Stability analysis of an eco-epidemiological model incorporating a prey refuge

The present paper deals with the problem of a predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, permanence, local and global stabilities are addressed. We have also studied the effect of discrete time delay on the model. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings

Mathematical Modeling And Experimental Studies On Biochemical Conversion Of Cr(Vi) Of Tannery Effluent To Cr(Iii) In A Chemostat

Biodegradation of hexavalent chromium present in tannery waste has been studied using Pseudomonas sp. (JUBTCr1) and Bacillus sp. (JUBTCr3) isolated from their native source. A 5L double-jacketed chemostat with 4L working volume has been used as contacting device for the kinetic investigation of the biodegradation process. Varying the feed volumetric rate from 118-133 ml/h for different inlet hexavalent chromium concentrations (30 to 90 mg/dm3), an attempt has been made to study the reaction engineering behavior of the system. It is observed that Haldane type substrate inhibited model can satisfactorily be used to predict the extent of bioconversion for different dilution rate. Using the kinetic parameters of proposed Haldane equation, a CSTR model was developed. Model prediction agreed well with experimental data

Violation of Bell's inequality for phase singular beams

We have considered optical beams with phase singularity and experimentally verified that these beams, although being classical, have properties of two mode entanglement in quantum states. We have observed the violation of Bell's inequality for continuous variables using the Wigner distribution function (WDF) proposed by Chowdhury et al. [Phys. Rev. A \textbf{88}, 013830 (2013)]. Our experiment establishes a new form of Bell's inequality in terms of the WDF which can be used for classical as well as quantum systems.Comment: 7 pages, 9 figures and 1 tabl

A Fuzzy Two-warehouse Inventory Model for Single Deteriorating Item with Selling-Price-Dependent Demand and Shortage under Partial-Backlogged condition

In this paper we have developed an inventory model for a single deteriorating item with two separate storage facilities (one is owned warehouse (OW) and the other a rented warehouse (RW)) and in which demand is selling- price dependent. Shortage is allowed and is partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. It is assumed that the holding cost of the rented warehouse is higher than that of owned warehouse. As demand, selling- price, holding- cost, shortage, lost- sale, deterioration- rate are uncertain in nature, we consider them as triangular fuzzy numbers and developed the model for fuzzy total cost function and is defuzzified by using Signed Distance and Centroid methods. In order to validate the proposed model, we compare the results of crisp and fuzzy models through a numerical example and based on the example the effect of different parameters have been rigorously studied by sensitivity analysis taking one parameter at a time keeping the other parameters unchanged

Stability and Bifurcation Analysis of a Delayed Three Species Food Chain Model with Crowley-Martin Response Function

In this paper we have studied the dynamical behaviors of three species prey-predator system. The interaction between prey and middle-predator is Crowley-Martin type functional response. Positivity and boundedness of the system are discussed. Stability analysis of the equilibrium points is presented. Permanence and Hopf-bifurcation of the system are analyzed under some conditions. The effect of discrete time-delay is studied, where the delay may be regarded as the gestation period of the super-predator. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Extensive numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically

Nonlinear Mode Coupling and Internal Resonances in MoS2 Nanoelectromechanical System

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here we report on all electrical actuation and detection of few layers MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances

On Indexed Absolute Matrix Summability of an Infinite Series

Some results have been established on absolute index Riesz summability factor of an infinite series. Furthermore, these kind of results can be extended by taking other parameters and an absolute index matrix summability factor of an infinite series or some weaker conditions. In the present paper a new result on generalized absolute index matrix summability factor of an infinite series has been established