Mathematical Methods in the Applied Sciences

doi: 10.1002/mma.5737pmid: N/A

No abstract is available for this article.

Qayyum, Sumaira; Hayat, Tasawar; Jabeen, Sumaira; Alsaedi, Ahmed

doi: 10.1002/mma.5997pmid: N/A

Research on optimization of entropy generation in nanofluid flow gained much interest. In this study, the Walter's‐B nanofluid flow is considered to analyze the irreversibility in cubic autocatalysis. Fluid motion is considered in presence of viscous dissipation, magnetohydrodynamics (MHD), radiation, and heat generation absorption. Homotopy analysis method (HAM) is employed to solve nonlinear ordinary differential system. Results show that fluid flow reduces for larger Weissenberg and Hartman numbers. Temperature gradually enhances for larger Weissenberg number and radiation parameter. For higher estimation of thermophoresis parameter, the temperature and concentration are enhanced. Opposite impact of Hartman and Weissenberg numbers is noticed for entropy generation and Bejan number. Disorderedness and Bejan number are reduced near the sheet, while the opposite trend is seen away from the sheet.

Cabrera, Inma P.; Cordero, Pablo; Muñoz‐Velasco, Emilio; Ojeda‐Aciego, Manuel; De Baets, Bernard

doi: 10.1002/mma.6302pmid: N/A

Fuzzy‐directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems.

ul Haq, Burhan; Naeem, Imran

doi: 10.1002/mma.6303pmid: N/A

This article presents the closed‐form solutions of two‐sector human capital–based Romer growth model. The partial Hamiltonian approach is effectively applied to some growth models in order to compute the closed‐form solutions for economic variables involved in the model. Pontryagin's maximum principle provides the set of first‐order system of ODEs, which are regarded as an essential criteria for optimality. The partial Hamiltonian approach is utilized to construct three first integrals of the system using the current value Hamiltonian. With the aid of these first integrals, we computed two distinct exact solutions of Romer model under certain parametric restrictions. The closed‐form expressions for control, state, and costate variables are presented explicitly as a function of t. We have graphically illustrated the solution curves and observed the effect of human capital parameter α on control and state variables. The growth rates of all economic variables are evaluated, and their long‐run behavior is predicted.

Chao, Na; Yang, Yongfu

doi: 10.1002/mma.6305pmid: N/A

The aim of this paper is to investigate smooth solutions to Cauchy (or periodic) problem for a nonisentropic Euler‐Maxwell system with small parameters. For initial data close to constant equilibrium states, we prove the global‐in‐time convergence of the Euler‐Maxwell system as parameters go to zero. The limit systems are the drift‐diffusion system and the nonisentropic Euler‐Poisson system, respectively.

Anacleto, María; Vidal, Claudio

doi: 10.1002/mma.6307pmid: N/A

In this paper, a delayed with Holling type II functional response (Beddington‐DeAngelis) and Allee effect predator‐prey model is considered. The growth of the prey is affected by the parameter M, which defines the Allee effect. In addition, the delay τ also influences the logistic growth of the prey, which can be interpreted as the maturity time or the gestation period. In the study of the characteristic equation, we observe that the delay τ also depends on the parameter M, which affects the dynamics in the prey population. Considering the delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. On the other hand, we find that the system can also suffer a Hopf bifurcation in the positive equilibrium when the delay passes through a sequence of critical values. In particular, we study the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions, an explicit algorithm is provided applying the normal form theory and center manifold reduction for the functional differential equations. Finally, numerical simulations that support the theoretical analysis are included.

Alsharidi, Abdulaziz K.; Khan, Ashfaq A.; Shepherd, John J.; Stacey, Andrew  J.

doi: 10.1002/mma.6315pmid: N/A

We construct the slowly varying limiting state solutions to a nonlinear dynamical system for anaerobic digestion with Monod‐based kinetics involving slowly varying model parameters arising from slow environmental variation. The advantage of these approximate solutions over numerical solutions is their applicability to a wide range of parameter values. We use these limiting state solutions to develop analytic approximations to the full nonlinear system by applying a multiscaling technique. The approximate solutions are shown to compare favorably with numerical solutions.

Sahoo, Sueet Millon; Raja Sekhar, T.; Raja Sekhar, G. P.

doi: 10.1002/mma.6316pmid: N/A

We derive exact solutions of one‐dimensional Euler system that accounts for gravity together with large friction. Certain optimal classes of subalgebra using Lie symmetry analysis are obtained for this system. We apply the reduction procedure to reduce the Euler system to a system of ordinary differential equations in terms of new similarity variable for each class of subalgebras leading to invariant solutions. The evolution of characteristic shock and its interaction with the weak discontinuity by using one of the invariant solutions is studied. Further, the properties of reflected and transmitted waves and jump in acceleration influenced by the incident wave have been characterized.

Bagarello, Fabio; Gargano, Francesco

doi: 10.1002/mma.6317pmid: N/A

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix A. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo‐Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix A and of its adjoint A†. Then, we consider an extension of the so‐called power method, for which we prove a fixed point theorem for A≠A† useful in the determination of the eigenvalues of A and A†. The two strategies are applied to some explicit problems. In particular, we compute the eigenvalues and the eigenvectors of the matrix arising from a recently proposed quantum mechanical system, the truncated Swanson model, and we check some asymptotic features of the Hessenberg matrix.

Sun, Wenbing; Liu, Qiong

doi: 10.1002/mma.6319pmid: N/A

In this paper, we establish a local fractional integral identity with a parameter λ on Yang's fractal sets. Using this identity, by generalized power mean inequality and generalized Hölder inequality, two Hermite‐Hadamard type local fractional integral inequalities for generalized harmonically convex functions are established. By giving some special values to the parameter, some inequalities with specific form can be obtained. Some applications to generalized special means are given.