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Search Results: 1 - 10 of 218 matches for " Dipendu Maity "
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Enumeration of Semi-Equivelar Maps on the Torus
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2013,
Abstract: Semi-equivelar maps are generalizations of equivelar maps. There are eight non-isomorphic types of semi-equivelar maps on the torus. These are of the types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{3, 6, 3, 6\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$, $\{3,12^{2}\}$, $\{4,6,12\}$, $\{3, 4, 6, 4\}$. In this article we attempt to classify these maps.
On enumeration of a class of maps on Klein bottle
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2015,
Abstract: We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of the types $\{3^{6}\}$, $\{4^{4}\}$, $\{6^{3}\}$, $\{3^{3},$ $4^{2}\}$, $\{3^{2},$ $4,$ $3,$ $4\}$, $\{3,$ $6,$ $3,$ $6\}$, $\{3^{4}, 6\}$, $\{4,$ $8^{2}\}$, $\{3, 12^{2}\}$, $\{4,$ $6,$ $12\}$, $\{3,$ $4,$ $6,$ $4\}$. In this article, we attempt to classify these maps.
Contractible Hamiltonian Cycles in Polyhedral Maps
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2012,
Abstract: We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps.
Hamiltonian Cycle in Semi-Equivelar Maps on the Torus
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2013,
Abstract: Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{6,3,6,3\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$, $\{3,12^{2}\}$, $\{4,6,12\}$, $\{6,4,3,4\}$ exist on the torus. In this article we show the existence of Hamiltonian cycle in each semi-equivelar map on the torus except the map of type $\{3,12^{2}\}$. This result gives the partial solution to the conjecture which is given by Gr$\ddot{u}$nbaum \cite{grunbaum} and Nash-Williams \cite{nash williams} that every 4-connected graph on the torus is Hamiltonian.
Triangulated map with minimum degree four is Hamiltonian
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2014,
Abstract: A $triangulation$ is an embedding of a graph on surfaces where every face has length three. In this article, we show the existence of contractible Hamiltonian cycle in triangulated maps of which minimum degree is four.
Some Centrally Symmetric Manifolds
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2014,
Abstract: We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g \geq 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons for each orientable genus $g = 2k-1$, $k\in \mathbb{N}$. We enumerate centrally symmetric triangulated manifolds of dimensions 2 and 3 with few vertices.
Hamiltonian Cycles in Polyhedral Maps
Dipendu Maity,Ashish Kumar Upadhyay
Mathematics , 2014,
Abstract: We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an algorithm to construct such cycles whenever it exists.
Some Semi - Equivelar Maps
Ashish K. Upadhyay,Anand K. Tiwari,Dipendu Maity
Mathematics , 2011,
Abstract: Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than $2-$Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that none of these are vertex transitive. We establish existence of 12-covered triangulations for this surface. We further construct double cover of these maps to show existence of semi-equivelar maps on the surface of double torus. We also construct several semi-equivelar maps on the surfaces of Euler characteristics -8 and -10 and on non-orientable surface of Euler characteristics -2.
Probiotics and human health: Synoptic review.
TK Maity, AK Maity
African Journal of Food, Agriculture, Nutrition and Development , 2009,
Abstract: The development of probiotic, functional foods aims to “kill two birds with one stone,” which is accomplished by providing a microbial stimulus to the host immune system by means of beneficial live microorganism cultures that are characteristic of the healthy, human gut microflora. Several probiotic preparations seem to have promise in prevention or treatment of various conditions. Probiotic bacteria reinforce the different lines of gut defense, which are immune exclusion, immune elimination, and immune regulation. They stimulate non-specific host resistance to microbial pathogens, thereby aiding in pathogen eradication. Best documented clinical application of probiotics is in the treatment of acute diarrhea. In humans, documented effects were reported for the alleviation of intestinal inflammation, normalization of gut mucosal dysfunction, and down-regulation of hypersensitivity reactions. The efficacy of probiotics in acute enteric infections and post-antibiotic syndromes is now established and there is emerging evidence for a role in alleviation of necrotizing enterocolitis, irritable bowel syndrome, and some forms of inflammatory bowel disease. Probiotics are gaining importance because of their innumerable benefits, e.g. treating lactose intolerance, hypercholesterol problem, cardiac diseases and managing cardiac problems like atherosclerosis and arteriosclerosis. However, adequate information by which the consumer and health professional can judge the efficacy and safety of retailed probiotics is lacking. Probiotic products have not been subjected to large-scale trials of efficacy that are used in the pharmaceutical industry. Without these trials and subsequent approval by fastidious regulatory agencies such as the FDA (USA), probiotics continue to languish in the self-care health market. However, the future is bright; enhanced understanding of the molecular details of host’s microflora flora interactions within the gut promises to yield new therapeutic targets and the potential to move from “bugs to drugs”. With the current focus on disease prevention and the quest for optimal health at all ages, the probiotics market potential is enormous. Health professionals are in an ideal position to help and guide their clients toward appropriate prophylactic and therapeutic uses of probiotics that deliver the desired beneficial health effects.
Multistep-ahead River Flow Prediction using LS-SVR at Daily Scale  [PDF]
Parag P. Bhagwat, Rajib Maity
Journal of Water Resource and Protection (JWARP) , 2012, DOI: 10.4236/jwarp.2012.47062
Abstract: In this study, potential of Least Square-Support Vector Regression (LS-SVR) approach is utilized to model the daily variation of river flow. Inherent complexity, unavailability of reasonably long data set and heterogeneous catchment response are the couple of issues that hinder the generalization of relationship between previous and forthcoming river flow magnitudes. The problem complexity may get enhanced with the influence of upstream dam releases. These issues are investigated by exploiting the capability of LS-SVR–an approach that considers Structural Risk Minimization (SRM) against the Empirical Risk Minimization (ERM)–used by other learning approaches, such as, Artificial Neural Network (ANN). This study is conducted in upper Narmada river basin in India having Bargi dam in its catchment, constructed in 1989. The river gauging station–Sandia is located few hundred kilometer downstream of Bargi dam. The model development is carried out with pre-construction flow regime and its performance is checked for both pre- and post-construction of the dam for any perceivable difference. It is found that the performances are similar for both the flow regimes, which indicates that the releases from the dam at daily scale for this gauging site may be ignored. In order to investigate the temporal horizon over which the prediction performance may be relied upon, a multistep-ahead prediction is carried out and the model performance is found to be reasonably good up to 5-day-ahead predictions though the performance is decreasing with the increase in lead-time. Skills of both LS-SVR and ANN are reported and it is found that the former performs better than the latter for all the lead-times in general, and shorter lead times in particular.
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