Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur P.O.-Botanic Garden, Howrah-711103, West Bengal, India
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In this paper, we have introduced a intuitionistic fuzzy mathematical programming with intuitionistic fuzzy number as co-efficient of objectives. Real world engineering problems are usually designed with imprecise parameter by the presence of many conflicting objectives. In this paper we develop an approach to solve multi-objective structural design using probabilistic operator. Here total integral values of triangular intuitionistic fuzzy number,and it has been used for imprecise applied load and material density in the test problem. In this paper we have considered a multi objective structural optimization model with weight and deflection as objectives and stress as constraint function. Here design variables are considered as cross sectional area of bars. This classical truss design example is presented here in to demonstrate the significance of our proposed optimization approach. Numerical example is given here to illustrate this structural model through this approximation method.
Department of Physics, Bareilly College, Bareilly, 243005, India
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Present communication reports the experimental values of the dielectric relaxation time () of 4 Methoxyaniline, 4 Ethoxyaniline, 2 Nitroaniline, 2 Chloro, 4 Nitroaniline, 2,6 Dichloroaniline and 2 Methoxy, 3 Nitroanilinein dilute solution of benzene at wavelength 3.13 cm in the microwave region. The measurements have been made at 293, 303 and 3130K, in order to calculate the free energy of activation for dipole orientation process (F). The experimental values ofhave been correlated with the calculated value of obtained using different theories of dielectric relaxation time ( ). It is concluded from this comparative study that the Murty equation is a better representation of the dielectric relaxationphenomenon. Thermo dynamical parameters like molar free energy of activation (F), molar enthalpy of activation (H) and molar entropy of activation (S) have been evaluated by considering the relaxation as the rate process. From the values of F for the various compounds investigated conclusion has been made that energy of activation increases with the size of molecule.
1Department of Mathematics, Indian Institute of Technology Madras, Chennai, India
2School of Computer Science and Engineering, VIT University, Vellore 632 014, India
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In this paper the new notion of MOD natural neutrosophic numbers Cognitive Maps (MOD-n-CMs) model which is based on MOD natural neutrosophic numbers and Neutrosophic Cognitive Maps (NCMs) is introduced. This model will find it various applications in the fields of engineering and science where indeterminacy plays a role.
Department of Mathematics, V.S.S.D. (P.G.) College, Kanpur
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In this paper, a non-linear control mathematical model is proposed and analyzed to study the effect of primary and secondary toxicants on the survival or the extinction of resource based population in aquatic environment. The model is formulated by using system of non-linear ordinary differential equations. In the analysis, all the feasible equilibrium points of the system have been obtained. The conditions for local and non-linear stability of the non-trivial equilibrium points have been carried out using a suitable Lyapunov function. It may be observed from the stability conditions that the density of the resource biomass (zooplankton population) and resource based biological species (fish population) would co-exist if their growth rates were more than the death (removal) rates of both the species due to toxicants both primary and secondary and also when their carrying capacities are positive.
Department of Mathematics, V.S.S.D. College, Kanpur (U.P.) India
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In this chapter we discuss the batch service vacation model. In such system, customers arrive according to a Poisson process and are served in batches of maximum size b and minimum thre shold a. The server takes a single vacation when it finds less than a customers after the service completion.
Remote Sensing Applications Centre, Madhya Pradesh Council of Science & Technology, Bhopal India
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Forest fires are a big threat to physical environment. It not only change the land use/ land cover pattern, vegetation type and cover, ecosystem, biodiversity of the area, but also harm the wealth, property, money, health even the life of the people in that area. In total, forest fire has great concern on human health and on the socio-economic situation of affected countries. It also has profound impacts on the chemical environment too by changing the composition of air, formation of clouds, increase in degree and duration of global temperature and all these in total, effect the climate change by producing toxic and harmful gasses in the environment. Remote sensing data is most promising data for such work as it have synoptic and repetitive coverage and mapping can be done at a lesser cost and shortest time than any conventional methods. Remote sensing technique together with GIS has been emphasized for mapping variables and integrating the same for generation of fire risk zonation maps in representative wildlife habitats of Madhya Pradesh. Satty’s Analytical Hierarchical Approach (AHP) is very effective for the development of models as it is a multi-parametric and logical one. Various spatial and non-spatial layers can be utilized analyzed in it and effective result can be synthesis. Overall 2.5% of the study area comes under very high risk zone and 53.8% as high risk zone, which shows a high need for fire aversion. Easily accessible areas which are more vulnerable of fire and most of them are deliberate because of anthropogenic reasons. Vegetation is in better condition at high elevations in contrast with the lower elevations, purely because of accessibility. An ggregate are of 7.1% is either under low or low fire hazard.