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Abstract: Abstract In 1959 Crawford S. Holling formulated a classification to model the action of the predators over their prey, doing empirical works. In this taxonomy, he introduced only three types of functional responses dependent only on the prey population, which are described by saturated functions. Later, various other types have been proposed, including the functional responses dependent on both populations. This work concerns the study of the Leslie–Gower type predator-prey model, incorporating the Rosenzweig functional response described by a power law. The elected function does not conform to the types proposed by Holling since it is unbounded, being, besides, non-differentiable for \(x = 0\) ; nonetheless, the obtained system is Lipschitzian. Moreover, the existence of a separatrix curve \(\Sigma \) in the phase plane is proven, which is divided into two complementary sectors. According to the position of the initial conditions with respect to the curve, the trajectories can have different \(\omega \) -limit sets, which can be the equilibrium \(\left( 0,0\right) \) , or a positive equilibrium, or a heteroclinic curve, or a stable limit cycle. These properties show the great difference of this model with the original Leslie–Gower model, in which a unique positive equilibrium exists, which is globally asymptotically stable, when it exists. Then, the analyzed system has a richer dynamic than the original system in which a linear functional response is considered, also unbounded. Numerical simulations and bifurcation diagrams are given to endorse our analytical results. PubDate: 2022-05-13

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Abstract: Abstract In this paper, we consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian and a superlinear reaction which need not satisfy the Ambrosetti–Robinowitz condition. By using variational tools together with truncation and comparison techniques and critical groups, we show the existence of at least five nontrivial smooth solutions, all with sign information: two positive, two negative and a nodal (sign-changing). PubDate: 2022-05-09

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Abstract: Abstract The higher-order nonlinear Boussinesq type wave equation describes the propagation of small amplitude long capillary–gravity waves on the surface of shallow water. Mathematical physics, shallow water waves, fluid dynamics, and fluid movement are all examples of this model. To acquire exact solutions in the form of solitary wave and complex functions solutions, we use the \(\left( {m + \frac{1}{{G^{\prime}}}} \right)\) -expansion method. These results aid mathematicians and physicians in comprehending the model's physical phenomena. This approach may be employed on different models in order to generate whole new solutions for nonlinear PDEs encountered in mathematical physics. PubDate: 2022-05-06

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Abstract: Abstract Mathematical model for propagation of cylindrical shock wave under the influence of azimuthal magnetic field in rotating medium with radiation heat flux for adiabatic flow condition, using Lie group of transformation method is formulated and similarity solutions are obtained. The medium ahead of the shock is assumed to be at rest. The density, magnetic field, azimuthal and axial fluid velocities are presumed to be varying in the undisturbed medium. We have obtained two different cases of potential solutions considering different cases for the arbitrary constants appearing in the expressions of infinitesimals. Numerical solutions are obtained in the case of power law shock path. Distributions of magnetogasdynamical quantities are discussed through figures. The effects of increase in ambient azimuthal fluid velocity variation index, strength of magnetic field and ambient density exponent are examined on shock strength and on the flow variables. It is observed that shock strength decreases due to increase in strength of magnetic field. Whereas there is increase in strength of shock due to increase in ambient density or ambient azimuthal fluid velocity variation index. In general, density, azimuthal fluid velocity, pressure, radial fluid velocity, temperature and radiation heat flux decrease as we move inwards from the shock to the axis of symmetry. Magnetic field, axial fluid velocity and non-dimensional azimuthal component of vorticity vector \(l_{\theta }\) increase as we move inwards from the shock to the axis of symmetry. Non dimensional axial component of vorticity vector \(l_{z}\) increases, attains the maximum and then decreases as we move inwards from the shock to the axis of symmetry. Numerical calculations are done and graphs are being plot using software Mathematica. PubDate: 2022-05-04

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Abstract: Abstract Pyrethroid-treated bed-nets (PTNs) protect individuals against malaria by blocking and repelling mosquitoes. We develop and analyze a PTNs malaria model that explicitly includes mosquito host choice (also known as feeding/biting preference) and Pyrethroid repellent effect. Our model reveals that mosquito biting/feeding preference on infectious hosts \(\pi \) and repellent effect r drive for the existence of both the endemic equilibrium points and the occurrence or elimination of backward bifurcation. The threshold parameters for the mosquito biting preference on infectious hosts \(\pi ^*\) and repellent effect \(r^*\) for the occurrence and elimination of backward bifurcation are computed. Moreover, it is shown that, increasing the mosquito host choice rate or decreasing the repellent effect rate, annihilates backward bifurcation, thus facilitating the control of malaria. Furthermore, we prove that the threshold of mosquito biting preference is a monotone increasing function of the repellent effect r. We show that the model exhibits both trans-critical forward bifurcation and backward bifurcation when either the mosquito host choice \(\pi \) crosses a threshold value \(\pi _1\) or the repellent effect r passes through a threshold repellent rate \(r_1\) . Sufficient conditions for the global asymptotic stability of the equilibrium point are derived. On the other hand, it is established that, decreasing the mosquito biting preference or increasing the rate of the repellent effect (i.e personal protection) or the combining both actions, decreases the malaria control reproduction number \(\mathcal R_0\) . Finally, the interplay between the bed-nets treated repellent effect and mosquito host choice and its potential on the dynamics of malaria is investigated and illustrated numerically. PubDate: 2022-05-04

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Abstract: Abstract Bovine tuberculosis (bTB) is a disease of major public health concern and economic importance. The disease affects the livelihood of rural livestock farmers, economies of developing countries, human and animal health. In this paper, both deterministic and continuous time Markov chain (CTMC) models are formulated and analyzed to study the dynamics of bovine tuberculosis in humans and cattle. The next generation matrix method is applied to compute the basic reproduction number \(\mathcal {R}_0\) for the deterministic model while the multitype branching process is applied to compute the stochastic threshold for CTMC model. The normalized forward sensitivity index method is used to compute sensitivity indices of model parameters with respect to basic reproduction number \(\mathcal {R}_0\) . The results reveal that infection rate among cattle is the most positive sensitive parameter whereas cattle’s natural death is the most negative sensitive parameter. This suggests that more efforts should be directed at reducing number of infected cattle for possible control of the spread of bTB in human and cattle populations. Numerical simulations for the CTMC stochastic model using 10,000 sample paths is carried out to compute probabilities for disease extinction by varying initial values for infected classes. The results show that, the solutions of CTMC stochastic model are relatively close to the deterministic model solutions. The possibility of bTB extinction is high when it emanates from either humans or infectious dairy products or from a small number of M. bovis bacteria from the environment. However, the disease outbreak occurs when it emerges from infected cattle population. Moreover, the results show that if bTB emerges from infected humans, cattle, dairy product and environment at the same time, then there is disease outbreak. Thus, any intervention measure that targets on reducing number of infected cattle will have significant impact to contain bTB in human and cattle populations. PubDate: 2022-04-15

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Abstract: Abstract In this paper we use the penalization method to prove the existence of solution for variational inequalities of Leray–Lions type, in the setting of Musielak spaces and where the Musielak function doesn’t satisfy the \(\Delta _2\) -condition. Here the right-hand side is in \(L^1.\) PubDate: 2022-04-12

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Abstract: Abstract In this paper, we develop the Littman–Stampacchia–Weinberger duality approach to obtain global \(W^{1,p}\) estimates for a class of elliptic problems involving Leray–Hardy operators and measure sources in a distributional framework associated to a dual formulation with a specific weight function. PubDate: 2022-04-12

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Abstract: Abstract The present article concentrates on the consequences of melting heat transfer on the chemically reactive flow of Eyring-Powell liquid flow via a semi-permeable curved channel in presence of applied magnetic field. The impacts of two types of chemical reaction namely, homogeneous and heterogeneous are considered in the concentration equation. In addition, the characteristics of heat transport phenomena is also examined with the application of thermal radiation. By adopting a scheme of curvilinear coordinates system along with some appropriate similarity conversions a nonlinear ordinary differential equations is attained. The numerical simulation of the determined velocity and transport equations are estimated by using the shooting procedure. The influence of pertinent factors on the flow equations, surface drag force and rate of heat transport are thoroughly discussed via graphs and table. It is noted from the current study that surface drag force and concentration of the liquid are rises with a rising value of the melting parameter, while fluid velocity and its temperature decreases. PubDate: 2022-04-12

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Abstract: Abstract Let \({\mathcal {C}} \subset {\mathbb {N}}^p\) be a finitely generated integer cone and \(S\subset {\mathcal {C}}\) be an affine semigroup such that the real cones generated by \({\mathcal {C}}\) and by S are equal. The semigroup S is called \({\mathcal {C}}\) -semigroup if \({\mathcal {C}}\setminus S\) is a finite set. In this paper, we characterize the \({\mathcal {C}}\) -semigroups from their minimal generating sets, and we give an algorithm to check if S is a \({\mathcal {C}}\) -semigroup and to compute its set of gaps. We also study the embedding dimension of \({\mathcal {C}}\) -semigroups obtaining a lower bound for it, and introduce some families of \({\mathcal {C}}\) -semigroups whose embedding dimension reaches our bound. In the last section, we present a method to obtain a decomposition of a \({\mathcal {C}}\) -semigroup into irreducible \({\mathcal {C}}\) -semigroups. PubDate: 2022-04-11

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Abstract: Abstract SARS-CoV-2 has caused severe respiratory illnesses and deaths since late 2019 and spreads globally. While asymptomatic cases play a crucial role in transmitting COVID-19, they do not contribute to the observed prevalence, which drives behavior change during the pandemic. This study aims to identify the effect of the proportion of asymptomatic infections on the magnitude of an epidemic under behavior change scenarios by developing a compartmental mathematical model. In this interest, we discuss three different behavior change cases separately: constant behavior change, instantaneous behavior change response to the disease’s perceived prevalence, and piecewise constant behavior change response to government policies. Our results imply that the proportion of asymptomatic infections which maximizes the spread of the epidemic depends on the nature of the dominant force driving behavior changes. PubDate: 2022-04-08

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Abstract: Abstract In this study, we propose a highly accurate technique for solving Volterra and Fredholm integral equations based on the blending of the Chebyshev pseudo methods. The application of the method leads Volterra and Fredholm integral equation to a system of linear algebraic equations that are easy to solve when compared to a integral equations. Some examples are solved and presented through graphs and tables and the obtained results are compared with those methods in the literature to illustrate the ability of the method. The results demonstrate that the new method is more efficient, converges and accurate to the exact solution. PubDate: 2022-04-06

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Abstract: Abstract Heat transport analysis corresponded to converging/diverging consideration has attained the attensions because of engineering and industrial utilization. Typical examples encompass cold drawing operation in polymer industry, enhancement of rate of heat transport during process of heat exchangers for milk flowing, molten polymers extrusion via converging dies, processing plants, power stations, and numerous others. Due to this fact, the present analysis has been established. The current research describes the hybrid nanofluid flow through convergent/divergent channel in the regime of hydromagnetic phenomenon. Here, water based nanoparticles i.e., graphene oxide and polystyrene are considered. Heat transport under the viscous dissipation and heat generation/ absorption is evaluated. Velocity slip condition is also imposed on channel wall. Suitable variables are employed to get strong form of non-dimensional coupled equations which are solved by using homotopic analytical technique. The results for velocity and temperature against pertinent parameters are analyzed through graphs. Effects of skin friction and Nusselt numbers are presented through graphs. The current investigation tells us that surface drag has diminished for Reynolds and Hartmann number. Furthermore, dissipative factor intensifies the heat transport rate. Owing by such applications, the present examination has been established. PubDate: 2022-04-06

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Abstract: Abstract The key interest in this paper to examine the heat and mass transport nature of Ti6Al4V–H20 based nanofluid flow and its interaction with a strong magnetic field. In this study significances of Hall current, magneto and thermo diffusions on the flow behavior are included. The induced magnetic field (IMF) and its consequences on the flow-field are also examined. The non-dimensional flow model is solved analytically by use of perturbation method. In order to scrutinize the effects of relevant flow parameters to the flow nature, the numerical values of flow behaviors corresponds to these parameters are depicted, and graphically and tabuly presented. This kind of a study has significant applications in nano science to explore the heat and mass transport characteristic of electrically conducting nanofluids. An important result noted from this study that, on incrementing the volumetric concentration of nanoparticles in the fluid employing resistance force which cause to reduce the flow velocity and enhance the temperature. The mass diffusion factor grows the flow velocity while it reduces the IMF along the main flow. A key fact noted that Hall current generates IMF by modifying the existing magnetic field. PubDate: 2022-04-04

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Abstract: Abstract We establish spatial a priori estimates for the solution u to a class of dilation invariant Kolmogorov equation, where u is assumed to only have a certain amount of regularity in the diffusion’s directions, i.e. \(x_{1}, \ldots , x_{m_{0}}\) . The result is that u is also regular with respect to the remaining directions. The approach we propose is based on the commutators identities and allows us to obtain a Sobolev exponent that does not depend on the integrability assumption of the right-hand side. Lastly, we provide a new proof for the optimal spatial regularity. PubDate: 2022-04-02

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Abstract: Abstract In this paper, we investigate the \(S_{0_n}\) -demicompactness of the restriction \(T_n\) of a bounded or unbounded linear operator T to \(\mathcal {R}(T^n)\) , where \(S_{0_n}\) is the restriction of a given bounded linear operator \(S_0\) to \(\mathcal {R}(T^n)\) . The results are formulated in terms of a condition of primality and the closedness of certain ranges. Moreover, we set forward some results on upper semi-Fredholm operators involving weak \(S_0\) -demicompactness class. In particular, we give a new characterization of the \(S_0\) -essential radius and localizations results of some \(S_0\) -essential spectra of T. An example of operator equations arising in transport theory is developed. PubDate: 2022-03-25

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Abstract: Abstract In this work, a refinement of the Cauchy–Schwarz inequality in inner product space is proved. A more general refinement of the Kato’s inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical radius inequalities are also pointed out. As shown in this work, these refinements generalize and refine some recent and old results obtained in literature. Among others, it is proved that if \(T\in \mathscr {B}\left( \mathscr {H}\right) \) , then $$\begin{aligned} \omega ^{2}\left( T\right)&\le \frac{1}{12} \left\ \left T \right +\left {T^* } \right \right\ ^2 + \frac{1}{3} \omega \left( T\right) \left\ \left T \right +\left {T^* } \right \right\ \\&\le \frac{1}{6} \left\ \left T \right ^2+ \left {T^* } \right ^2 \right\ + \frac{1}{3} \omega \left( T\right) \left\ \left T \right +\left {T^* } \right \right\ , \end{aligned}$$ which refines the recent inequality obtained by Kittaneh and Moradi in [10]. PubDate: 2022-03-23

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Abstract: Abstract In this note, we present an exact solution for the semi-stationary compressible Stokes problem in \({\mathbb {R}}^{N}\) . In the case of radial symmetry, an exact solution with velocity of the form \(c(t)r^{s}\) is obtained for \(s=\frac{1-N\gamma +\gamma }{\gamma +1}\) , where \(\gamma >1\) is the adiabatic index and \(r= x \) . Some interesting properties of the exact solution are analyzed. PubDate: 2021-12-31 DOI: 10.1007/s11587-021-00684-z

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Abstract: Abstract In this paper, we develop the extended Weibull family of distributions to a bivariate class using the Farlie–Gumbel–Morgenstern copula. This is called the bivariate Farlie–Gumbel–Morgenstern extended Weibull family, and some of its properties are investigated. Some special cases of this family and their correlation coefficient are found. Also, the maximum correlation coefficient of most special cases is investigated. We study the concomitants of generalized order statistics from this new class of Morgenstern bivariate distribution and obtain some relevant relations for single and product moments of concomitants. Some well-known information measures such as the Shannon entropy and extropy for concomitants are derived. PubDate: 2021-12-31 DOI: 10.1007/s11587-021-00680-3

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Abstract: Abstract This paper is concerned with the existence and non-existence of positive periodic solutions for \(\frac{\partial u}{\partial t}-\mathrm {div} ( \nabla u ^{p-2} \nabla u )= u^{q}(a-b u^{\beta })\) with \(p>1\) , where \(a=a(x,t)\) and \(b=b(x,t)\) are positive periodic functions. Some numerical simulation also be implemented to verify our results. PubDate: 2021-12-31 DOI: 10.1007/s11587-021-00683-0