Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Now showing 1 - 20 of 870

Simultaneous effect of two toxicants on biological species: a mathematical model
(World Scientific, 1996) Dubey, Balram
In this paper, a mathematical model to study the simultaneous effect of two toxicants (one is more toxic than the other) on the growth and survival of a biological species is proposed. The cases of instantaneous spill, constant and periodic emissions of each of the toxicant into the environment are considered. It is shown that in the case of an instantaneous spill of each of the toxicant into the environment, the species after its initial decrease in density may recover to its original level after a period of time, the magnitude of which depends on the toxicity and washout rate of each of the toxicant. However, if both the toxicants are emitted with constant rates, the species in the habitat is doomed to extinction sooner than the case of a single toxicant having the same influx and washout rates as one of them, the extinction rate becoming faster with the increase in toxicity and emission rate of the other toxicant. It is also shown that for a small amplitude periodic emission of the toxicant with a constant mean, the stability behavior of the system is same as that of the case of the constant emission. It is found further through the model study that if suitable efforts are made to reduce the emission rate of each of the toxicant at the source and its concentration in the environment by some removal mechanism, an appropriate level of species density can be maintained.
Effect of changing habitat on survival of species
(Elsevier, 1996) Dubey, Balram
In this paper, a mathematical model is proposed to study the growth and existence (survival) of resource-biomass-dependent species in a forested habitat which is being depleted due to the pressure of industrialization (population). It is shown that as the pressure of industrialization increases, the biomass density decreases, leading to lowering of the density of species and its eventual extinction if this pressure continues unabatedly. However, if suitable efforts are made to conserve the resource biomass and to control the pressure of industralization in the forested habitat, the survival of resource-biomass-dependent species can be ensured.
Effect of changing habitat on species: Application to Keoladeo National Park, India, Ecol. Model.
(Elsevier, 1996-04) Dubey, Balram
In this paper, a mathematical model is proposed to study the effect of ecological changes caused by the excessive growth of wild grasses such as Paspalum distichum on the existence of various species in the Keoladeo National Wetland Park, Bharatpur, Rajasthan, India. In the model the growth rate of several species, such as floating vegetation (Nymphoides indicum, Nymphoides cristatum, Nymphaea nouchali and Nymphaea stellata), fishes, waterfowl, etc. and the corresponding carrying capacity of the wetland are assumed to decrease with the increase in biomass density of wild grasses. By analysing the model it is shown that if the wild grasses are not controlled, the existence of various other species will be threatened. It is shown through the model study that if the growth of wild grasses is controlled, either by allowing a managed number of buffaloes to graze them or by using some other mechanism to remove them, then the other species in the wetland will boom. Keeping in view the growth of Paspalum distichum and using the corresponding parameters for this wetland in the model, the number of buffaloes to be permitted for grazing has also been calculated for management purposes.
Effect of environmentally degraded soil on crop yield: The role of conservation, Ecol. Model., 86: 235-240, 1996.
(Elsevier, 1996-05) Dubey, Balram
In this paper the effect of fertile top soil degraded by environmental factors such as acid rain and wind on crop yield is studied by considering a single-sector economic growth model. It is shown that if these environmental factors continue to increase without control, the fertile top soil depth tends to zero and consequently the crop yield becomes negligible. However, if suitable measures are taken to fertilize the top soil and to control the acid rain, the crop yield may be maintained at a desired level.
Modelling the depletion of forestry resources: Effects of two interacting populations
(Elsevier, 1997-08) Dubey, Balram
In this paper, a general mathematical model to study the effects of two interacting populations on the depletion of resources is proposed and analysed. In modelling the system, it is assumed that the resource is a common food for both the populations while one of the population is a supplementary food for the other. A model to conserve the resource is also presented.
Modelling the depletion and conservation of forestry resources: effects of population and pollution
(Springer, 1997-11) Dubey, Balram
In this paper, a mathematical model is proposed to study the depletion of resources in a forest habitat due to the increase of both population and pollution. It is shown that if the rate of pollutant emission into the environment is either population dependent, constant, or periodic, the equilibrium biomass density of the resource settles down to a lower equilibrium than its original carrying capacity, the magnitude of which decreases as the equilibrium levels of the density of population and the concentration of pollutant increase. However, in the case of an instantaneous spill of pollutant into the environment, the equilibrium biomass density decreases with the increase of the equilibrium density of population only. It is found that if the population density and the emission rate of pollutant increase without control, the forestry resource may become extinct. A conservation model is also proposed, the analysis of which shows that the resource biomass can be maintained at a desired level by conserving the forestry resource and by controlling the growth of population and the emission rate of pollutant in the habitat.
Models for the Survival of Species Dependent on Resource in Industrial Environments
(Elsevier, 1999-03) Dubey, Balram
In this paper, a mathematical model to study the survival of species dependent on a resource under the industrialization pressure in a given region with diffusion is proposed and analyzed. In the absence of diffusion, criteria for local stability, instability, and global stability are obtained. A model to conserve the resource biomass and to control the undesired level of industrialization pressure is also presented.
Effects of Toxicants (pollutants) on a Biological Species — Some Mathematical Models
(Springer, 2000) Dubey, Balram
It is well recognized that the deterioration of our environment by various kinds of industrial discharges (toxic effluents, pollutants) to the environment has very undesirable consequences on all living beings including plants. There are many examples of how air pollutants (primary and secondary) can destroy the character and productivity of vast areas of forests, agricultural crops and vegetation (Kozlowski, 1975,1980; Davis, 1972; Manning, 1975; Pack & Sulzback, 1976; Constantinidou & Kozlowski, 1979a,b;Garseded et al., 1981; Henriksson & Pearson, 1981; Norby & Kozlowski, 1981 ; Reinert & Gray, 1981 ; Smith, 1981 ; Stan & Schicker, 1982; McLaughlin,
Analytical investigation of the hydromagnetic flow in a porous medium due to periodically heated oscillating plate
(International Journal of Applied Mechanics and Engineering, 2000) Sharma, Bhupendra Kumar
The Stokes second problem in the presence of a magnetic field in a porous medium is considered. The flow is due to an oscillating plate at the bottom of the porous medium of finite thickness and fully saturated with the viscous incompressible liquid. The plate is kept at oscillating temperature and a transverse uniform magnetic field is applied normal to the plate. It is assumed that the flow in the porous medium is governed by the Brinkman equations. The flows at the interface (porous medium-clear fluid boundary) are matched by the conditions suggested by Ochao-Tapia and Whittaker. Approximate solutions for velocity, temperature field, skin-friction and rate of heat transfer are calculated and effects of various parameters upon them are examined.
A model for the allelopathic effect on two competing species
(Elsevier, 2000-05) Dubey, Balram
In this paper, a mathematical model is proposed and analysed to study the coexistence of two competing plant species in a finite habitat by assuming that each species produces a toxic substance affecting the other species. The diffusion of toxic substances is also considered in the model. It is shown that the usual existence criteria between two competing species in the absence of toxicant may be changed if each species produces toxicant in large amount affecting the other. In case of no diffusion criteria for local stability, instability and global stability of the system are obtained. In case of allelopathy, where one species produces toxicant and affects the other, it is found that the affected species may be driven to extinction. It is also found that diffusion has a stabilizing effect on the system.
Modelling the Interaction of Two Biological Species in a Polluted Environment
(Elsevier, 2000-06) Dubey, Balram
In this paper a mathematical model is proposed and analysed to study the effect of an environmental pollutant on two interacting biological species. The interaction between the two species is considered to be of three types, namely, competition, cooperation, and prey–predator. In each case criteria for local stability, instability, and global stability of the nonnegative equilibria of the system are obtained. The effect of diffusion on the equilibrium state of the system is also studied.
Existence and survival of two competing species in a polluted environment: a mathematical model
(World Scientific, 2001) Dubey, Balram
In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.
Tuberculosis of frontal bone: a case report
(Indian Journal of Tuberculosis, 2001) Sharma, Bhupendra Kumar
The occurrence of tuberculosis in the flat bones of skull is very rare. With the resurgence of tuberculosis the world over, there have been reports of unusual sites being affected by the disease. But cases of frontal bone tuberculosis are still few. According to Mehrotra1 who reported a case of frontal bone tuberculosis in a child, although tuberculosis is very common in the Indian subcontinent yet tuberculous disease of skull is rare. To the best of our knowledge, only six cases of tuberculosis of frontal bone have been reported in the world literature. The youngest patient affected by tuberculous osteitis of frontal bone was a 3 year old male child presenting with a 12 month history of sinuses over the frontal bone2. The diagnosis in this case was made by biopsy of the bone edges.
Descent principle in modular Galois theory
(IAS, 2001-05) Keskar, Pradipkumar H.
We propound a descent principle by which previously constructed equations over GF.qn/.X/ may be deformed to have incarnations over GF.q/.X/ without changing their Galois groups. Currently this is achieved by starting with a vectorial (= additive) q-polynomial of q-degreemwith Galois group GL.m; q/ and then, under suitable conditions, enlarging its Galois group to GL.m; qn/ by forming its generalized iterate relative to an auxiliary irreducible polynomial of degree n. Elsewhere this was proved under certain conditions by using the classification of finite simple groups, and under some other conditions by using Kantor’s classification of linear groups containing a Singer cycle. Now under different conditions we prove it by using Cameron-Kantor’s classification of two-transitive linear groups.
A predator–prey interaction model with self and cross-diffusion
(Elsevier, 2001-07) Dubey, Balram
In this paper, a mathematical model for a predator–prey interaction with self and cross-diffusion is proposed and analysed. Criteria for local stability, instability and global stability are obtained. The effect of the critical wave length which can drive a system to instability is investigated. The effect of time-varying cross-diffusivity on the stability of the system is also examined.
State Dependent Multi channel Queuing System with Ordered Entry
(MERC, 2002) Shekhar, Chandra
In the present study, we analyze the multi-channel service system with ordered entryfrom finite-source and finite-storage at each channel. The arrival and service rates are assumedto be state dependent. The steady state probabilities of the system are obtained by usingChapmann-Kolmogorov equations. Some other performance indices viz. utilization of servers,expected number of units in the system and expected number of units at each channel have beenderived. A computational algorithm is developed to determine the optimal allocation of storagespace facilitated in front of three heterogeneous servers. Sensitivity analysis has been carried outto study the effect of variation of different parameters on the system performance.
A resource dependent fishery model with optimal harvesting policy
(World Scientific, 2002) Dubey, Balram
A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.
A Theorem Relating Multidimensional Generalized Weyl Fractional Integral, Laplace and Varma Transforms with Applications
(Tamsui Oxford Journal of Mathematical Sciences, 2002-07) Mathur, Trilok
The main aim of this paper is to establish a theorem which asserts an interesting relationship between the multidimensional Laplace transform, the multidimensional Varma transform and the generalized Weyl fractional integral involving product of a general class of multivariable polynomials and a generalized polynomial set. By specializing the various parameters involved, this general theorem would readily yield several (known and new) results involving simpler integral operators. Further, the theorem is applied to evaluate the generalized Weyl fractional integrals of Fox’s H-function and the (Srivastava – Panda) H-function of several complex variables
A model for an inshore-offshore fishery
(World Scientific, 2003) Dubey, Balram
In this paper, a nonlinear mathematical model to study the dynamics of an inshore-offshore fishery under variable harvesting is proposed and analyzed. Criteria for local stability, instability and global stability of the system are derived. The optimal harvesting policy is discussed by considering taxation as a control instrument. It is shown that the fishery resources can be protected from overexploitation by increasing the tax and discount rates.
Injection and suction e ects on three-dimensional unsteady ow and heat transfer between two parallel porous plates
(Redalyc, 2003) Sharma, Bhupendra Kumar
The problem of unsteady three-dimensional ow of an incompressible viscous uid between two horizontal parallel porous plates with transverse sinusoidal injection of the uid at the stationary plate and with constant suction through the plate in uniform motion has been studied. The moving plate is kept at oscillating wall temperature while the stationary plate is at constant temperature. Analytical expressions for velocity, temperature, and rate of heat transfer are obtained and discussed with the help of graphs and tables