Search results for: dynamic programming equation

Authors: Ih-Ching Hsu

Abstract:

Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Olukunle C. Olawole, Dilip Kumar De

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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: Tunjo Perič, Marin Fatović

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In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology is tested on the example of flour purchase for a bakery with two decision makers.

Keywords: cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection

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Authors: Nicoly Coelho, Eduardo Vieira Vilas Boas, Paulo Orestes Formigoni

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Faced with the remarkable developments in the various segments of modern engineering, provided by the increasing technological development, professionals of all educational areas need to overcome the difficulties generated due to the good understanding of those who are starting their academic journey. Aiming to overcome these difficulties, this article aims at an introduction to the basic study of numerical methods applied to fluid mechanics and thermodynamics, demonstrating the modeling and simulations with its substance, and a detailed explanation of the fundamental numerical solution for the use of finite difference method, using SCILAB, a free software easily accessible as it is free and can be used for any research center or university, anywhere, both in developed and developing countries. It is known that the Computational Fluid Dynamics (CFD) is a necessary tool for engineers and professionals who study fluid mechanics, however, the teaching of this area of knowledge in undergraduate programs faced some difficulties due to software costs and the degree of difficulty of mathematical problems involved in this way the matter is treated only in postgraduate courses. This work aims to bring the use of DFC low cost in teaching Transport Phenomena for graduation analyzing a small classic case of fundamental thermodynamics with Scilab® program. The study starts from the basic theory involving the equation the partial differential equation governing heat transfer problem, implies the need for mastery of students, discretization processes that include the basic principles of series expansion Taylor responsible for generating a system capable of convergence check equations using the concepts of Sassenfeld, finally coming to be solved by Gauss-Seidel method. In this work we demonstrated processes involving both simple problems solved manually, as well as the complex problems that required computer implementation, for which we use a small algorithm with less than 200 lines in Scilab® in heat transfer study of a heated plate in rectangular shape on four sides with different temperatures on either side, producing a two-dimensional transport with colored graphic simulation. With the spread of computer technology, numerous programs have emerged requiring great researcher programming skills. Thinking that this ability to program DFC is the main problem to be overcome, both by students and by researchers, we present in this article a hint of use of programs with less complex interface, thus enabling less difficulty in producing graphical modeling and simulation for DFC with an extension of the programming area of experience for undergraduates.

Keywords: numerical methods, finite difference method, heat transfer, Scilab

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: T. T. Tham

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The aim of this study is to propose an integrated approach to determine the most suitable programs, based on Quality Function Deployment (QFD), Sensitivity Analysis (SA) and Multi-Objective Linear Programming model (MOLP). Firstly, QFD is used to determine business requirements and transform them into business and supply chain programs. From the QFD, technical scores of all programs are obtained. All programs are then evaluated through five criteria (productivity, quality, cost, technical score, and feasibility). Sets of weight of these criteria are built using Sensitivity Analysis. Multi-Objective Linear Programming model is applied to select suitable programs according to multiple conflicting objectives under a budget constraint. A case study from the Sai Gon-Mien Tay Beer Company is given to illustrate the proposed methodology. The outcome of the study provides a comprehensive picture for companies to select suitable programs to obtain the optimal solution according to their preference.

Keywords: business program, multi-objective linear programming model, quality function deployment, sensitivity analysis, supply chain management

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Authors: Zhiqiang Yan, Chen Fan, Beicheng Xia

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Urban lakes play an invaluable role in urban water systems such as flood control, landscape, entertainment, and energy utilization, and have suffered from severe eutrophication over the past few years. To investigate the ecological response of main aquatic species and system stability to chlorine interference in shallow urban lakes, a mini system dynamic model, based on the competition and predation of main aquatic species and TP circulation, was developed. The main species of submerged macrophyte, phytoplankton, zooplankton, benthos and TP in water and sediment were simulated as variables in the model with the interference of chlorine which effect function was attenuation equation. The model was validated by the data which was investigated in the Lotus Lake in Guangzhou from October 1, 2015 to January 31, 2016. Furthermore, the eco-exergy was used to analyze the change in complexity of the shallow urban lake. The results showed the correlation coefficient between observed and simulated values of all components presented significant. Chlorine showed a significant inhibitory effect on Microcystis aeruginosa，Rachionus plicatilis, Diaphanosoma brachyurum Liévin and Mesocyclops leuckarti (Claus).The outbreak of Spiroggra spp. inhibited the growth of Vallisneria natans (Lour.) Hara, caused a gradual decrease of eco-exergy, reflecting the breakdown of ecosystem internal equilibria. It was concluded that the study gives important insight into using chlorine to achieve eutrophication control and understand mechanism process.

Keywords: system dynamic model, urban lake, chlorine, eco-exergy

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Authors: Divine Agozie, Muesser Nat, Eric Afful-Dadzie

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This examination attempts an analysis of the effect of business intelligence and analytics (BI&A) capabilities on organizational role stressors and the implications of such an effect on performance. Two hundred twenty-eight responses gathered from seventy-six firms across Ghana were analyzed using the Partial Least Squares Structural Equation Modelling (PLS-SEM) approach to validate the hypothesized relationships identified in the research model. Findings suggest both endogenous and exogenous dependencies of the sensing capability on the multiple role requirements of personnel. Further, transforming capability increases role conflict, whereas driving capability of BI&A systems impacts role conflict and role ambiguity. This study poses many practical insights to firms seeking to acquire analytics capabilities to drive performance and data-driven decision-making. It is important for firms to consider balancing role changes and task requirements before implementing and post-implementation stages of BI&A innovations.

Keywords: business intelligence and analytics, dynamic capabilities view, organizational stressors, structural equation modelling

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Authors: Rouhallah Bagheri, Morteza Mahmoudi, Hadi Moheb-Alizadeh

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In this paper, we develop a supplier selection and order allocation multi-objective model in stochastic environment in which purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. To do so, we use dependent chance programming (DCP) that maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. After transforming the above mentioned stochastic multi-objective programming problem into a stochastic single objective problem using minimum deviation method, we apply a genetic algorithm to get the later single objective problem solved. The employed genetic algorithm performs a simulation process in order to calculate the stochastic objective function as its fitness function. At the end, we explore the impact of stochastic parameters on the given solution via a sensitivity analysis exploiting coefficient of variation. The results show that as stochastic parameters have greater coefficients of variation, the value of objective function in the stochastic single objective programming problem is worsened.

Keywords: dependent chance programming, genetic algorithm, minimum deviation method, order allocation, supplier selection

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Authors: Qiming Wang

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Dynamic polymer networks (DPNs) crosslinked by dynamic bonds have received intensive attention because of their special crack-healing capability. Diverse DPNs have been synthesized using a number of dynamic bonds, including dynamic covalent bond, hydrogen bond, ionic bond, metal-ligand coordination, hydrophobic interaction, and others. Despite the promising success in the polymer synthesis, the fundamental understanding of their self-healing mechanics is still at the very beginning. Especially, a general analytical model to understand the interfacial self-healing behaviors of DPNs has not been established. Here, we develop polymer-network based analytical theories that can mechanistically model the constitutive behaviors and interfacial self-healing behaviors of DPNs. We consider that the DPN is composed of interpenetrating networks crosslinked by dynamic bonds. bonds obey a force-dependent chemical kinetics. During the self-healing process, we consider the The network chains follow inhomogeneous chain-length distributions and the dynamic polymer chains diffuse across the interface to reform the dynamic bonds, being modeled by a diffusion-reaction theory. The theories can predict the stress-stretch behaviors of original and self-healed DPNs, as well as the healing strength in a function of healing time. We show that the theoretically predicted healing behaviors can consistently match the documented experimental results of DPNs with various dynamic bonds, including dynamic covalent bonds (diarylbibenzofuranone and olefin metathesis), hydrogen bonds, and ionic bonds. We expect our model to be a powerful tool for the self-healing community to invent, design, understand, and optimize self-healing DPNs with various dynamic bonds.

Keywords: self-healing polymers, dynamic covalent bonds, hydrogen bonds, ionic bonds

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Manwendra Kumar Tripathi, Subhas Ganguly

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A few glass forming ability expressions in terms of characteristic temperatures have been proposed in the literature. Attempts have been made to correlate the expression with the critical diameter of the bulk metallic glass composition. However, with the advent of new alloys, many exceptions have been noted and reported. In the present approach, a genetic programming based code which generates an expression in terms of input variables, i.e., three characteristic temperatures viz. glass transition temperature (Tg), onset crystallization temperature (Tx) and offset temperature of melting (Tl) with maximum correlation with a critical diameter (Dmax). The expression evolved shows improved correlation with the critical diameter. In addition, the expression can be explained on the basis of time-temperature transformation curve.

Keywords: glass forming ability, genetic programming, bulk metallic glass, critical diameter

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Authors: Monika Kamocka, Radoslaw Mania

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The design of Fiber Metal Laminates - combining thin aluminum sheets and prepreg layers, allows creating a hybrid structure with high strength to weight ratio. This feature makes FMLs very attractive for aerospace industry, where thin-walled structures are commonly used. Nevertheless, those structures are prone to buckling phenomenon. Buckling could occur also under static load as well as dynamic pulse loads. In this paper, the problem of dynamic buckling of open cross-section FML profiles under axial dynamic compression in the form of pulse load of finite duration is investigated. In the numerical model, material properties of FML constituents were assumed as nonlinear elastic-plastic aluminum and linear-elastic glass-fiber-reinforced composite. The influence of pulse shape was investigated. Sinusoidal and rectangular pulse loads of finite duration were compared in two ways, i.e. with respect to magnitude and force pulse. The dynamic critical buckling load was determined based on Budiansky-Hutchinson, Ari Gur, and Simonetta dynamic buckling criteria.

Keywords: dynamic buckling, dynamic stability, Fiber Metal Laminate, Finite Element Method

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Anthony Credoz, Nathalie Nief, Remy Hedacq, Salvador Jordana, Laurent Cazes

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Groundwater monitoring is classically performed in a network of piezometers in industrial sites. Groundwater flow parameters, such as direction, sense and velocity, are deduced from indirect measurements between two or more piezometers. Groundwater sampling is generally done on the whole column of water inside each borehole to provide concentration values for each piezometer location. These flow and concentration values give a global ‘static’ image of potential plume of contaminants evolution in the shallow aquifer with huge uncertainties in time and space scales and mass discharge dynamic. TOTAL R&D Subsurface Environmental team is challenging this classical approach with an innovative dynamic way of characterization of shallow aquifer groundwater. The current study aims at optimizing the tools and methodologies for (i) a direct and multilevel measurement of groundwater velocities in each piezometer and, (ii) a calculation of potential flux of dissolved contaminant in the shallow aquifer. Lab-scale experiments have been designed to test commercial and R&D tools in a controlled sandbox. Multiphysics modeling were performed and took into account Darcy equation in porous media and Navier-Stockes equation in the borehole. The first step of the current study focused on groundwater flow at porous media/piezometer interface. Huge uncertainties from direct flow rate measurements in the borehole versus Darcy flow rate in the porous media were characterized during experiments and modeling. The structure and location of the tools in the borehole also impacted the results and uncertainties of velocity measurement. In parallel, direct-push tool was tested and presented more accurate results. The second step of the study focused on mass flux of dissolved contaminant in groundwater. Several active and passive commercial and R&D tools have been tested in sandbox and reactive transport modeling has been performed to validate the experiments at the lab-scale. Some tools will be selected and deployed in field assays to better assess the mass discharge of dissolved contaminants in an industrial site. The long-term subsurface environmental strategy is targeting an in-situ, real-time, remote and cost-effective monitoring of groundwater.

Keywords: dynamic characterization, groundwater flow, lab-scale, mass flux

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Authors: Taehan Lee

Abstract:

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: integer programming, multicommodity network design, routing, shortest path

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Authors: Dao Phuong Nam, Do Trong Tan, Pham Tam Thanh, Le Duy Tung, Tran Hoang Anh

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This paper considers the problem of cascade control system for unmanned aerial vehicles (UAVs). Due to the complicated modelling technique of UAV, it is necessary to separate them into two subsystems. The proposed cascade control structure is a hierarchical scheme including a robust control for inner subsystem based on H infinity theory and trajectory generator using genetic algorithm (GA), outer loop control law based on multi-parametric programming (MPP) technique to overcome the disadvantage of a big amount of calculations. Simulation results are presented to show that the equivalent path has been found and obtained by proposed cascade control scheme.

Keywords: genetic algorithm, GA, H infinity, multi-parametric programming, MPP, unmanned aerial vehicles, UAVs

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Authors: Oluwaseun K. Oyebode, Josiah A. Adeyemo

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Hydrological modelling plays a crucial role in the planning and management of water resources, most especially in water stressed regions where the need to effectively manage the available water resources is of critical importance. However, due to the complex, nonlinear and dynamic behaviour of hydro-climatic interactions, achieving reliable modelling of water resource systems and accurate projection of hydrological parameters are extremely challenging. Although a significant number of modelling techniques (process-based and data-driven) have been developed and adopted in that regard, the field of hydrological modelling is still considered as one that has sluggishly progressed over the past decades. This is majorly as a result of the identification of some degree of uncertainty in the methodologies and results of techniques adopted. In recent times, evolutionary computation (EC) techniques have been developed and introduced in response to the search for efficient and reliable means of providing accurate solutions to hydrological related problems. This paper presents a comprehensive review of the underlying principles, methodological needs and applications of a promising evolutionary computation modelling technique – genetic programming (GP). It examines the specific characteristics of the technique which makes it suitable to solving hydrological modelling problems. It discusses the opportunities inherent in the application of GP in water related-studies such as rainfall estimation, rainfall-runoff modelling, streamflow forecasting, sediment transport modelling, water quality modelling and groundwater modelling among others. Furthermore, the means by which such opportunities could be harnessed in the near future are discussed. In all, a case for total embracement of GP and its variants in hydrological modelling studies is made so as to put in place strategies that would translate into achieving meaningful progress as it relates to modelling of water resource systems, and also positively influence decision-making by relevant stakeholders.

Keywords: computational modelling, evolutionary algorithms, genetic programming, hydrological modelling

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Authors: Wajahat Ali, Shakeel Javaid

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In this study, we have developed a mathematical programming model for a solid transportation problem with three objective functions arranged in hierarchical order. The mathematical programming models with more than one objective function to be solved in hierarchical order is termed as a multi-level programming model. Our study explores a Multi-Level Solid Transportation Problem with Uncertain Parameters (MLSTPWU). The proposed MLSTPWU model consists of three objective functions, viz. minimization of transportation cost, minimization of total transportation time, and minimization of deterioration during transportation. These three objective functions are supposed to be solved by decision-makers at three consecutive levels. Three constraint functions are added to the model, restricting the total availability, total demand, and capacity of modes of transportation. All the parameters involved in the model are assumed to be uncertain in nature. A solution method based on fuzzy logic is also discussed to obtain the compromise solution for the proposed model. Further, a simulated numerical example is discussed to establish the efficiency and applicability of the proposed model.

Keywords: solid transportation problem, multi-level programming, uncertain variable, uncertain environment

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Authors: Candida Petrogalli, Giovanni Incerti, Luigi Solazzi

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This paper describes three lumped parameters models for the study of the dynamic behaviour of a boom crane. The models proposed here allow evaluating the fluctuations of the load arising from the rope and structure elasticity and from the type of the motion command imposed by the winch. A calculation software was developed in order to determine the actual acceleration of the lifted mass and the dynamic overload during the lifting phase. Some application examples are presented, with the aim of showing the correlation between the magnitude of the stress and the type of the employed motion command.

Keywords: crane, dynamic model, overloading condition, vibration

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Authors: Yuan Xu, Xun Liang, Meina Zhang

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The rise and attenuation of the public opinion broadcast of an emergent accident, in the social network, has a close relationship with the dynamic development of its subevents cluster. In this article, we take Tianjin Port explosion's subevents as an example to research the dynamic propagation discipline of Internet public opinion in a sudden accident, and analyze the overall structure of dynamic propagation to propose four different routes for subevents clusters propagation. We also generate network diagrams for the dynamic public opinion propagation, analyze each propagation type specifically. Based on this, suggestions on the supervision and guidance of Internet public opinion broadcast can be made.

Keywords: network dynamic transmission modes, emergent subevents clusters, Tianjin Port explosion, public opinion supervision

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Authors: Philippe Larvet

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This paper presents the concept of an object-based programming language where tests (if... then... else) and control structures (while, repeat, for...) disappear and are replaced by conditions on data. According to the object paradigm, by using this concept, data are still embedded inside objects, as variable-value couples, but object methods are expressed into the form of logical propositions (‘conditions on data’ or COD).For instance : variable1 = value1 AND variable2 > value2 => variable3 = value3. Implementing this approach, a central inference engine turns and examines objects one after another, collecting all CODs of each object. CODs are considered as rules in a rule-based system: the left part of each proposition (left side of the ‘=>‘ sign) is the premise and the right part is the conclusion. So, premises are evaluated and conclusions are fired. Conclusions modify the variable-value couples of the object and the engine goes to examine the next object. The paper develops the principles of writing CODs instead of complex algorithms. Through samples, the paper also presents several hints for implementing a simple mechanism able to process this ‘COD language’. The proposed approach can be used within the context of simulation, process control, industrial systems validation, etc. By writing simple and rigorous conditions on data, instead of using classical and long-to-learn languages, engineers and specialists can easily simulate and validate the functioning of complex systems.

Keywords: conditions on data, logical proposition, programming without code, object-oriented programming, system simulation, system validation

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Authors: Hamid Hamli Benzahar

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The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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Authors: Shreeyam, Ranjan Kumar Sah, Shivangi

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Recognizing and solving handwritten mathematical expressions can be a challenging task, particularly when certain characters are segmented and classified. This project proposes a solution that uses Convolutional Neural Network (CNN) and image processing techniques to accurately solve various types of equations, including arithmetic, quadratic, and trigonometric equations, as well as logical operations like logical AND, OR, NOT, NAND, XOR, and NOR. The proposed solution also provides a graphical solution, allowing users to visualize equations and their solutions. In addition to equation solving, the platform, called CNNCalc, offers a comprehensive learning experience for students. It provides educational content, a quiz platform, and a coding platform for practicing programming skills in different languages like C, Python, and Java. This all-in-one solution makes the learning process engaging and enjoyable for students. The proposed methodology includes horizontal compact projection analysis and survey for segmentation and binarization, as well as connected component analysis and integrated connected component analysis for character classification. The compact projection algorithm compresses the horizontal projections to remove noise and obtain a clearer image, contributing to the accuracy of character segmentation. Experimental results demonstrate the effectiveness of the proposed solution in solving a wide range of mathematical equations. CNNCalc provides a powerful and user-friendly platform for solving equations, learning, and practicing programming skills. With its comprehensive features and accurate results, CNNCalc is poised to revolutionize the way students learn and solve mathematical equations. The platform utilizes a custom-designed Convolutional Neural Network (CNN) with image processing techniques to accurately recognize and classify symbols within handwritten equations. The compact projection algorithm effectively removes noise from horizontal projections, leading to clearer images and improved character segmentation. Experimental results demonstrate the accuracy and effectiveness of the proposed solution in solving a wide range of equations, including arithmetic, quadratic, trigonometric, and logical operations. CNNCalc features a user-friendly interface with a graphical representation of equations being solved, making it an interactive and engaging learning experience for users. The platform also includes tutorials, testing capabilities, and programming features in languages such as C, Python, and Java. Users can track their progress and work towards improving their skills. CNNCalc is poised to revolutionize the way students learn and solve mathematical equations with its comprehensive features and accurate results.

Keywords: AL, ML, hand written equation solver, maths, computer, CNNCalc, convolutional neural networks

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Authors: H. Kazemi Esfeh, V. Akbari, M. Ehdaei, T. N. G. Borhani, A. Shamiri, M. Najafi

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In an industrial fluidized bed polymerization reactor, particle size distribution (PSD) plays a significant role in the reactor efficiency evaluation. The computational fluid dynamic (CFD) models coupled with population balance equation (CFD-PBM) have been extensively employed to investigate the flow behavior in the poly-disperse multiphase fluidized bed reactors (FBRs) utilizing ANSYS Fluent code. In this study, an existing CFD-PBM/ DQMOM coupled modeling framework has been used to highlight its potential to analyze the industrial-scale gas phase polymerization reactor. The predicted results reveal an acceptable agreement with the observed industrial data in terms of pressure drop and bed height. The simulated results also indicate that the higher particle growth rate can be achieved for bigger particles. Hence, the 2D CFD-PBM/DQMOM coupled model can be used as a reliable tool for analyzing and improving the design and operation of the gas phase polymerization FBRs.

Keywords: computational fluid dynamics, population balance equation, fluidized bed polymerization reactor, direct quadrature method of moments

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Authors: Janne Engblom, Elias Oikarinen

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A panel dataset is one that follows a given sample of individuals over time, and thus provides multiple observations on each individual in the sample. Panel data models include a variety of fixed and random effects models which form a wide range of linear models. A special case of panel data models are dynamic in nature. A complication regarding a dynamic panel data model that includes the lagged dependent variable is endogeneity bias of estimates. Several approaches have been developed to account for this problem. In this paper, the panel models were estimated using the Arellano-Bover/Blundell-Bond Generalized method of moments (GMM) estimator which is an extension of the Arellano-Bond model where past values and different transformations of past values of the potentially problematic independent variable are used as instruments together with other instrumental variables. The Arellano–Bover/Blundell–Bond estimator augments Arellano–Bond by making an additional assumption that first differences of instrument variables are uncorrelated with the fixed effects. This allows the introduction of more instruments and can dramatically improve efficiency. It builds a system of two equations—the original equation and the transformed one—and is also known as system GMM. In this study, Finnish housing price dynamics were examined empirically by using the Arellano–Bover/Blundell–Bond estimation technique together with ordinary OLS. The aim of the analysis was to provide a comparison between conventional fixed-effects panel data models and dynamic panel data models. The Arellano–Bover/Blundell–Bond estimator is suitable for this analysis for a number of reasons: It is a general estimator designed for situations with 1) a linear functional relationship; 2) one left-hand-side variable that is dynamic, depending on its own past realizations; 3) independent variables that are not strictly exogenous, meaning they are correlated with past and possibly current realizations of the error; 4) fixed individual effects; and 5) heteroskedasticity and autocorrelation within individuals but not across them. Based on data of 14 Finnish cities over 1988-2012 differences of short-run housing price dynamics estimates were considerable when different models and instrumenting were used. Especially, the use of different instrumental variables caused variation of model estimates together with their statistical significance. This was particularly clear when comparing estimates of OLS with different dynamic panel data models. Estimates provided by dynamic panel data models were more in line with theory of housing price dynamics.

Keywords: dynamic model, fixed effects, panel data, price dynamics

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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