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Flow maximization is a fundamental problem in mathematics, there are several algorithms available to solve this problem, but these algorithms have some limitations. This paper presents the flow maximization problem as a Linear Programming Problem (L.P.P.). The solution given by L.P.P. formulation of the problem and provided by Ford Fulkerson algorithm is same. This paper also compares the single path flow and k-splitting of the flow and suggests that k-splitting of flow is better than single path flow. [ABSTRACT FROM AUTHOR]

At this moment in time, an outbreak of COVID-19 is transmitting from human to human. Different parts have different quality of life (e.g., India compared to Russia), which implies the impact varies in each part of the world. Although clinical vaccines are available to cure, the question is how to minimize the spread without considering the vaccine. In this paper, via a mathematical model, the transmission dynamics of novel coronavirus with quarantine and isolation facilities have been proposed. The examination of the proposed model is set in motion with the boundedness and positivity of the solution, sole disease-free equilibrium, and local stability. Then, the condition for the existence of sole endemic equilibrium and its local stability has established. In addition, the global stability of the endemic equilibrium for a special case has been investigated. Further, it has shown that the system undergoes a transcritical bifurcation. A threshold analysis has also performed to examine the effect of quarantine on transmission dynamics. Lastly, numerical simulations are giving support to theoretical results. [ABSTRACT FROM AUTHOR]

In this paper a method to obtain a non-dominated point for the multi-objective transportation problem is presented. The superiority of this method over the other existing methods is that the presented non-dominated point is the closest solution to the ideal solution of that problem. The presented method does not need to have the ideal point and other parameters to find this solution. Also, the calculative load of this method is less than other methods in the literature. [ABSTRACT FROM AUTHOR]

The present paper deals with profit modelling and comparison between two dissimilar systems under two types of failures based on Markovian Birth-Death process. Type I failure is minor in the sense that the work is in a reduced capacity whereas type II failure is major because it causes the entire system failure. Both systems consist of four subsystems arranged in series-parallel with three possible states: working with full capacity, reduced capacity and failed state. The systems are attended to by two repairmen in tandem. Through the transition diagrams, systems of differential difference equations are developed and solved recursively to obtain the steady-state availability, busy period of repair men, and profit function. Profit matrices for each subsystem have been developed for different combinations of failure and repair rates. Furthermore, we compare the profit for the two systems and find that system I is more profitable than system II. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in three-dimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are various effective instruments while carrying out all these studies. One of these effective tools is graphs. Graphs are have made a great contribution to the development of algebraic topology. Along with this support, knot theory has taken an important place in low dimensional manifold topology. In 1984, Jones introduced a new polynomial for knots. The discovery of that polynomial opened a new era in knot theory. In a short time, this polynomial was defined by algebraic arguments and its combinatorial definition was made. The Jones polynomials of knot graphs and their applications were introduced by Murasugi. T. UÄŸur and A. Kopuzlu found an algorithm for the Jones polynomials of torus knots K(2, q) in 2006. In this paper, first of all, it has been obtained signed graphs of the twist knots which are a special family of knots. We subsequently compute the Jones polynomials for graphs of twist knots. We will consider signed graphs associated with each twist knot diagrams. [ABSTRACT FROM AUTHOR]

Modeling of inventory problems provides a good insight to retailers and distributors to maintain stock of different items such as seasonal products, perishable goods and daily useable goods etc. The deterioration of all these items exists to a certain extent due to several reasons like mishandling, evaporation, decay, environmental conditions, transportation etc. It is found from the literature that previously many of the researchers have developed inventory model ignoring deterioration and drawn conclusion. In the absence of deterioration parameter, an inventory model cannot be completely realistic. In this paper, we have made an attempt to extend an inventory model with ramp-type demand and price discount on back order where deterioration was not taken into account. In our study, deterioration and constant holding cost are taken into consideration keeping all other parameters same. As a result, the inventory cost function is newly constructed in the presence of deterioration. The objective of this investigation is to obtain optimal cycle length, time of occurrence of shortages and corresponding inventory cost. This extended model is solved for minimum value of average inventory cost analytically. A theorem is framed to characterize the optimal solution. To validate the proposed model, a numerical example is taken and convexity of the cost function is verified. In order to study the effect of changes of different parameters of the inventory system on optimal cycle length, time of occurrence of shortages and average inventory cost, sensitivity analyses have been performed. Also, the numerical result and sensitivity analyses are graphically presented in the respective section of this paper to demonstrate the model. This study reveals that a better solution can be obtained in the presence of our newly introduced assumptions in the existing model. [ABSTRACT FROM AUTHOR]

In this paper first we define a new functional which is a weighted version of the functional defined by Dragomir and Fedotov. Then, some inequalities involving this functional are obtained. Finally, we apply this result to establish new bounds for weighted Chebysev functional. [ABSTRACT FROM AUTHOR]

The paper presents the study of dispersion of contaminants in unsteady laminar flow of an incompressible fluid (groundwater) bounded by an upper porous layer and lower impermeable layer with interphase mass transfer. An analytical solution of unsteady advection dispersion based on Aris-Barton method of moments is presented up to the second moment about the mean in axial direction. [ABSTRACT FROM AUTHOR]

The domination integrity of a connected graph G = (V (G);E(G)) is denoted as DI(G) and defined by DI(G) = min{|S| + m(G - S)}, where S is a dominating set and m(G - S) is the order of a maximum component of G-S. This paper discusses domination integrity of line splitting graph and central graph of some graphs. [ABSTRACT FROM AUTHOR]

Approximate analytical solutions of Boussinesq equation are widely used for approximation of subsurface seepage flow in confined and unconfined aquifers under varying hydrological conditions. In this paper, we use a 2-dimensional linearized Boussinesq equation to simulate the water table fluctuations in an isotropic aquifer overlying a semi pervious bed under multiple localized recharge and withdrawal. The unconfined aquifer is considered to be in contact with two water bodies of constant water head along opposite cost lines, while the remaining two faces have no flow condition. The mathematical model is solved analytically using finite Fourier sine transform and the application of the results is illustrated with a numerical example. It is observed that the vertical flow through the base of the aquifer is an important factor in the determination of groundwater mound and cone of depression. [ABSTRACT FROM AUTHOR]

This paper aims to estimate the basic reproduction number for Avian Influenza outbreak in local and global poultry industries. In this concern, we apply the SEIAVR compartmental model which is developed based on the well-known SEIR model. The SEIAVR model provides the mathematical formulations of the basic reproduction number, final size relationship and a relationship between these two phenomena. The developed model Equations are solved numerically with the help of Range-Kutta method and the values of initial parameters are taken from the several literatures and reports. The calculated result of basic reproduction number shows that it is locally and globally stable if it is less than and greater than one at disease free equilibrium and at endemic equilibrium, respectively. Furthermore, we have compared among the calculated susceptive, expose, infective, removal, virus and asymptotic compartments where infection rate and expose period are observed very sensitive compared to other parameters. In addition, the model result of infective is compared with the field data and other's model where the present model shows good performance against the field data. [ABSTRACT FROM AUTHOR]

The role and importance of the industrial sector in the economic development necessitate the need to collect and to analyze accurate and timely data for exact planning. As the occurrence of outliers in establishment surveys are common due to the structure of the economy, the evaluation of survey data by identifying and investigating outliers, prior to the release of data, is necessary. In this paper, different robust multivariate outlier detection methods based on the Mahalanobis distance with blocked adaptive computationally efficient outlier nominators algorithm, minimum volume ellipsoid estimator, minimum covariance determinant estimator and Stahel-Donoho estimator are used in the context of a real dataset. Also some univariate outlier detection methods such as Hadi and Simonoff's method, and Hidiroglou-Barthelot's method for periodic manufacturing surveys are applied. The real data set is extracted from the Iranian Manufacturing Establishment Survey. These data are collected each year by the Statistical Center of Iran using sampling weights. In this paper, in addition to comparing different multivariate and univariate robust outlier detection methods, a new empirical method for reducing the effect of outliers based on the value modification method is introduced and applied on some important variables such as input and output. In this paper, a new four-step algorithm is introduced to adjust the input and output values of the manufacturing establishments which are under-reported or over- reported. A simulation study for investigating the performance of our method is also presented. [ABSTRACT FROM AUTHOR]

This paper presents an analytic study for the steady drainage of magnetohydrodynamic (MHD) Sisko fluid film down a vertical belt. The fluid film is assumed to be electrically conducting in the presence of a uniform transverse magnetic field. An analytic solution for the resulting non linear ordinary differential equation is obtained using the Adomian decomposition method. The effects of various available parameters especially the Hartmann number are observed on the velocity profile, shear stress and vorticity vector to get a physical insight of the problem. Furthermore, the shear thinning and shear thickening characteristics of the Sisko fluid are discussed. The physical quantities discussed for the Sisko fluid film have also been discussed for the Newtonian fluid film and comparison between them made. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent on the density of immune cells. Further, external infusion of T cells (immune cells) reduces the concentration of cancer cells and infected cells in the blood. It is observed that the infected cells decrease with the increase in antigenicity rate or stimulation rate of immune response due to abnormal cancer cells present in the blood. This indicates that immune cells kill cancer cells on being stimulated and as antigenicity rate increases rate of destruction of cancer cells also increase leading to decrease in the concentration of cancer cells in the body. This decrease in cancer cells further causes decrease in the concentration of infected or dysfunctional cells in the body. [ABSTRACT FROM AUTHOR]

In this paper, a special case of finite difference method called non-standard finite difference (NSFD) method was studied to compute the numerical solutions of the nonlinear mathematical model of the interaction between tumor cells and oncolytic viruses. The global stability of the equilibrium points of the discrete model is investigated by using the Lyapunov stability theorem. Some conditions were gained for the local asymptotical stability of the equilibrium points of the system. Finally, numerical simulations are carried out to illustrate the main theoretical results. The discrete system is dynamically consistent with its continuous model, it preserves essential properties, such as positivity, boundedness of the solution, stability properties of the equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type growth and nonlinear interactions. The model is analyzed qualitatively using the stability theory of ordinary differential equations and computer simulations. By analyzing the model, it is shown that under appropriate conditions, gaseous pollutants and particulate matters would be removed from the atmosphere and their respective equilibrium levels would depend upon the intensity of rain caused by cloud droplets, emission rate of pollutants, the rate of raindrops falling on the ground, etc. It is pointed out that, if due to unfavorable atmospheric conditions cloud droplets are not formed, rain may not occur and pollutants would not be removed. [ABSTRACT FROM AUTHOR]

This paper develops a new class of joint modeling of mixed correlated ordinal and continuous responses with elliptically contoured errors. This joint model includes the latent variable approach of using an elliptically contoured distribution for mixed ordinal and continuous responses. A Markov Chain Monte Carlo sampling algorithm is described for estimating the posterior distribution of the parameters. For sensitivity analysis to investigate the perturbation from associate responses, it is demonstrated how one can use some elements of covariance structure. Influence of small perturbation of these elements on the posterior normal curvature is also studied. To illustrate the application of such modeling the data (medical) is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, a new matrix method based on exponential polynomials and collocation points is proposed to obtain approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential equations. The method converts the model problem into a system of nonlinear algebraic equations by means of the matrix operations and the collocation points. The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all numerical computations have been made by using a computer program written in Maple. [ABSTRACT FROM AUTHOR]

In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The latter generalization imposes three different nonlinearities and extremely intensifies the complexity of the problem. The code successfully manages to provide parametric solution for this case. Finally, for the sake of exemplification, a relevant practical and real-world case study, about a silicon fin, for the complex nonlinear problem is given. It is shown that the numerical results are very close to those calculated by the classical Finite Difference Method (FDM). [ABSTRACT FROM AUTHOR]

It is well recognized that the greenhouse gas such as Chlorofluoro Carbon (CFC) is responsible directly or indirectly for the increase in the average global temperature of the Earth. The presence of CFC is responsible for the depletion of ozone concentration in the atmosphere due to which the heat accompanied with the sun rays are less absorbed causing increase in the atmospheric temperature of the Earth. The increase in the temperature level directly or indirectly affects the dynamics of interacting species systems. Therefore, in this paper a mathematical model is proposed and analyzed using stability theory to asses the effects of increasing temperature due to the greenhouse gas CFC on the survival or extinction of populations in a prey-predator system. A threshold value in terms of a stress parameter is obtained which determines the extinction or existence of populations in the underlying system. [ABSTRACT FROM AUTHOR]

This research aims to study atmospheric internal waves which occur within the fluid rather than on the surface. The mathematical model of the shallow fluid hypothesis leads to a coupled nonlinear system of partial differential equations. In the shallow flow model, the primary assumption is that vertical size is smaller than horizontal size. This model can precisely replicate atmospheric internal waves because waves are dispersed over a vast horizontal area. A semi-analytical approach, namely modified differential transform, is applied successfully in this research. The proposed method obtains an approximate analytical solution in the form of convergent series without any linearization, perturbation, or calculation of unneeded terms, which is a significant advantage over other existing methods. To test the effectiveness and accuracy of the proposed method, obtained results are compared with Elzaki Adomain Decomposition Method, Modified Differential Transform Method, and Homotopy Analysis Method. [ABSTRACT FROM AUTHOR]

Let G = (V,E) be a graph. A subset X of E is called an edge dominating set of G if every edge in E - X is adjacent to some edge in X . An edge dominating set which intersects every maximum matching inG is called matching transversal edge dominating set. The minimum cardinality of a matching transversal edge dominating set is called the matching transversal edge domination number of G and is denoted by γmt(G). In this paper, we begin an investigation of this parameter. [ABSTRACT FROM AUTHOR]

In this paper, we have present the solution of Bianchi type VI0 space-time by solving the Rosen’s field equations with massless scalar field Φ and with constant scalar potential V(Φ) for flat region. It is observed that the scalar field Φ is an increasing function of time and affects the physical parameters of the model and leads to non-inflationary type solution of model, which contradicts the inflationary scenario. Other geometrical and physical properties of the model in relation to this non-inflationary model are also studied. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to depict the effect of time, thermal, and diffusion phase lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of DPLT and DPLD models. The upper and lower surfaces of the ring are traction-free and subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of time, diffusion, and thermal phase-lags are shown on the various components. Some particular results are also deduced from the present investigation. [ABSTRACT FROM AUTHOR]

This article introduces the matrix differential transform method (MDTM) to apply to matrix partial differential equations (MPDEs) and employs it for solving matrix Fisher equations, matrix Burgers equations and matrix KdV equations. We show how the MDTM applies to the linear part and nonlinear part of any MPDE and give various examples of MPDEs to illustrate the efficiency of the method. The results obtained are in excellent agreement with the exact solution and show that the proposed method is powerful, accurate, and easy. [ABSTRACT FROM AUTHOR]

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions to the posed problem. At first, we employ the transform method, and then the Adomian decomposition method to obtain the solutions that shall be useful to provide information about the effect of medical care in the annihilation of gliomas. Finally, we discuss the applicability of this model with numerical simulations and graphical representations. [ABSTRACT FROM AUTHOR]

The sum cordial labeling is a variant of cordial labeling. In this paper, we investigate 3-Total Super Sum Cordial labeling. This labeling is discussed by applying union operation on some of the graphs. A vertex labeling is assigned as a whole number within the range. For each edge of the graph, assign the label, according to some definite rule, defined for the investigated labeling. Any graph which satisfies 3-Total Super Sum Cordial labeling is known as the 3-Total Super Sum Cordial graphs. Here, we prove that some of the graphs like the union of Cycle and Path graphs, the union of Cycle and Complete Bipartite graph and the union of Path and Complete Bipartite graph satisfy the investigated labeling and hence are called the 3-Total Super Sum Cordial graphs. [ABSTRACT FROM AUTHOR]

A set S of vertices in a graph G is called an independent dominating set if S is both independent and dominating. The independent domination number of G is the minimum cardinality of an independent dominating set in G. In this paper, we investigate the exact value of independent domination number for some wheel related graphs. [ABSTRACT FROM AUTHOR]

In this paper we study Kaluza-Klein type cosmological model of the universe filled with an ideal fluid obeying an inhomogeneous equation of state depending on time. It is shown that there appears a quasi-periodic universe, which repeats the cycles of phantom type space acceleration. [ABSTRACT FROM AUTHOR]

SEIR mathematical model of childhood diseases measles, chickenpox, mumps, rubella incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. Driven by seasonality these diseases are characterized by annual oscillations with variable contact rate which is a periodic function of time in years. Homotopy Analysis Method (HAM) is considered in this paper to obtain a semi analytic approximate solution of non-linear simultaneous differential equations. Mathematica is used to carry out the computations. Results established through graphs show the validity and potential of HAM for amplitude of variation greater than zero. Also, when it is equal to zero both HAM and Runge-Kutta method graphs are compared. [ABSTRACT FROM AUTHOR]

The present paper deals with the theoretical study of thermal radiation and chemical reaction on free convective heat and mass transfer flow of a Newtonian viscous incompressible fluid past a suddenly accelerated semi--infinite vertical permeable plate immersed in Darcian absorption media. The fluid media is considered as optically thick and the Rosselend radiative heat flux model is incorporated in the energy equation. The governing equation of motions are first non- dimensionalised and then transformed into a set of ordinary differential equations by employing a suitable periodic transformation. The closed form of the expression for velocity, temperature and concentration fields as well as skin-friction, Nusselt and Sherwood numbers are obtained in terms of various physical parameters present. The effect of parameters like thermal radiation, first order chemical reaction, radiation absorption co-efficient and permeability parameter on the flow variables are obtained numerically and illustrated through graphs and tables. It is observed that, the absorption parameter and radiation parameter increase the temperature as well as the fluid velocity, while the skin--friction is found to be decreasing due to an increase in thermal radiation parameter. It is also observed that, some of the transportation phenomena accelerate due to the presence of chemical reaction parameter. [ABSTRACT FROM AUTHOR]

In this paper, LRS Bianchi type I string fluid cosmological model with magnetic field in bimetric theory of gravitation is investigated by assuming barotropic equation of state for pressure and density and assuming the bulk viscosity to be inversely proportional to the scalar expansion. The source of energy momentum tensor is a bulk viscous fluid containing one dimensional string with electromagnetic field. The physical and geometrical properties of the model are discussed. The bulk viscosity affected the whole properties of the model. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is proposed to study the impact of toxic metals on plant growth dynamics due to transfer of the toxic metal in plant tissues. In the model, it is assumed that the plant uptakes the metal from the soil through the roots and then it is transfered in the plant tissues and cells by transport mechanisms. It is observed experimently that when toxic (heavy) metals combines with the nutrient they form a complex compound due to which nutrient loses its inherent properties and the natural charaterstics of the nutrient are damaged. It is noticed that due to the presence of toxic (heavy) metal in the plant tissues and loss of inherent properties of nutrient due to reaction with the toxic metal, the growth rate of the plant decreases. In order to understand the impact on plant growth dynamics, we have studied two models: One model for a plant growth with no toxic effect and the other model for plant growth with toxic effect. From the analysis of the models the criteria for plant growth with and without toxic effects are derived. The numerical simulation to support the analytical results is done using MathLab. [ABSTRACT FROM AUTHOR]

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal stress with respect to time. The formulation of the current model is based on the number of non-linear ordinary differential equations with suitable initial and boundary conditions. The transformations of glucokinase were studied using mathematical and computational simulations in order to estimate the concentration of native and denatured enzyme forms with respect to different rate constants and under various thermal changes. The results obtained in this model were verified with the empirical outcome of Sanchez Ruiz et al. and Weinhouse for the validity and efficacy of the formulated model. [ABSTRACT FROM AUTHOR]

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical analysis of the novel model without including competitions among the two herbivores reveals that the number of equilibrium states and their local stability depends on the type of interaction between the stressors: synergistic or additive or antagonistic. Our numerical results, based on value of parameters available, suggest that a sustainable system requires significant herbivore inter- or intra-species competition or both types. Additionally, our numerical findings indicate that competition and interaction of additive type promotes coexistence equilibrium states with the highest plant biomass. Furthermore, the system can exhibit periodic behavior and show the potential for multi-stability. [ABSTRACT FROM AUTHOR]

We consider mathematical modeling of blood glucose-insulin regulatory system with the additional effect of the secreted insulin by the pancreatic beta cells and in the presence of an external energy input to such system. Such modeling system is investigated to determine the time-dependent nonlinear dynamics that take place by the quantities, which represent the glucose and insulin concentrations in the blood, insulin action as well as in the absence or presence of secreted insulin due to the pancreatic beta cells. Using both analytical and numerical procedures, we determine such quantities versus time for both diabetes patients and normal human and for different values of the parameters. We find that the nonlinear effect of the dynamics of the investigated regulatory system increases the values of the insulin action and the glucose and insulin concentrations. In the absence of the beta cells effects, which can correspond to the case of severe type 1 diabetes, the plasma glucose is higher and the insulin action and the insulin concentration are less active than the corresponding ones for the case in the presence of beta cells, which is relevant for type 2 diabetes or moderate type 1 diabetes patients. For the present system, smaller values of the parameters of the model, which represent kinetics of the glucose and insulin action, insulin sensitivity, insulin secretion enhancement and the plasma insulin decay rate, can lead to notably lower values of the glucose concentration. In the presence of the secreted insulin by the pancreatic beta cells the insulin action and the insulin concentration are more effective to reduce the blood glucose, which can help to improve the diabetes patient's health. [ABSTRACT FROM AUTHOR]

We have studied the locally rotationally symmetric (LRS) Bianchi type-I line element in ƒ(R; T) (R is the Ricci scalar and T is the trace of the stress energy tensor) theory of gravity in presence of EoS parameter. The simplest case of ƒ(R; T) gravity, i.e. first choice, is considered. The "gamma-law" equations of state are considered to explore the role of particle creation in the early universe. The exact solutions of the field equations are obtained using the scalar expansion proportional to the shear. The physical and kinematical properties of the model are studied. [ABSTRACT FROM AUTHOR]

A mathematical model describing the spread of spilled oil through the soil is discussed. The spread of spilled oil in soil is controlled by the flow of water and is described by multiphase equations. In this context, the two-phase flow characteristics of oil-water flow with varying viscosity in the subsurface coupled to an advective-diffusion equation are examined to study the transport of oil. The terms that model the interaction between the multiple phases are introduced at the boundary, such as the slip condition at the porous-fluid interface, shear stress condition at the fluid-fluid interface, and the continuity of velocity at both the interfaces. The effect of various physical parameters such as Schmidt number, retardation factor, viscosity ratio, porous and slip parameter on the velocity and concentration profiles are discussed in detail with the help of graphs. The surface plots of velocity and concentration of oil against axial distance at different time are also analyzed. The obtained results show that the velocity of oil accelerates linearly with axial length and there is a decrease in the concentration of the spilled oil through the media. The validity of the results obtained is verified by comparison with available experimental result, and good agreement is found. [ABSTRACT FROM AUTHOR]

We introduce a method for aggregation of experts' opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst. [ABSTRACT FROM AUTHOR]

The present mathematical analysis, the study of blood flow through the model of a composite stenosed catheterized artery with permeable wall, has been performed to investigate the blood flow characteristics. The expressions for the blood flow characteristics-the impedance (resistance to flow), the wall shear stress distribution in stenosis region, the shear stress at the throat of the stenosis have been derived. The results obtained are displayed graphically and discussed briefly. [ABSTRACT FROM AUTHOR]

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization. [ABSTRACT FROM AUTHOR]

We propose and analyze a water born disease model introducing water-to-person and person-to-person transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the presence of water-to-person contact. It is shown that in the presence of water-to-person transmission, the model system globally stable around both the disease-free and endemic equilibria. Lastly, some numerical simulations are provided to verify our analytical results. [ABSTRACT FROM AUTHOR]