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Funding: Peter J. Cameron acknowledges the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no. EP/R014604/1), where he held a Simons Fellowship. For this research, T. Kavaskar was supported by the University Grant Commissions Start-Up Grant, Government of India grant No. F. 30-464/2019 (BSR) dated 27.03. T. Tamizh Chelvam was supported by CSIR Emeritus Scientist Scheme (No. 21 (1123)/20/EMR-II) of Council of Scientific and Industrial Research, Government of India. The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with a and b adjacent if ab=0. We show that the class of zero-divisor graphs is universal, in the sense that every finite graph is isomorphic to an induced subgraph of a zero-divisor graph. This remains true for various restricted classes of rings, including boolean rings, products of fields, and local rings. But in more restricted classes, the zero-divisor graphs do not form a universal family. For example, the zero-divisor graph of a local ring whose maximal ideal is principal is a threshold graph; and every threshold graph is embeddable in the zero-divisor graph of such a ring. More generally, we give necessary and sufficient conditions on a non-local ring for which its zero-divisor graph to be a threshold graph. In addition, we show that there is a countable local ring whose zero-divisor graph embeds the Rado graph , and hence every finite or countable graph, as induced subgraph. Finally, we consider embeddings in related graphs such as the 2-dimensional dot product graph. Publisher PDF

Topological indices are parameters associated with graphs that have many applications in different areas such as mathematical chemistry. Among various topological indices, the Wiener index is classical \cite{w}. In this paper, we prove a formula for the Wiener index and more general $m$-Steiner Wiener index of an arbitrary graph $G$ in terms of the cardinalities of its twin classes. In particular, we will show that calculating these parameters for the graph $G$ can be reduced to calculating the same for a much smaller graph (in general) called the reduced graph of $G$. As applications of our main result, the $m$-Steiner Wiener index is explicitly calculated for various important classes of graphs from the literature including \begin{enumerate} \item[(a)] Power graphs associated with finite groups, \item[(b)] Zero divisor graphs and the ideal-based zero divisor graphs associated with commutative rings with unity, and \item[(c)] Comaximal ideal graphs associated with commutative rings with unity. \end{enumerate} We have also found an upper bound on the $m$-Steiner Wiener index of an infinite class of graphs called the completely joined graphs. As a corollary of this result, we explicitly calculate the $m$-Steiner Wiener index of the complete multipartite graphs.

Stanley's Tree Isomorphism Conjecture posits that the chromatic symmetric function can distinguish non-isomorphic trees. While already established for caterpillars and other subclasses of trees, we prove the conjecture's validity for a new class of trees that generalize proper caterpillars, thus confirming the conjecture for a broader class of trees., Comment: 11 pages

The transportation industry is transitioning from conventional Internal Combustion Engine Vehicles (ICVs) to Electric Vehicles (EVs) due to the depletion of fossil fuels and the rise in non-traditional energy sources. EVs are emerging as the new leaders in the industry. Some essential requirements necessary for the widespread adoption of EVs include sufficient charging stations with numerous chargers, less to no wait time before charging, quick charging, and better range. To enable a quicker transition from ICVs to EVs, commercial organizations and governments would have to put in a mammoth effort, given the low number of installed chargers in developing nations such as India. One solution to lower the waiting time is to have multiple vehicles charging simultaneously, which might involve charging two- and four-wheelers simultaneously, even though their battery voltage ratings differ. This paper begins by providing the details of the power sources for EV charging, the charging levels and connector types, along with the specifications of some of the commercial chargers. The necessity of AC-DC converters in EV charging systems is addressed along with the power quality concerns due to the increased penetration of EVs. Next, a review of the existing research and technology of isolated DC-DC converters for simultaneous charging of EV batteries is provided. Further, several potential isolated DC-DC converter topologies for simultaneous charging are described with their design and loss estimation. A summary of the existing products and projects with simultaneous charging features is provided. Finally, insight is given into the future of simultaneous charging.

The proposed research explores Multi-Walled Carbon Nanotube’s (MWCNT’s) effect on the mechanical buckling behavior of glass fiber-enhanced thermosetting composites using UTM and the load vs displacement curve is plotted. Using the inflection point method, the critical buckling load is obtained from the load vs displacement curve for beams with three different volume fractions of MWCNT. The nonlinear finite element method is used to numerically obtain the load vs deflection curve and the numerical results are compared with the experimental results, and a close match is found with the experimental results. It is observed that the nonlinearity associated with the structure can significantly reduce the critical buckling load. The critical buckling load is found to increase and reported a 27.4% increase in buckling load with 0.3 wt.% of MWCNT which could be accounted for the increase in flexural modulus of the material.

Let $\mathfrak g$ be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra in short) with the associated graph $G$. Any such $\mathfrak g$ is constructed from a free Lie superalgebra by introducing three different sets of relations on the generators: (1) Chevalley relations, (2) Serre relations, and (3) Commutation relations coming from the graph $G$. By Chevalley relations we get a triangular decomposition $\mathfrak g = \mathfrak{ n_+} \oplus \mathfrak h \oplus \mathfrak n_{-}$ and each roots space $\mathfrak{ g_{\alpha}}$ is either contained in $\mathfrak{n_+}$ or $\mathfrak{ n_{-}}$. In particular, each $\mathfrak{ g_{\alpha}}$ involves only the relations (2) and (3). In this paper, we are interested in the root spaces of $\mathfrak g$ which are independent of the Serre relations. We call these roots free roots$^{1}$ of $\mathfrak g$. Since these root spaces involve only commutation relations coming from the graph $G$ we can study them combinatorially. We use heaps of pieces to study these roots and prove many combinatorial properties. We construct two different bases for these root spaces of $\mathfrak g$: One by extending the Lalonde's Lyndon heap basis of free partially commutative Lie algebras to the case of free partially commutative Lie superalgebras and the other by extending the basis given in \cite{akv17} for the free root spaces of Borcherds algebras to the case of BKM superalgebras. This is done by studying the combinatorial properties of super Lyndon heaps. We also discuss a few other combinatorial properties of free roots.

Let $G$ be a simple graph and let $\mathcal{L}(G)$ be the free partially commutative Lie algebra associated to $G$. In this paper, using heaps of pieces, we prove an expression for the generalized $\textbf k$-chromatic polynomial of $G$ in terms of dimensions of the grade spaces of $\mathcal{L}(G)$. This will give us a new interpretation for the chromatic polynomials in terms of multilinear heaps and Lyndon length. The classical results of Stanley, and Greene and Zaslavsky regarding the acyclic orientations of $G$ are obtained as corollaries. A heap with a unique minimal piece is said to be a pyramid and our main theorem is proved using the properties of pyramids. For this reason, we prove two important properties of pyramids namely the pyramid proportionality lemma, and the pyramid and Lyndon heap lemma. In the last section, we will introduce the $(m,\lambda)$-labelling on acyclic orientations which is similar to Stanley's $\lambda$-compatible pairs. As an application of our main theorem, using this $(m,\lambda)$-labelled acyclic orientations, we will prove the reciprocity theorem for the derivatives of the chromatic polynomials.

This inquisition is to abstraction the inert contents of fly bottom ash. Fly bottom ash is the biggest pollution in land. Fly bottom ash occupy more space and it causes land pollution. Utilization of fly bottom ash in different region. It is a material which capture and store atmospheric carbon di oxide. Fly ash is mostly used in construction works. Mixing of some minerals in fly ash like Calcium sulphate dihydrate and calcium hydrated and it will increase the ability of using fly bottom ash in construction works. The main reason for choosing the construction region is the maximum demand is on construction works now a days. Using calcium sulphate dehydrate and calcium hydrated for increasing the strength of bricks. Pollution made by a thermal industry are more and so using some technology to reduce it. Dr. V. Vijayan | Arunkumar. G | Hari Thangam. G | Muthukumar. S | Ahamed Ibrahim. B "Investigaton and Preparation of Fly Bottom Ash and Discussion on Fly Ash Composition - A Review" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: https://www.ijtsrd.com/papers/ijtsrd20260.pdf

This paper describes the enhancement of thermal performance of heat pipe using SiO2 and TiO2 nano fliuds. The experimentation explains about the effects of heat pipe inclination and heat input on the thermal efficiency and thermal resistance. Heat pipe is an advance type of heat exchanger which transfers huge amount of heat due to the effect of capillary action and phase change heat transfer principle. Recent developments in the heat pipe with high thermal conductivity through nano fluids. This paper reviews, influence of various factors such as heat pipe tilt angle, charged amount of working fluid, nanoparticles type, size, mass volume fraction and its effect on the improvement of thermal efficiency, heat transfer capacity and reduction in thermal resistance. The nano fluid preparation and the analysis of its thermal characteristics also have been reviewed. Arunkumar. G | Dr. P. Navaneetha Krishnan | Dr. T. Senthil Kumar "Experimental Enhancement of Heat Transfer Analysis on Heat Pipe using SiO2 and TiO2 Nano Fluid" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: https://www.ijtsrd.com/papers/ijtsrd13094.pdf

Calocybe indica (Milky mushroom) is one of the easily available and culturable mushrooms at relatively low cost. It comprises economic source of protein enriched with antioxidants and immune enhancing factors required for human health. Medicinal property of C. indica is due to the presence of polysaccharides, proteins, aminoacids, terpenes, terpenoids and phenols. In this study, methanolic extract of C.indica was used for invitro antioxidant, Protein denaturation inhibition, Nitric oxide scavenging and Membrane stabilization assays. Total Antioxidant activity (TAA) and phenolic content of Laboratory grown C. indica by phosphomolybdenum method was equivalent to that of ascorbic acid. Antiinflammatory effect was estimated by protein denaturation inhibition assay exhibits inhibition of 66.80 % at 1000 µg/ml. C.indica also found to possess nitric oxide scavenging activity capable of 69.76 % inhibition at 1000 µg/ml. Membrane stabilization assay revealed that methanolic extract of C.indica provides 55.83 % membrane stabilization. Key words: C. indica, Antioxidant, Antiinflammatory, Nitric oxide, Membrane stabilization

Rajappan Revathi,1 Ramachandran Venkatesha Perumal,2 Karkala Sreedhara Ranganath Pai,3 Govindakarnavar Arunkumar,4 Dharmarajan Sriram,5 Suvarna Ganesh Kini1 1Department of Pharmaceutical Chemistry, Manipal College of Pharmaceutical Sciences, Manipal University, Manipal, 2Bharathi College of Pharmacy, Bharathi Nagara, 3Department of Pharmacology, Manipal College of Pharmaceutical Sciences, Manipal University, Manipal, 4Manipal Centre of Virus Research, Manipal University, Manipal, Karnataka, India; 5Pharmacy Group, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, India Abstract: Tuberculosis remains one of the major grievous diseases worldwide. The emergence of resistance to antituberculosis drugs emphasize the necessity to discover new therapeutic agents for preferential tuberculosis therapy. In this study, various novel 1-(1H-benzimidazol-2-ylmethyl)piperidin-4-imine derivatives were developed and checked for favorable pharmacokinetic parameters based on drug-likeness explained by Lipinski’s rule of five. All 20 of the novel chemical entities were found to possess a favorable pharmacokinetic profile since they were not violating Lipinski’s rule of five. The title compounds were also synthesized, characterized, and tested for ex vivo antitubercular activity against Mycobacterium tuberculosis H37Rv (ATCC27294). The results revealed that four compounds (2-[1-(1H-benzimidazol-2-ylmethyl)piperidin-4-ylidene]hydrazinecarbothioamide, 2-[1-(1H-benzimidazol-2-ylmethyl)piperidin-4-ylidene]-N-hydroxyhydrazinecarbo-thioamide, 1-[1-(1H-benzimidazol-2-ylmethyl)piperidin-4-ylidene]guanidine, and 2-[1-(1H-benzimidazol-2-ylmethyl)piperidin-4-ylidene]hydrazinecarboxamide) were the most potent (minimum inhibitory concentration 6.25 µg/mL) antitubercular agents, with less toxicity (selectivity index more than 10). The molecules were also subjected to three-dimensional molecular docking on the crystal structure of enoyl-acyl carrier protein (EACP) reductase enzyme (code 1ZID, Protein Data Bank), which represents a good prediction of the interactions between the molecules and EACP reductase with minimum binding energy. Keywords: enoyl-acyl carrier protein reductase, Schiff’s reaction, benzimidazole, Mycobacterium tuberculosis

The term ‘ancient DNA’ (aDNA) is coming of age, with over 1,200 hits in the PubMed database,\ud beginning in the early 1980s with the studies of ‘molecular paleontology’. Rooted in cloning\ud and limited sequencing of DNA from ancient remains during the pre-PCR era, the field has\ud made incredible progress since the introduction of PCR and next-generation sequencing. Over\ud the last decade, aDNA analysis ushered in a new era in genomics and became the method of\ud choice for reconstructing the history of organisms, their biogeography, and migration routes,\ud with applications in evolutionary biology, population genetics, archaeogenetics, paleoepidemiology,\ud and many other areas. This change was brought by development of new strategies\ud for coping with the challenges in studying aDNA due to damage and fragmentation, scarce\ud samples, significant historical gaps, and limited applicability of population genetics methods. In this review, we describe the state-of-the-art achievements in aDNA studies, with particular focus\ud on human evolution and demographic history. We present the current experimental and theoretical\ud procedures for handling and analysing highly degraded aDNA. We also review the challenges\ud in the rapidly growing field of ancient epigenomics. Advancement of aDNA tools and\ud methods signifies a new era in population genetics and evolutionary medicine research.

Sino-orbital aspergillosis in a 61-year-old male with uncontrolled non-insulin dependent diabetes mellitus presented with three months history of left ear pain, left side headache with mucopurulent nasal discharge and one week history of progressive swelling and pain with difficulty in opening of the left eye and sudden loss of vision. In spite of surgical debridement and medical management with amphotericin B and itraconazole his visual outcome was poor and the infection was unabated at one month follow up.

The UAB-ITREOH program has initiated a skill-based MPH program at Manipal University (MU), India, in 2009, to address the critical need for trained public health professionals and build institutional public health training capacity in the country.Funds from Fogarty have supported the curriculum development and specialized training of MU faculty to teach in the MPH program.The program has been successfully launched and is gaining momentum. The lessons learned from our experiences as well as several challenges faced from the initialization to execution of the program are described in the article.Government support is crucial for raising the profile of this program by accreditation, creating job opportunities and by recognizing these professionals as leaders in the public health sector.