## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (204.172 recursos)

Journal of Applied Mathematics

1. #### Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field

NiCastro, J. R. A. J.
This paper explores aspects of two-sided similarity modeling using cylindrical geometry for radiating shock waves embedded in a medium with a magnetic field. Two-sided similarity solution techniques may be used to link states influenced by long range near instantaneous fields that continually modify the pre- and postshock zones. Emergent radiation scaling relations are immediately available from consistent homologies. For both small angle and large angle measurements, an approximate analytic technique in the vicinity of luminous fronts together with the high symmetry implications delineated in Lemma provides direct access to the homology parameters. The parameters obtained using this process can augment...

2. #### Erratum to “Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab”

Gaspar, José M.

3. #### The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator

Carkovs, Jevgeņijs; Goldšteine, Jolanta; Šadurskis, Kārlis
We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey. We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem. If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the...

4. #### A Stochastic TB Model for a Crowded Environment

Maku Vyambwera, Sibaliwe; Witbooi, Peter
We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability...

5. #### Numerical Procedures for Random Differential Equations

Ben Said, Mohamed; Azrar, Lahcen; Sarsri, Driss
Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the...

6. #### Teaching-Learning-Based Optimization with Learning Enthusiasm Mechanism and Its Application in Chemical Engineering

Chen, Xu; Xu, Bin; Yu, Kunjie; Du, Wenli
Teaching-learning-based optimization (TLBO) is a population-based metaheuristic search algorithm inspired by the teaching and learning process in a classroom. It has been successfully applied to many scientific and engineering applications in the past few years. In the basic TLBO and most of its variants, all the learners have the same probability of getting knowledge from others. However, in the real world, learners are different, and each learner’s learning enthusiasm is not the same, resulting in different probabilities of acquiring knowledge. Motivated by this phenomenon, this study introduces a learning enthusiasm mechanism into the basic TLBO and proposes a learning enthusiasm...

7. #### The Maximal Length of 2-Path in Random Critical Graphs

Rasendrahasina, Vonjy; Ravelomanana, Vlady; Aly Raonenantsoamihaja, Liva
Given a graph, its $2$ -core is the maximal subgraph of $G$ without vertices of degree $\mathrm{1}$ . A $\mathrm{2}$ -path in a connected graph is a simple path in its $\mathrm{2}$ -core such that all vertices in the path have degree $\mathrm{2}$ , except the endpoints which have degree $\geqslant\mathrm{3}$ . Consider the Erdős-Rényi random graph $\mathbb{G}(n,M)$ built with $n$ vertices and $M$ edges uniformly randomly chosen from the set of $(\begin{smallmatrix}n\\[5pt] 2\end{smallmatrix})$ edges. Let ${\xi }_{n,M}$ be the maximum $\mathrm{2}$ -path length of $\mathbb{G}(n,M)$ . In this paper, we determine that there exists a constant $c(\lambda )$ such...

8. #### An Optimal Investment Strategy and Multiperiod Deposit Insurance Pricing Model for Commercial Banks

Muller, Grant E.
We employ the method of stochastic optimal control to derive the optimal investment strategy for maximizing an expected exponential utility of a commercial bank’s capital at some future date $T>\mathrm{0}$ . In addition, we derive a multiperiod deposit insurance (DI) pricing model that incorporates the explicit solution of the optimal control problem and an asset value reset rule comparable to the typical practice of insolvency resolution by insuring agencies. By way of numerical simulations, we study the effects of changes in the DI coverage horizon, the risk associated with the asset portfolio of the bank, and the bank’s initial leverage...

9. #### Applied Artificial Bee Colony Optimization Algorithm in Fire Evacuation Routing System

Wang, Chen; Wood, Lincoln C.; Li, Heng; Aw, Zhenye; Keshavarzsaleh, Abolfazl
Every minute counts in an event of fire evacuation where evacuees need to make immediate routing decisions in a condition of low visibility, low environmental familiarity, and high anxiety. However, the existing fire evacuation routing models using various algorithm such as ant colony optimization or particle swarm optimization can neither properly interpret the delay caused by congestion during evacuation nor determine the best layout of emergency exit guidance signs; thus bee colony optimization is expected to solve the problem. This study aims to develop a fire evacuation routing model “Bee-Fire” using artificial bee colony optimization (BCO) and to test the...

10. #### The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

Hieu, D. V.; Hai, N. Q.; Hung, D. T.
The Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyze five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th-Order Runge-Kutta Method, and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully applied to a lot of practical engineering and physical problems.

11. #### A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems

Sendur, Ali
The disproportionality in the problem parameters of the convection-diffusion-reaction equation may lead to the formation of layer structures in some parts of the problem domain which are difficult to resolve by the standard numerical algorithms. Therefore the use of a stabilized numerical method is inevitable. In this work, we employ and compare three classical stabilized finite element formulations, namely, the Streamline-Upwind Petrov-Galerkin (SUPG), Galerkin/Least-Squares (GLS), and Subgrid Scale (SGS) methods, and a recent Link-Cutting Bubble (LCB) strategy proposed by Brezzi and his coworkers for the numerical solution of the convection-diffusion-reaction equation, especially in the case of small diffusion. On the...

12. #### A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

Kizito, Mohammed; Tumwiine, Julius
Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number ${\mathcal{R}}_{\mathrm{0}}<\mathrm{1}$ and the disease will be wiped out of the population. For ${\mathcal{R}}_{\mathrm{0}}\ge \mathrm{1},$ the endemic equilibrium is globally stable and the disease persists. We infer the effect of...

13. #### On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Kasumo, Christian; Kasozi, Juma; Kuznetsov, Dmitry
We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model. To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance. Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind. We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters. Numerical examples with both light- and heavy-tailed distributions are given. The results show that proportional reinsurance increases the...

14. #### A Stochastic Model for Malaria Transmission Dynamics

Mbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.
Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic...

15. #### Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Gaspar, José M.
This paper aims to connect the bridge between analytical results and the use of the computer for numerical simulations in economics. We address the analytical properties of a simple dynamic aggregate demand and aggregate supply (AD-AS) model and solve it numerically. The model undergoes a bifurcation as its steady state smoothly interchanges stability depending on the relationship between the impact of real interest rate on demand for liquidity and how fast agents revise their expectations on inflation. Using code embedded into a unique function in Matlab, we plot the numerical solutions of the model and simulate different dynamic adjustments using...

16. #### Understanding Dengue Control for Short- and Long-Term Intervention with a Mathematical Model Approach

Bustamam, A.; Aldila, D.; Yuwanda, A.
A mathematical model of dengue diseases transmission will be discussed in this paper. Various interventions, such as vaccination of adults and newborns, the use of insecticides or fumigation, and also the enforcement of mechanical controls, will be considered when analyzing the best intervention for controlling the spread of dengue. From model analysis, we find three types of equilibrium points which will be built upon the dengue model. In this paper, these points are the mosquito-free equilibrium, disease-free equilibrium (with and without vaccinated compartment), and endemic equilibrium. Basic reproduction number as an endemic indicator has been found analytically. Based on analytical...

17. #### Corrigendum to “Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines”

Gomes, Francisco Regis Abreu; Mateus, Geraldo Robson

18. #### Corrigendum to “Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines”

Gomes, Francisco Regis Abreu; Mateus, Geraldo Robson

19. #### An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

Wikan, Arild
A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a...

20. #### An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

Wikan, Arild
A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a...

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