Experimental and Numerical evaluation of mine pillar design

Mining is an art of extracting valuable minerals or other geological materials from the earth, usually from an ore body, vein or (coal) seam with minimum unit cost within acceptable social, legal, and regulatory constraints. There are two major methods of underground mining of coal: Bord& Pillar Method and Longwall Method. Pillars are mostly encountered in the former method. Pillar is the structural element and form an integral part of a mine on which the stability of the mine depends. A pillar support is intended to control rock mass displacement right through the zone of influence of mining, while mining activities proceeds. If pillars are made too small increasing the extraction percentage, it would affect the stability of the mine and vice-versa. An economic design of a support system implies that ore committed to pillar support be minimum, while fulfilling the vital requirements of assuring the global stability of the mine structure. This project critically studies the different optimum combination of pillar dimensions that could be effectively incorporated in the mines. Geotechnical factors of a nearby underground coal mine has been determined in the laboratory. Different approaches of pillar design have been compared. Variation of safety factors with width to height ratio of pillar, extraction percentage and depth of cover has been determined and conclusion has been made. The safety and feasibility of mining method is obtained through an optimum correlation between safety factor and extraction percentage. Numerical modeling has been done to evaluate the maximum stress induced over the pillar and gallery and also to calculate the deformation in the pillar and the sagging in gallery due to induced stress. ANSYS.13 3-D software was used in numerical modeling. Different mining parameters were changed to measure the effects on stress behavior, deformation and sagging in gallery

Cut Locus of Submanifolds: A Geometric and Topological Viewpoint

Associated to every closed, embedded submanifold $N$ of a connected Riemannian manifold $M$, there is the distance function $d_N$ which measures the distance of a point in $M$ from $N$. We analyze the square of this function and show that it is Morse-Bott on the complement of the cut locus $\mathrm{Cu}(N)$ of $N$, provided $M$ is complete. Moreover, the gradient flow lines provide a deformation retraction of $M-\mathrm{Cu}(N)$ to $N$. If $M$ is a closed manifold, then we prove that the Thom space of the normal bundle of $N$ is homeomorphic to $M/\mathrm{Cu}(N)$. We also discuss several interesting results which are either applications of these or related observations regarding the theory of cut locus. These results include, but are not limited to, a computation of the local homology of singular matrices, a classification of the homotopy type of the cut locus of a homology sphere inside a sphere, a deformation of the indefinite unitary group $U(p,q)$ to $U(p)\times U(q)$ and a geometric deformation of $GL(n,\mathbb{R} )$ to $O(n,\mathbb{R} )$ which is different from the Gram-Schmidt retraction. \bigskip \noindent If a compact Lie group $G$ acts on a Riemannian manifold $M$ freely then $M/G$ is a manifold. In addition, if the action is isometric, then the metric of $M$ induces a metric on $M/G$. We show that if $N$ is a $G$-invariant submanifold of $M$, then the cut locus $\mathrm{Cu}(N)$ is $G$-invariant, and $\mathrm{Cu}(N)/G = \mathrm{Cu}\left( N/G \right)$ in $M/G$. An application of this result to complex projective hypersurfaces has been provided.Comment: 121 pages, 33 figures, PhD Thesi

The image of polynomials on upper triangular matrix algebras

Let $p$ be a polynomial in non-commutative variables $x_1,x_2,\cdots,x_n$ with constant term zero over an algebraically closed field $K$. The object of study in this paper is the image of this kind of polynomial over the algebra of upper triangular matrices $T_m(K)$. We introduce a family of polynomials called multi-index $p$-inductive polynomials for a given polynomial $p$. Using this family we will show that, if $p$ is a polynomial identity of $T_t(K)$ but not of $T_{t+1}(K)$, then $p \left(T_m(K)\right)\subseteq T_m(K)^{(t-1)}$. Equality is achieved in the case $t=1$ and $m-1$. An example has been provided to show that equality does not hold in general. We prove that in all cases $p(T_m(K))+p(T_m(K))=T_m(k)^{(t-1)}$. It has also been shown that the image of $T_m(K)^\times$ under a word map is Zariski dense in $T_m(K)^\times$.Comment: 29 pages, 6 figures, comments are welcome; This concludes result about all the case

COVID-19 and tuberculosis reactivation: a systematic review assessing most common risk factors

COVID-19 as a pandemic not only shifted the focus of the healthcare system from other diseases but also affected the disease progression of infections like tuberculosis which remained a leading killer in the past worldwide. COVID-19 itself is said to reactivate latent tuberculosis as shown in animal experiments. Immunomodulators such as corticosteroids and tocilizumab which are being used for covid treatment even further predisposes patients to tuberculosis reactivation and increased progression of the disease. Diabetes is already known to be a risk factor for tuberculosis reactivation and impact tuberculosis progression and worsen the situation. The exact mechanism of interaction of covid-19 and tuberculosis and their effect on each other remains unknown. Considering high prevalence of tuberculosis and the current scenario of covid-19 in world, there is need to study the impact of covid-19 infection on tuberculosis progression or reactivation and commonly associated risk factors. We conducted a systematic search of the online databases to collect data of patients who had tuberculosis reactivation or increased progression of disease after covid-19 infection. Data of a total of 18 patients was retrieved and used for the syntheses of the study. Diabetes was present in 50% of the patients. 55.5% patients were administered corticosteroids for covid-19 treatment later presenting with tuberculosis. Tocilizumab however was administered to 22.2% patients who also received corticosteroids. 27.7% patients suffered tuberculosis reactivation after covid-19 infection without history of diabetes and corticosteroid or tocilizumab administration. None of the patients were reported to have HIV infection. Major risk factors present in patients included corticosteroid administration and diabetes. However, tuberculosis reactivation was seen even in absence of these factors indicating that covid-19 infection may itself be responsible for tuberculosis reactivation. The exact mechanism however remains unknown and further clinical studies are needed to know the same

On the Cut Locus of Submanifolds of a Finsler Manifold

In this paper, we investigate the cut locus of submanifolds in a Finsler manifolds, a natural generalization of Riemannian manifolds. We explore the deformation and characterization of the cut locus, extending the results of \cite{BaPr21}. We also obtain a generalization of Klingenberg's lemma for closed geodesic (\cite{Kli59}) in the Finsler setting.Comment: 22 pages, 6 figures and comments are welcom

A systematic review of reactivation of tuberculosis due to use of corticosteroids for COVID-19 treatment between January 2020 to January 2022

Coronavirus-19 disease became a matter of concern for the whole world and WHO declared it as pandemic on 11 March 2020. Soon a number of clinical trials started to check for the treatment modalities, to compare their efficacy and safety. Out of which corticosteroids in trials showed decrease in mortality in severe COVID-19 patients. However existing diseases such as tuberculosis still remains a leading killer and matter of concern. One out of four individuals are said to be having tuberculosis (mostly in inactive form or latent form) but there remains a threat of reactivation of tuberculosis in presence of risk factors such as corticosteroid administration as it causes immunosuppression. This is a retrospective observational study on reactivation of tuberculosis due to corticosteroids used in COVID-19 treatment. Most commonly given corticosteroid was found to be dexamethasone and the duration of corticosteroid therapy ranged between 5 to 12 days. Majority of patients (5 out of 6) showed reactivation of tuberculosis within 30 days of starting of corticosteroid therapy and most common co-morbidity associated was found to be diabetes mellitus followed by hypertension in such patients. Symptoms of 4 out of 6 patients resolved after starting of anti-tubercular therapy

Analgesic activity of allopurinol and febuxostat in experimental animals

Background: Currently, two classes of analgesics, nonsteroidal anti-inflammatory drugs (NSAIDs) and opioid analgesics are used to manage pain in different clinical situations. Chronic uses of these drugs have various adverse effects like gastric ulceration/bleeding, analgesic nephropathy and respiratory depression, physical dependence, addiction, respectively. Xanthine oxidase inhibitors, used for chronic gout, might have a role in alleviation of pain, as per literature survey. Hence, the present study was carried out to evaluate the potential analgesic activity of allopurinol and febuxostat in different experimental models.Methods: The analgesic activity of allopurinol and febuxostat was assessed by employing two different experimental pain models-tail flick latency model in rats for central analgesia and acetic acid induced writhing model in mice for peripheral analgesia and was compared with tramadol and aspirin.Results: Allopurinol and febuxostat produced significant central and peripheral analgesic effects as is evident from increase in reaction time in tail flick test and inhibition in number of writhes in acetic acid induced writhing test.Conclusions: The results of the present study demonstrate marked analgesic effect of allopurinol and febuxostat