Flavonoid Contents of Hydroalcoholic Extract of Leaves of Lagerstroemia Parviflora Roxb

Plants have served human beings as a natural source for treatments and therapies from ancient times, amongst them medicinal herbs have gain attention because of its wide use and less side effects. In the recent years plant research has increased throughout the world and a huge amount of evidences have been collected to show immense potential of medicinal plants used in various traditional systems. Lagerstroemia parviflora Roxb (L. parviflora, Lythraceae) is a medium-sized deciduous plant indigenous to India and available even up to a height of 900m in the Himalayas. The plant is used for the treatment of syphilis, sores, and carbuncles. The aim of the present study was to determine qualitative and quantitative phytochemical and in vitro antioxidant activity of leaf of L. Parviflora. Qualitative analysis of various phytochemical constituents and quantitative analysis of total phenol and flavonoids were determined by the well-known test protocol available in the literature. Quantitative analysis of phenolic and flavonoids was carried out by Folins Ciocalteau reagent method and aluminium chloride method respectively. The in vitro antioxidant activity of hydroalcoholic extract of the leaf was assessed against DPPH assay method using standard protocols. Phytochemical analysis revealed the presence of phenols, flavonoids, saponins glycosides etc. The total phenolic and flavonoids content of L. Parviflora leaves of hydroalcoholic extract was 3.541 and 0.927mg/100mg respectively. The activities of hydroalcoholic leaves extract against DPPH assay method were concentration dependent with IC 50 values of ascorbic acid and extracts 17.681and 62.669μg/ml respectively. These studies provided information for correct identification of this plant material. The diverse array of phytochemicals present in the plant thus suggests its therapeutic potentials which may be explored in drug manufacturing industry as well as in traditional medicine. Keywords: Lagerstroemia parviflora Roxb, Qualitative, Quantitative phytochemical, Antioxidant