Search results for: Ricatti equation mapping approach

Authors: Humayun Murshed, Shibly Abdullah

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This paper focuses on sharing experience gained through a pilot project undertaken to teach an introductory accounting subject linking real-life ground realities with the fundamental concepts of accounting. In view of the practical dimensions of Accounting it has been observed that adopting a teaching approach based on practical illustrations help students to motivate and generate interests to take accounting profession as their career. The paper reports that students’ perception about accounting as ‘dreary’ has been changed to ‘interesting’ due to adoption of practice based approach in teaching. The authors argue that ‘concept mapping’ can play a vital role in facilitating practice based education in accounting which promotes a rewarding learning experience among the students. The paper considers taking into account generic skills development, student centric learning, development of innovative assessment tasks, making students aware of the potential benefits of practice based education primarily through concept mapping, and engaging them both inside and outside of the class rooms are critical for ensuring success of this approach.

Keywords: accounting education, pedagogy, practice-based education, concept mapping

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Authors: Babatunde J. Falaye

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In this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously E_nl-D (shifted Deng-Fan).

Keywords: Schrödinger equation, exact quantization rule, functional analysis, Deng-Fan potential

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Ahmad Aslizadeh, Farid Ghaderi

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Mapping organizational knowledge is an innovative concept and useful instrument of representation, capturing and visualization of implicit and explicit knowledge. There are a diversity of methods, instruments and techniques presented by different researchers following mapping organizational knowledge to reach determined goals. Implicating of these methods, it is necessary to know their exigencies and conditions in which those can be used. Integrating identified methods of knowledge mapping and comparing them would help knowledge managers to select the appropriate methods. This research conducted to presenting a model and framework to map organizational knowledge. At first, knowledge maps, their applications and necessity are introduced because of extracting comparative framework and detection of their structure. At the next step techniques of researchers such as Eppler, Kim, Egbu, Tandukar and Ebner as knowledge mapping models are presented and surveyed. Finally, they compare and a superior model would be introduced.

Keywords: knowledge mapping, knowledge management, comparative study, business and management

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Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Ajibola Isola, Shattri Mansor, Ojogbane Sani, Olugbemi Tope

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The cadastral map is the rationale behind city management planning and development. For years, cadastral maps have been produced by ground and photogrammetry platforms. Recent evolution in photogrammetry and remote sensing sensors ignites the use of Unmanned Aerial Vehicle systems (UAVs) for cadastral mapping. Despite the time-saving and multi-dimensional cost-effectiveness of the UAV platform, issues related to cadastral map accuracy are a hindrance to the wide applicability of UAVs' cadastral mapping. This study aims to present an approach leading to the generation and assessing the credibility of UAV cadastral mapping. Different sets of Red, Green, and Blue (RGB) photos were obtained from the Tarot 680-hexacopter UAV platform flown over the Universiti Putra Malaysia campus sports complex at an altitude range of 70 m, 100 m, and 250. Before flying the UAV, twenty-eight ground control points were evenly established in the study area with a real-time kinematic differential global positioning system. The second phase of the study utilizes an image-matching algorithm for photos alignment wherein camera calibration parameters and ten of the established ground control points were used for estimating the inner, relative, and absolute orientations of the photos. The resulting orthoimages are exported to ArcGIS software for digitization. Visual, tabular, and graphical assessments of the resulting cadastral maps showed a different level of accuracy. The results of the study show a gradual approach for generating UAV cadastral mapping and that the cadastral map acquired at 70 m altitude produced better results.

Keywords: aerial mapping, orthomosaic, cadastral map, flying altitude, image processing

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: T. K. Tee, M. N. A. Azman, S. Mohamed, M. Muhammad, M. M. Mohamad, J. Md Yunos, M. H. Yee, W. Othman

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Buzan mind mapping is an efficient system of note-taking that makes revision a fun thing to do for students. Tony Buzan has been teaching children all over the world for the past thirty years and has proved that mind maps are the magic formula in the classroom for everyone. The purpose of this paper is to discuss the importance of Buzan mind mapping as a note-taking technique for the secondary school students. This paper also examines the mind mapping technique, advantages and disadvantages of hand-drawn mind maps. Samples of students’ mind maps were presented and discussed.

Keywords: Buzan mind mapping, note-taking technique, hand-drawn, mind maps

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: complex potential, conformal mapping, image well theory, Laplace’s equation, superposition principle

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Authors: Gulshan Sachdeva, Ram Bilash

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In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

Keywords: exergy analysis, Gouy-Stodola, refrigeration, vapor absorption

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Abdul Rahman Hamdan

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The Fourth Industrial Revolution (4IR) has brought unprecedented technological advancements that have disrupted many industries worldwide. In keeping up with the technological advances and rapid disruption by the introduction of many technological advancements brought forth by the 4IR, the use of technology road mapping has emerged as one of the critical tools for organizations to leverage. Technology road mapping can be used by many companies to guide them to become more adaptable and anticipate future transformation and innovation, and avoid being redundant or irrelevant due to the rapid changes in technological advancement. This research paper provides a comprehensive analysis of technology road mapping within the context of the 4IR. The objectives of the paper are to provide companies with practical insights and a strategic framework of technology road mapping for them to navigate the fast-changing nature of the 4IR. This study also contributes to the understanding and practice of technology road mapping in the 4IR and, at the same time, provides organizations with the necessary tools and critical insight to navigate the 4IR transformation by leveraging technology road mapping. Based on the literature review and case studies, the study analyses key principles, methodologies, and best practices in technology road mapping and integrates them with the unique characteristics and challenges of the 4IR. The research paper gives the background of the fourth industrial revolution. It explores the disruptive potential of technologies in the 4IR and the critical need for technology road mapping that consists of strategic planning and foresight to remain competitive and relevant in the 4IR era. It also highlights the importance of technology road mapping as an organisation’s proactive approach to align the organisation’s objectives and resources to their technology and product development in meeting the fast-evolving technological 4IR landscape. The paper also includes the theoretical foundations of technology road mapping and examines various methodological approaches, and identifies external stakeholders in the process, such as external experts, stakeholders, collaborative platforms, and cross-functional teams to ensure an integrated and robust technological roadmap for the organisation. Moreover, this study presents a comprehensive framework for technology road mapping in the 4IR by incorporating key elements and processes such as technology assessment, competitive intelligence, risk analysis, and resource allocation. It provides a framework for implementing technology road mapping from strategic planning, goal setting, and technology scanning to road mapping visualisation, implementation planning, monitoring, and evaluation. In addition, the study also addresses the challenges and limitations related to technology roadmapping in 4IR, including the gap analysis. In conclusion of the study, the study will propose a set of practical recommendations for organizations that intend to leverage technology road mapping as a strategic tool in the 4IR in driving innovation and becoming competitive in the current and future ecosystem.

Keywords: technology management, technology road mapping, technology transfer, technology planning

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Authors: Stefano Zappacosta, Cristiano Bove, Maria Carmela Marinelli, Paola di Lauro, Katarina Spasenovic, Lorenzo Ostano, Giuseppe Aiello, Marco Pietrosanto

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This paper proposes a novel neural network approach for assessing flood hazard mapping. The core of the model is a machine learning component fed by frequency ratios, namely statistical correlations between flood event occurrences and a selected number of topographic properties. The proposed hybrid model can be used to classify four different increasing levels of hazard. The classification capability was compared with the flood hazard mapping River Basin Plans (PAI) designed by the Italian Institute for Environmental Research and Defence, ISPRA (Istituto Superiore per la Protezione e la Ricerca Ambientale). The study area of Piemonte, an Italian region, has been considered without loss of generality. The frequency ratios may be used as a standalone block to model the flood hazard mapping. Nevertheless, the mixture with a neural network improves the classification power of several percentage points, and may be proposed as a basic tool to model the flood hazard map in a wider scope.

Keywords: flood modeling, hazard map, neural networks, hydrogeological risk, flood risk assessment

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Authors: J. R. Bhalla, Gautam, Gurcharan Singh, Sanjeev Naval

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Mathematics is everywhere behind the every things on the earth as well as in the universe. Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. Now a day’s we can made and apply an equation on a complex geometry through applied mathematics. Here we work and focus on to create a formula which apply in the field of civil engineering in new concrete technology. In this paper our target is to make a formula which is applied on “BAUT” Metal Aggregate. In this paper our approach is to make formulation and equation on special “BAUT” Metal Aggregate by Applied Mathematical Study Case 1. BASIC PHYSICAL FORMULATION 2. ADVANCE EQUATION which shows the mechanical performance of special metal aggregates for concrete technology. In case 1. Basic physical formulation shows the surface area and volume manually and in case 2. Advance equation shows the mechanical performance has been discussed, the metal aggregates which had outstandingly qualities to resist shear, tension and compression forces. In this paper coarse metal aggregates is 20 mm which used for making high performance concrete (H.P.C).

Keywords: applied mathematical study case, special metal aggregates, concrete technology, basic physical formulation, advance equation

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Authors: G. Shabib, Esam H. Abd-Elhameed, G. Magdy

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In this paper, a comparison of discrete time PID, PSS controllers is presented through small signal stability of power system comprising of one machine connected to infinite bus system. This comparison achieved by using a new approach of discretization which converts the S-domain model of analog controllers to a Z-domain model to enhance the damping of a single machine power system. The new method utilizes the Plant Input Mapping (PIM) algorithm. The proposed algorithm is stable for any sampling rate, as well as it takes the closed loop characteristic into consideration. On the other hand, the traditional discretization methods such as Tustin’s method is produce satisfactory results only; when the sampling period is sufficiently low.

Keywords: PSS, power system stabilizer PID, proportional-integral-derivative PIM, plant input mapping

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Samuel Ahamefula Mba

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Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Jana Gutierez Chvalkovska, Michal Mejstrik, Matej Urban

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There are pending discussions over the mapping of country export potential in order to refocus export strategy of firms and its evidence-based promotion by the Export Credit Agencies (ECAs) and other permitted vehicles of governments. In this paper we develop our version of an applied model that offers “stepwise” elimination of unattractive markets. We modify and calibrate the model for the particular features of the Czech Republic and specific pilot cases where we apply an individual approach to each sector.

Keywords: export strategy, modeling export, calibration, export promotion

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Zeyu Zhou, Xiaojun Bi

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Due to the limited environmental parameters and the limited resolution of the sensor, the universal existence of the mixed pixels in the process of remote sensing images restricts the spatial resolution of the remote sensing images. Sub-pixel mapping technology can effectively improve the spatial resolution. As the bilinear interpolation algorithm inevitably produces the edge blur effect, which leads to the inaccurate sub-pixel mapping results. In order to avoid the edge blur effect that affects the sub-pixel mapping results in the interpolation process, this paper presents a new edge-directed interpolation algorithm which uses the covariance adaptive interpolation algorithm on the edge of the low-resolution image and uses bilinear interpolation algorithm in the low-resolution image smooth area. By using the edge-directed interpolation algorithm, the super-resolution of the image with low resolution is obtained, and we get the percentage of each sub-pixel under a certain type of high-resolution image. Then we rely on the probability value as a soft attribute estimate and carry out sub-pixel scale under the ‘hard classification’. Finally, we get the result of sub-pixel mapping. Through the experiment, we compare the algorithm and the bilinear algorithm given in this paper to the results of the sub-pixel mapping method. It is found that the sub-pixel mapping method based on the edge-directed interpolation algorithm has better edge effect and higher mapping accuracy. The results of the paper meet our original intention of the question. At the same time, the method does not require iterative computation and training of samples, making it easier to implement.

Keywords: remote sensing images, sub-pixel mapping, bilinear interpolation, edge-directed interpolation

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Noriko Hanakawa, Masaki Obana

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A simulation tool has been proposed for big-scale projection mapping events. The tool has four main functions based on Mapbox and Unity utilities. The first function is building a 3D model of real cities by MapBox. The second function is a movie projection to some buildings in real cities by Unity. The third function is a movie sending function from a PC to a virtual projector. The fourth function is mapping movies with fitting buildings. The simulation tool was adapted to a real projection mapping event that was held in 2019. The event has been finished. The event had a serious problem in the movie projection to the target building. The extra tents were set in front of the target building. The tents became the obstacles to the movie projection. The simulation tool can be reappeared the problems of the event. Therefore, if the simulation tool was developed before the 2019 projection mapping event, the problem of the tents’ obstacles could be avoided with the simulation tool. In addition, we confirmed that the simulation tool is useful to make a plan of future projection mapping events in order to avoid obstacles of various extra equipment such as utility poles, planting trees, monument towers.

Keywords: projection mapping, projector position, real 3D map, avoiding obstacles

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Authors: M. K. Benhaoua, A. K. Singh, A. E. Benyamina, P. Boulet

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Mapping parallelized tasks of applications onto these MPSoCs can be done either at design time (static) or at run-time (dynamic). Static mapping strategies find the best placement of tasks at design-time, and hence, these are not suitable for dynamic workload and seem incapable of runtime resource management. The number of tasks or applications executing in MPSoC platform can exceed the available resources, requiring efficient run-time mapping strategies to meet these constraints. This paper describes a new Spiral Dynamic Task Mapping heuristic for mapping applications onto NoC-based Heterogeneous MPSoC. This heuristic is based on packing strategy and routing Algorithm proposed also in this paper. Heuristic try to map the tasks of an application in a clustering region to reduce the communication overhead between the communicating tasks. The heuristic proposed in this paper attempts to map the tasks of an application that are most related to each other in a spiral manner and to find the best possible path load that minimizes the communication overhead. In this context, we have realized a simulation environment for experimental evaluations to map applications with varying number of tasks onto an 8x8 NoC-based Heterogeneous MPSoCs platform, we demonstrate that the new mapping heuristics with the new modified dijkstra routing algorithm proposed are capable of reducing the total execution time and energy consumption of applications when compared to state-of-the-art run-time mapping heuristics reported in the literature.

Keywords: multiprocessor system on chip, MPSoC, network on chip, NoC, heterogeneous architectures, run-time mapping heuristics, routing algorithm

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Ahmet Kaya

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Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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