Search results for: best and worst optimal solutions

Authors: Nishant Shrivastava, D. K. Sehgal

Abstract:

In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.

Keywords: finite elements, Lagrangian, optimal stress location, serendipity

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Authors: F. G Okibe, C. E Gimba, V. O Ajibola, I. G Ndukwe, E. D. Paul

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A full factorial experimental design technique at two levels and four factors (24) was used to optimize the adsorption at 615 nm of Xylene Cyanol ff in aqueous solutions onto activated carbon prepared from brachystegia eurycoma seed hulls by chemical carbonization method. The effect of pH (3 and 5), initial dye concentration (20 and 60 mg/l), adsorbent dosage (0.01 and 0.05 g), and contact time (30 and 60 min) on removal efficiency of the adsorbent for the dye were investigated at 298K. From the analysis of variance, response surface and cube plot, adsorbent dosage was observed to be the most significant factor affecting the adsorption process. However, from the interaction between the variables studied, the optimum removal efficiency was 96.80 % achieved with adsorbent dosage of 0.05 g, contact time 45 minutes, pH 3, and initial dye concentration 60 mg/l.

Keywords: factorial experimental design, adsorption, optimization, brachystegia eurycoma, xylene cyanol ff

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Authors: Anuar Ishak

Abstract:

The characteristics of stagnation point flow of a nanofluid towards a stretching/shrinking sheet are investigated. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.

Keywords: dual solutions, heat transfer, forced convection, nanofluid, stability analysis

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Authors: Kruti Jaruriya

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Distribution of arsenic (As) and its compound and related toxicology are serious concerns. This is particularly so since millions worldwide are suffering from toxicity due to drinking of As-contaminated groundwater. The Bengal delta plain, formed by the Ganga– Padma–Meghna–Brahmaputra river basin, covering several districts of West Bengal, India and Bangladesh is considered as the worst As affected alluvial basin. However, some equally affected, if not more, areas are emerging in upper Brahmaputra plains. The present study was carried out to examine As contamination trends in the worst affected part of Assam, India. Arsenic (As) mobilization to the groundwater of Brahmaputra floodplains was investigated in Titabor, Jorhat District, located in the North Eastern part of India. The groundwater and the aquifer geochemistry were characterized. The groundwater is characterized by high dissolved Fe, Mn, and HCO-3 and low concentrations of NO-3 and SO2-4 indicating anoxic conditions prevailing in the groundwater. Fifty groundwater samples collected from shallow and deep tubewells of Titabor, Jorhat district (Assam) were examined. Along with total As, examination of concentration levels of other key parameters, viz., pH, EC, Fe, Mn , Mg2+, Ca2+, Na+, K+, PO43- , HCO-3 , NO3- ,Cl - and SO42- was also carried out. In respect to the permissible guideline of World Health Organization (WHO: As 0.01 ppm, Fe 1.0 ppm, and Mn 0.3 ppm for potable water), the range of As concentration in the groundwater varied from 0.014 to 0.604 mg/L with mean concentration 0.184 mg/L. The present study showed that out of the 50 groundwater samples,100%, 54%, and 42% were found contaminated with higher metal contents (for total As, Fe, and Mn, respectively). The results of hydrogeochemical study revealed that the reductive dissolution of MnOOH and FeOOH represents an important mechanism of arsenic release in the study area along with major cations playing an important role in leaching of As into the groundwater. Arsenic released by oxidation of pyrite, as water levels are drawn down and air enters the aquifer, contributes negligibly to the problem of As pollution. Identification of the mechanism of As release to groundwater helps to provide a framework to guide the placement of new water wells so that they will have acceptable concentrations of As.

Keywords: arsenic, assam, brahmaputra floodplain, groundwater, hydrogeochemistry

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Zhenjie Liu

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This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

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Authors: Thomas Wetere

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Background: The coronavirus disease 2019 (COVID-19) pandemic (COVID-19) virus infection is a severe infectious disease with the highly transmissible variant, which become the global public health treat now. It has taken the life of more than 4 million people so far. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. Methodology: To end the global COVID-19 pandemic, implementation of multiple population-wide strategies, including vaccination, environmental factors, Government action, testing, and contact tracing, is required. In this article, a new mathematical model incorporating both temperature and government action to study the dynamics of the COVID-19 pandemic has been developed and comprehensively analysed. The model considers eight stages of infection: susceptible (S), infected Asymptomatic and Undetected(IAU ), infected Asymptomatic and detected(IAD), infected symptomatic and Undetected(ISU ), infected Symptomatic and detected(ISD), Hospitalized or threatened(H), Recovered(R) and Died(D). Results: The existence as well as non-negativity of the solution to the model is also verified, and the basic reproduction number is calculated. Besides, stability conditions are also checked, and finally, simulation results are compared with real data. The results demonstrates that effective government action will need to be combined with vaccination to end the ongoing COVID-19 pandemic. Conclusion: Vaccination and Government action are highly the crucial measures to control the COVID-19 pandemic. Besides, as the cost of vaccination might be high, we recommend an optimal control to reduce the cost and number of infected individuals. Moreover, in order to prevent COVID-19 pandemic, through the analysis of the model, the government must strictly manage the policy on COVID-19 and carry it out. This, in turn, helps for health campaigning and raising health literacy which plays a role to control the quick spread of the disease. We finally strongly believe that our study will play its own role in the current effort of controlling the pandemic.

Keywords: modeling, COVID-19, MCMC, stability

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Authors: Imèn Khanchouch, Malika Charrad, Mohamed Limam

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The interpretation of the quality of clusters and the determination of the optimal number of clusters is still a crucial problem in clustering. We focus in this paper on multi-SOM clustering method which overcomes the problem of extracting the number of clusters from the SOM map through the use of a clustering validity index. We then tested multi-SOM using real and artificial data sets with different evaluation criteria not used previously such as Davies Bouldin index, Dunn index and silhouette index. The developed multi-SOM algorithm is compared to k-means and Birch methods. Results show that it is more efficient than classical clustering methods.

Keywords: clustering, SOM, multi-SOM, DB index, Dunn index, silhouette index

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Authors: Andrey V. Timofeev

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The paper presents new results concerning selection of optimal information fusion formula for ensembles of C-OTDR channels. The goal of information fusion is to create an integral classificator designed for effective classification of seismoacoustic target events. The LPBoost (LP-β and LP-B variants), the Multiple Kernel Learning, and Weighing of Inversely as Lipschitz Constants (WILC) approaches were compared. The WILC is a brand new approach to optimal fusion of Lipschitz Classifiers Ensembles. Results of practical usage are presented.

Keywords: Lipschitz Classifier, classifiers ensembles, LPBoost, C-OTDR systems

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Authors: Ali Heidari, Hany Saleem

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The tailwater requirements are important criteria in the design of the stilling basins as energy dissipation of the spillways. The adequate tailwater level that ensures the hydraulic jump inside the basin should be fulfilled by the river's natural water level and the apron depth downstream of the chute. The requirements of the hydraulic jump should mainly be checked for the design flood, however, the drawn jump condition should not be critical in the discharges lesser than the design flood. The tailwater requirement is not met in Almatti dam, built in 2005 in India, and the jump sweep out from the basin, resulting in significant scour in the apron and end sill of the basin. This paper discusses different hydraulic solutions as sustainable solutions for the rehabilitation program. The deep apron alternative is proposed for the fewer bays of the spillway as the most cost-effective, sustainable solution. The apron level of 15 gates out of 26 gates should decrease by 5.4 m compared to the existing design to ensure a safe hydraulic jump up to the discharge of 10,000 m3/s i.e. 30% of the updated PMF.

Keywords: dam, spillway, stilling basin, Almatti

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Authors: Gaurav Kumar Sinha

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As the world grapples with climate challenges, this study highlights the instrumental role of AWS services in amplifying the impact of LCVs. Their ability to harness the cloud, data analytics, and scalable infrastructure offered by AWS empowers LCVs to innovate, scale, and drive meaningful change in the quest for a sustainable future. This study serves as a rallying cry, urging stakeholders to recognize, embrace, and maximize the potential of AWS-powered solutions in advancing sustainable and resilient global initiatives.

Keywords: low carbon ventures, sustainability solutions, AWS services, data analytics

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Arash Rahmani, Ahmad Ghanbari, Abbas Baghernezhad, Babak Safaei

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In the design of parallel manipulators, usually mean value of a dexterity measure over the workspace volume is considered as the objective function to be used in optimization algorithms. The mentioned indexes in a hybrid parallel manipulator (HPM) are quite complicated to solve thanks to infinite solutions for every point within the workspace of the redundant manipulators. In this paper, spatial isotropic design axioms are extended as a well-known method for optimum design of manipulators. An upper limit for the isotropy measure of HPM is calculated and instead of computing and minimizing isotropy measure, minimizing the obtained limit is considered. To this end, two different objective functions are suggested which are obtained from objective functions of comprising modules. Finally, by using genetic algorithm (GA), the best geometric parameters for a specific hybrid parallel robot which is composed of two modified Gough-Stewart platforms (MGSP) are achieved.

Keywords: hybrid manipulator, spatial isotropy, genetic algorithm, optimum design

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Mohammed Darwish

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Workplace injuries cost organizations significant amount of money. Causes of injuries at workplace are very well documented in the literature and attributed to variety of reasons. One important reason is the long working-hours. The purpose of this paper is to develop a mathematical model that finds the optimal working-hours at workplace. The developed model minimizes the expected total cost which consists of the expected cost incurred due to unsafe conditions of workplace, the other cost is related to the lost production due to work incidents, and the production cost.

Keywords: 8-hour workday, mathematical model, optimal working hours, workplace injuries

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Authors: Trung Hieu Tran, Jesse O'Hanley, Russell Fowler

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When in-wheel wireless charging technology for electric vehicles becomes mature, a need for such integrated charging stations network development is essential. In this paper, we thus investigate the optimisation problem of in-wheel wireless electric vehicle charging network design. A mixed-integer linear programming model is formulated to solve into optimality the problem. In addition, a meta-heuristic algorithm is proposed for efficiently solving large-sized instances within a reasonable computation time. A parallel computing strategy is integrated into the algorithm to speed up its computation time. Experimental results carried out on the benchmark instances show that our model and algorithm can find the optimal solutions and their potential for practical applications.

Keywords: electric vehicle, wireless charging station, mathematical programming, meta-heuristic algorithm, parallel computing

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Authors: Kanita Beširević

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Open-source software development activities highly rely on Internet gathering communities volunteering in software development projects. Additionally, the libraries and cultural institutions share their metadata in the form of linked metadata to enable dissemination and enrichment. The open-source software provides free alternatives to traditional software solutions. The article aims to investigate the ever-increasing options for the digital library open source software adoption. The software available is presented and compared to other software solutions as well as to their previous versions. The top three open-source digital library software solutions are presented and compared. The comparison criteria are adopted from the UNESCO study by Bankier, J., & Gleason, K. Institutional Repository Software Comparison comprising of twelve criteria to appraise software, namely: infrastructure, front-end design, content discovery, publication tools, interoperability, and preservation. This article adopts a descriptive methodology based on data and information collected through selected software websites and the literature review.

Keywords: open source software, digital library, DSpace, Fedora, Greenstone

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Authors: Ruchika Goyal, Ashwani Kumar, Sandeep Jain

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The experimental data for anticancer potential of curcumin nanoparticles was calculated by means of eclectic data. The optimal descriptors were examined using Monte Carlo method based CORAL SEA software. The statistical quality of the model is following: n = 14, R² = 0.6809, Q² = 0.5943, s = 0.175, MAE = 0.114, F = 26 (sub-training set), n =5, R²= 0.9529, Q² = 0.7982, s = 0.086, MAE = 0.068, F = 61, Av Rm² = 0.7601, ∆R²m = 0.0840, k = 0.9856 and kk = 1.0146 (test set) and n = 5, R² = 0.6075 (validation set). This data can be used to build predictive QSAR models for anticancer activity.

Keywords: anticancer potential, curcumin, model, nanoparticles, optimal descriptors, QSAR

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Authors: Godwin Makaudze

Abstract:

The majority of women in contemporary Zimbabwe continue to hold marginalised and insignificant positions in society and to be accorded negative and stereotyped images in literature. In light of this, government and civic organisations and even writers channel many resources, time, and efforts towards the emancipation of the female gender. Using the Africana womanist and socio-historical literary theories and focussing on two post-colonial novels, this paper re-engages the dis-empowerment of women in contemporary Zimbabwe, examining the believed causes and suggested solutions. The paper observes that the writers whip the already whipped by blaming patriarchy, African men and cultural practices as the underlying causes of such a sorry state of affairs while at the same time celebrating war against all these, as well as education, unity among women, Christianity and single motherhood as panaceas to the problem. The paper concludes that the writers’ anger is misdirected as they have fallen trap to the very popular yet mythical victim-blame motif espoused by many writers who focus on Shona people’s problems.

Keywords: cultural practices, female dis-empowerment, patriarchy, Shona novel, solutions, Zimbabwe

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Authors: A. Belay, B. Kebede

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The concentration- and temperature-dependent refractive indices of solutions extracted from defective and non-defective coffee beans have been investigated using a He–Ne laser. The refractive index has a linear relationship with the presumed concentration of the coffee solutions in the range of 0.5–3%. Higher and lower values of refractive index were obtained for immature and non-defective coffee beans, respectively. The Refractive index of bean extracts can be successfully used to separate defective from non-defective beans.

Keywords: coffee extract, refractive index, temperature dependence

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: F. Gökgöz, M. E. Atmaca

Abstract:

Electricity has an indispensable role in human daily life, technological development and economy. It is a special product or service that should be instantaneously generated and consumed. Sources of the world are limited so that effective and efficient use of them is very important not only for human life and environment but also for technological and economic development. Competitive electricity market is one of the important way that provides suitable platform for effective and efficient use of electricity. Besides benefits, it brings along some risks that should be carefully managed by a market player like Electricity Generation Company. Risk management is an essential part in market players’ decision making. In this paper, risk management through diversification is applied with the help of Value at Risk methods for case studies. Performance of optimal electricity sale solutions are measured and the portfolio performance has been evaluated via Sharpe-Ratio, and compared with conventional approach. Biennial historical electricity price data of Turkish Day Ahead Market are used to demonstrate the approach.

Keywords: electricity market, portfolio optimization, risk management, value at risk

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Authors: Tomáš Bublík, Miroslav Virius

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This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and sub graph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, scripthon source code recognition

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Authors: L. Marcos Domínguez, Nils Rage, Ongun B. Kazanci, Bjarne W. Olesen

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Thermally Activated Building Systems (TABS) have proven to be an energy-efficient solution to provide buildings with an optimal indoor thermal environment. This solution uses the structure of the building to store heat, reduce the peak loads, and decrease the primary energy demand. TABS require the heated or cooled surfaces to be as exposed as possible to the indoor space, but exposing the bare concrete surfaces has a diminishing effect on the acoustic qualities of the spaces in a building. Acoustic solutions capable of providing optimal acoustic comfort and allowing the heat exchange between the TABS and the room are desirable. In this study, the effects of free-hanging units on the cooling performance of TABS and the occupants’ thermal comfort was measured in a full-scale TABS laboratory. Investigations demonstrate that the use of free-hanging sound absorbers are compatible with the performance of TABS and the occupant’s thermal comfort, but an appropriate acoustic design is needed to find the most suitable solution for each case. The results show a reduction of 11% of the cooling performance of the TABS when 43% of the ceiling area is covered with free-hanging horizontal sound absorbers, of 23% for 60% ceiling coverage ratio and of 36% for 80% coverage. Measurements in actual buildings showed an increase of the room operative temperature of 0.3 K when 50% of the ceiling surface is covered with horizontal panels and of 0.8 to 1 K for a 70% coverage ratio. According to numerical simulations using a new TRNSYS Type, the use of comfort ventilation has a considerable influence on the thermal conditions in the room; if the ventilation is removed, then the operative temperature increases by 1.8 K for a 60%-covered ceiling.

Keywords: acoustic comfort, concrete core activation, full-scale measurements, thermally activated building systems, TRNSys

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Authors: Shao-Yuan Huang

Abstract:

We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

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Authors: Abdulai Abubakari

Abstract:

The rollercoaster relationship between farmers and herders in Sub-Saharan Africa has compelled most governments to undertake different mitigating strategies. Over the past two decades, the expulsion of migrant herdsmen, the killing of cattle and human beings, and fines have been used by the state and aggrieved individuals to resolve the conflicts. Unlike this paper, most of the research conducted on this subject matter has been largely theoretical and lacks practical solutions to the conflicts. This paper is unique because it focuses on concrete strategies and practical solutions to ending the century-old phenomenon of farmer-herder conflicts in Ghana. The paper employed power or compete (fight) theory as well as compromise and negotiation theories in the analyses. The paper employed, basically, socio-anthropological methods: interviews, focus group discussions, and observations to gather data. The paper found that compromises through negotiation with the stakeholders are the best ways of resolving these conflicts. Through this, we support the compromise and negotiation approach rather than expulsion to resolve farmer-herder conflicts.

Keywords: farmer-herder, conflict, prevention, strategies, stakeholders

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Silas A. Ihedioha

Abstract:

In this work; it is considered that an investor’s portfolio is comprised of two assets; a risky stock which price process is driven by the geometric Brownian motion and a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aimed at the optimization of the investor’s expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation HJB) was obtained from which an ordinary differential equation (ODE) obtained via elimination of variables. The solution to the ODE gave the closed form solution of the investor’s problem. It was found the optimal investment in the risky asset is horizon dependent and a ratio of the total amount available for investment and the relative risk aversion coefficient.

Keywords: optimal, investment, Ornstein-Uhlenbeck, utility maximization, stochastic interest rate, maximum principle

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Ali H. Daraji, Jack M. Hale, Ye Jianqiao

Abstract:

With the extensive use of high specific strength structures to optimise the loading capacity and material cost in aerospace and most engineering applications, much effort has been expended to develop intelligent structures for active vibration reduction and structural health monitoring. These structures are highly flexible, inherently low internal damping and associated with large vibration and long decay time. The modification of such structures by adding lightweight piezoelectric sensors and actuators at efficient locations integrated with an optimal control scheme is considered an effective solution for structural vibration monitoring and controlling. The size and location of sensor and actuator are important research topics to investigate their effects on the level of vibration detection and reduction and the amount of energy provided by a controller. Several methodologies have been presented to determine the optimal location of a limited number of sensors and actuators for small-scale structures. However, these studies have tackled this problem directly, measuring the fitness function based on eigenvalues and eigenvectors achieved with numerous combinations of sensor/actuator pair locations and converging on an optimal set using heuristic optimisation techniques such as the genetic algorithms. This is computationally expensive for small- and large-scale structures subject to optimise a number of s/a pairs to suppress multiple vibration modes. This paper proposes an efficient method to determine optimal locations for a limited number of sensor/actuator pairs for active vibration reduction of a flexible structure based on finite element method and Hamilton’s principle. The current work takes the simplified approach of modelling a structure with sensors at all locations, subjecting it to an external force to excite the various modes of interest and noting the locations of sensors giving the largest average percentage sensors effectiveness measured by dividing all sensor output voltage over the maximum for each mode. The methodology was implemented for a cantilever plate under external force excitation to find the optimal distribution of six sensor/actuator pairs to suppress the first six modes of vibration. It is shown that the results of the optimal sensor locations give good agreement with published optimal locations, but with very much reduced computational effort and higher effectiveness. Furthermore, it is shown that collocated sensor/actuator pairs placed in these locations give very effective active vibration reduction using optimal linear quadratic control scheme.

Keywords: optimisation, plate, sensor effectiveness, vibration control

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