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Common fixed point theorem and invariant approximation in complete linear metric spaces
Hemant Kumar Nashine 영남수학회 2012 East Asian mathematical journal Vol.28 No.5
A common fixed point result of Gregus type for subcompati- ble mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metriz- able locally convex spaces. Invariant approximation results have also been determined as its application
Hemant Kumar Gupta,Vikas Maheshwari,Vandana Vikas Thakery 보안공학연구지원센터 2016 International Journal of Hybrid Information Techno Vol.9 No.11
Brain tumour is the largest problem in the world. Few researchers have worked in that area. In the paper brain tumour is detected by the three different parameter of the proposed antenna namely return-loss of the antenna, current density of the brain phantom model with tumour and without tumour and specific absorption rate (SAR) with and without tumour. None of the previous work detects a tumour by three different parameter simultaneously. Initially the proposed antenna is designed at 2.45GHz and then applies different technology to make it ultra wide band. Antenna frequency is shifted and it become the ultra wide band and gives a bandwidth of 2.89GHz.S11 parameter of antenna achieved maximum at 7.624GHz that is 45.76dB. Found current density of the antenna is 770.6A/m2, SAR of the antenna is 2.67*106Watt/m3.Brain is assumed as a single layer Brain Phantom model in which brain is considered as centre radius of sphere of 10mm radius and placed in contact with upper part of the antenna, dielectric constant of brain is assumed as 45.8.it gives a return loss with brain model is 31.89dB at 7.61GHz and current density is 801.24A/m2, SAR of the brain phantom model with antenna is 3.15*106 Watt/m3.Now triangular shape tumor is assumed with dielectric constant of the tumor is 52.06 and it gives a return loss with tumor 32.26 at 7.544GHz.current density with tumor is 960.3A/m2, SAR of the phantom model with tumor and antenna is 3.069*106A/m2.The paper detect tumors by three different parameter simultaneously that is very important aspect.
A Comparative QSPR Study of Alkanes with the Help of Computational Chemistry
Kumar, Srivastava Hemant Korean Chemical Society 2009 Bulletin of the Korean Chemical Society Vol.30 No.1
The development of a variety of methods like AM1, PM3, PM5 and DFT now allows the calculation of atomic and molecular properties with high precision as well as the treatment of large molecules with predictive power. In this paper, these methods have been used to calculate a number of quantum chemical descriptors (like Klopman atomic softness in terms of $E_n^{\ddag}\;and\;E_m^{\ddag}$, chemical hardness, global softness, electronegativity, chemical potential, electrophilicity index, heat of formation, total energy etc.) for 75 alkanes to predict their boiling point values. The 3D modeling, geometry optimization and semiempirical & DFT calculations of all the alkanes have been made with the help of CAChe software. The calculated quantum chemical descriptors have been correlated with observed boiling point by using multiple linear regression (MLR) analysis. The predicted values of boiling point are very close to the observed values. The values of correlation coefficient ($r^2$) and cross validation coefficient ($r_{cv}^2$) also indicates the generated QSPR models are valuable and the comparison of all the methods indicate that the DFT method is most reliable while the addition of Klopman atomic softness $E_n^{\ddag}$ in DFT method improves the result and provides best correlation.
Hemant Kumar,Shilesh Kumari 대한수학회 2010 대한수학회보 Vol.47 No.6
In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.
Hemant Kumar Nashine,Zoran Kadelburg 대한수학회 2015 대한수학회보 Vol.52 No.3
We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized Φ-contractive conditions in Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.
Natural product-derived pharmacological modulators of Nrf2/ARE pathway for chronic diseases
Kumar, Hemant,Kim, In-Su,More, Sandeep Vasant,Kim, Byung-Wook,Choi, Dong-Kug The Royal Society of Chemistry 2014 Natural product reports Vol.31 No.1
<P>Covering: 2000 to 2013</P><P>Oxidative stress is the central component of chronic diseases. The nuclear factor erythroid 2-related factor 2/antioxidant response element (Nrf2/ARE) pathway is vital in the up-regulation of cytoprotective genes and enzymes in response to oxidative stress and treatment with certain dietary phytochemicals. Herein, we classify bioactive compounds derived from natural products that are Nrf2/ARE pathway activators and recapitulate the molecular mechanisms for inducing Nrf2 to provide favorable effects in experimental models of chronic diseases. Moreover, pharmacological inhibition of Nrf2 signalling has emerged as promising strategy against multi-drug resistance thereby improving the treatment efficacy. We have also enlisted natural product-derived inhibitors of Nrf2/ARE pathway.</P> <P>Graphic Abstract</P><P>Herein, we summarize and classify >110 modulators of the Nrf2/ARE pathway derived from natural products. This review explains the favorable role of Nrf2 modulators for chronic diseases. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=c3np70065h'> </P>
The Role of Free Radicals in the Aging Brain and Parkinson’s Disease: Convergence and Parallelism
Kumar, Hemant,Lim, Hyung-Woo,More, Sandeep Vasant,Kim, Byung-Wook,Koppula, Sushruta,Kim, In Su,Choi, Dong-Kug Molecular Diversity Preservation International (MD 2012 INTERNATIONAL JOURNAL OF MOLECULAR SCIENCES Vol.13 No.8
<P>Free radical production and their targeted action on biomolecules have roles in aging and age-related disorders such as Parkinson’s disease (PD). There is an age-associated increase in oxidative damage to the brain, and aging is considered a risk factor for PD. Dopaminergic neurons show linear fallout of 5–10% per decade with aging; however, the rate and intensity of neuronal loss in patients with PD is more marked than that of aging. Here, we enumerate the common link between aging and PD at the cellular level with special reference to oxidative damage caused by free radicals. Oxidative damage includes mitochondrial dysfunction, dopamine auto-oxidation, α-synuclein aggregation, glial cell activation, alterations in calcium signaling, and excess free iron. Moreover, neurons encounter more oxidative stress as a counteracting mechanism with advancing age does not function properly. Alterations in transcriptional activity of various pathways, including nuclear factor erythroid 2-related factor 2, glycogen synthase kinase 3β, mitogen activated protein kinase, nuclear factor kappa B, and reduced activity of superoxide dismutase, catalase and glutathione with aging might be correlated with the increased incidence of PD.</P>
COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE
Hemant Kumar Nashine,김종규 영남수학회 2010 East Asian mathematical journal Vol.26 No.1
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.
Gastrodin Protects Apoptotic Dopaminergic Neurons in a Toxin-Induced Parkinson's Disease Model
Kumar, Hemant,Kim, In-Su,More, Sandeep Vasant,Kim, Byung-Wook,Bahk, Young-Yil,Choi, Dong-Kug Hindawi Publishing Corporation 2013 Evidence-based Complementary and Alternative Medic Vol.2013 No.-
<P><I>Gastrodia elata</I> (GE) Blume is one of the most important traditional plants in Oriental countries and has been used for centuries to improve various conditions. The phenolic glucoside gastrodin is an active constituent of GE. The aim of this study was to investigate the neuroprotective role of gastrodin in 1-methyl-4-phenylpyridinium (MPP<SUP>+</SUP>)/1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine- (MPTP) induced human dopaminergic SH-SY5Y cells and mouse model of Parkinson's disease (PD), respectively. Gastrodin significantly and dose dependently protected dopaminergic neurons against neurotoxicity through regulating free radicals, Bax/Bcl-2 mRNA, caspase-3, and cleaved poly(ADP-ribose) polymerase (PARP) in SH-SY5Y cells stressed with MPP<SUP>+</SUP>. Gastrodin also showed neuroprotective effects in the subchronic MPTP mouse PD model by ameliorating bradykinesia and motor impairment in the pole and rotarod tests, respectively. Consistent with this finding, gastrodin prevented dopamine depletion and reduced reactive astrogliosis caused by MPTP as assessed by immunohistochemistry and immunoblotting in the substantiae nigrae and striatata of mice. Moreover, gastrodin was also effective in preventing neuronal apoptosis by attenuating antioxidant and antiapoptotic activities in these brain areas. These results strongly suggest that gastrodin has protective effects in experimental PD models and that it may be developed as a clinical candidate to ameliorate PD symptoms.</P>