Search results for: mathematical optimizations

Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: T. M. Ismail, M. A. El-Salam

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A mathematical model study was carried out to investigate gasification of biomass fuels using high-temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promising way in its capability and sensitivity for the parameter effects that influence the gasification process.

Keywords: computational fluid dynamics, gasification, biomass fuel, fixed bed gasifier

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Authors: C. C. Lv, Y. L. Sun, D. W. Zuo

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Cemented carbide balls are usually implemented in industry under the environment of high speed, high temperature, corrosiveness and strong collisions. However, its application is limited due to high fabrication cost, processing efficiency and quality. A novel eccentric lapping method with two rotatable lapping plates was proposed in this paper. A mathematical model was constructed to analyze the influence of each design parameter on this lapping method. To validate this new lapping method, an orthogonal experiment was conducted with cemented carbide balls (YG6). The simulation model was verified and the optimal lapping parameters were derived. The results show that the surface roundness of the balls reaches to 0.65um from 2um in 1 hour using this lapping method. So, using this novel lapping method, it can effectively improve the machining precision and efficiency of cemented carbide balls.

Keywords: cemented carbide balls, eccentric lapping, high precision, lapping tracks, V-groove

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Authors: Maria Grazia Albanesi, Riccardo Amadeo

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This study presents a new model of the human image quality assessment process: the aim is to highlight the foundations of the image quality metrics proposed in literature, by identifying the cognitive/physiological or mathematical principles of their development and the relation with the actual human quality assessment process. The model allows to create a novel categorization of objective and subjective image quality metrics. Our work includes an overview of the most used or effective objective metrics in literature, and, for each of them, we underline its main characteristics, with reference to the rationale of the proposed model and categorization. From the results of this operation, we underline a problem that affects all the presented metrics: the fact that many aspects of human biases are not taken in account at all. We then propose a possible methodology to address this issue.

Keywords: eye-tracking, image quality assessment metric, MOS, quality of user experience, visual perception

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Authors: Mejri Achref

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This paper proposes an energy management strategy for an electrical hybrid vehicle which is composed of a Proton Exchange Membrane (PEM) fuel cell and a supercapacitor storage device. In this paper, the mathematical model for the proposed power train, comprising the PEM Fuel Cell, supercapacitor, boost converter, inverter, and vehicular structure, was modeled in MATLAB/Simulink. The proposed algorithm is evaluated for the Highway Fuel Economy Test (HWFET) driving cycle. The obtained results demonstrate the effectiveness of the proposed energy management strategy in reduction of hydrogen consumption.

Keywords: proton exchange membrane fuel cell, hybrid vehicle, hydrogen consumption, energy management strategy

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Authors: Erika Ruíz, Luis Amaya, Diego Carreño

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The main objective of this study is to design a mathematical model for the logistics of mining collection centers in the northern region of the department of Boyacá (Colombia), determining the structure that facilitates the flow of products along the supply chain. In order to achieve this, it is necessary to define a suitable design of the distribution network, taking into account the products, customer’s characteristics and the availability of information. Likewise, some other aspects must be defined, such as number and capacity of collection centers to establish, routes that must be taken to deliver products to the customers, among others. This research will use one of the operation research problems, which is used in the design of distribution networks known as Location Routing Problem (LRP).

Keywords: location routing problem, logistic, mining collection, model

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Authors: Razieh Khalafi

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Myocardial infarction (MI) or acute myocardial infarction (AMI), commonly known as a heart attack, occurs when blood flow stops to part of the heart causing damage to the heart muscle. An ECG can often show evidence of a previous heart attack or one that's in progress. The patterns on the ECG may indicate which part of your heart has been damaged, as well as the extent of the damage. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. In this research by considering ECG signal as a random walk we work on forecasting the oncoming heart attack by analyzing the ECG signals using the correlation dimension. In order to test the model a set of ECG signals for patients before and after heart attack was used and the strength of model for forecasting the behavior of these signals were checked. Results shows this methodology can forecast the ECG and accordingly heart attack with high accuracy.

Keywords: heart attack, ECG, random walk, correlation dimension, forecasting

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Authors: Asowata Osamede, Trudy Sutherland

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The purpose of this paper is to assess the available power from a Renewable Energy Source (off-grid photovoltaic (PV) panel) in the Southern Hemisphere using anisotropic model. Direct solar radiation is the driving force in photovoltaics. In a basic PV panels in the Southern Hemisphere, Power conversion is eminent, and this is achieved by the PV cells converting solar energy into electrical energy. In this research, the results was determined for a 6 month period from September 2022 through February 2023. Preliminary results, which include Normal Probability plot, data analysis - R2 value, effective conversion-time per week and work-time per day, indicate a favorably comparison between the empirical results and the simulation results.

Keywords: power-conversion, mathematical model, PV panels, DC-DC converters, direct solar radiation

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Authors: Pascal Mwenge, Jefrey Pilusa, Tumisang Seodigeng

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The current study investigated the effect of catalyst ratio and methanol to oil ratio on biodiesel production by using central composite design. Biodiesel was produced by transesterification using sodium hydroxide as a homogeneous catalyst, a laboratory scale reactor consisting of flat bottom flask mounts with a reflux condenser and a heating plate was used to produce biodiesel. Key parameters, including, time, temperature and mixing rate were kept constant at 60 minutes, 60 ^oC and 600 RPM, respectively. From the results obtained, it was observed that the biodiesel yield depends on catalyst ratio and methanol to oil ratio. The highest yield of 50.65% was obtained at catalyst ratio of 0.5 wt.% and methanol to oil mole ratio 10.5. The analysis of variances of biodiesel yield showed the R Squared value of 0.8387. A quadratic mathematical model was developed to predict the biodiesel yield in the specified parameters ranges.

Keywords: ANOVA, biodiesel, catalyst, CCD, transesterification

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Authors: C. V. Pietreanu, S. E. Zaharia, C. Dinu

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Hazard assessment and risks quantification are key components for estimating the impact of existing regulations. But since regulatory compliance cannot cover all risks in aviation, the authors point out that by studying causal factors and eliminating uncertainty, an accurate analysis can be outlined. The research debuts by making delimitations on notions, as confusion on the terms over time has reflected in less rigorous analysis. Throughout this paper, it will be emphasized the fact that the variation in human performance and organizational factors represent the biggest threat from an operational perspective. Therefore, advanced risk assessment methods analyzed by the authors aim to understand vulnerabilities of the system given by a nonlinear behavior. Ultimately, the mathematical modeling of existing hazards and risks by eliminating uncertainty implies establishing an optimal solution (i.e. risk minimization).

Keywords: control, human factor, optimization, risk management, uncertainty

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Authors: Yasser Abo El-Magd, Wael Fawzy Mohamed

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Due to the great development in construction and building field, there are many projects and huge works appeared which consume many construction materials. Accordingly, that causes difficulty in handling traditional transportation means (ordinary cranes) due to their limited capacity; there is an urgent need to use high capacity cranes such as tower cranes. However, with regard to their high expense, we have to take into consideration selecting what type of cranes to be utilized which has been discussed by many researchers. In this research, a proposed technique was created to select the suitable type of crane and the best place for crane erection, in addition to minimum radius for requested crane in order to minimize cost. To fulfill that target, a computer program is designed to numerate these problems, demonstrating an example explaining how to apply program and the result donated the best place.

Keywords: tower crane, jib length, operating time, location, feasible area

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Authors: Y. Galerkin, K. Soldatova, A. Drozdov

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The 6th version of Universal modeling method for centrifugal compressor stage calculation is described. Identification of the new mathematical model was made. As a result of identification the uniform set of empirical coefficients is received. The efficiency definition error is 0,86 % at a design point. The efficiency definition error at five flow rate points (except a point of the maximum flow rate) is 1,22 %. Several variants of the stage with 3D impellers designed by 6th version program and quasi three-dimensional calculation programs were compared by their gas dynamic performances CFD (NUMECA FINE TURBO). Performance comparison demonstrated general principles of design validity and leads to some design recommendations.

Keywords: compressor design, loss model, performance prediction, test data, model stages, flow rate coefficient, work coefficient

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Authors: M. Wigwe, J. G Akpa, E. N Wami

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Mathematical models of the absorber of a glycol dehydration facility was developed using the principles of conservation of mass and energy. Models which predict variation of the water content of gas in mole fraction, variation of gas and liquid temperatures across the parking height were developed. These models contain contributions from bulk and diffusion flows. The effect of diffusion on the process occurring in the absorber was studied in this work. The models were validated using the initial conditions in the plant data from Company W TEG unit in Nigeria. The results obtained showed that the effect of diffusion was noticed between z=0 and z=0.004 m. A deviation from plant data of 0% was observed for the gas water content at a residence time of 20 seconds, at z=0.004 m. Similarly, deviations of 1.584% and 2.844% were observed for the gas and TEG temperatures.

Keywords: separations, absorption, simulation, dehydration, water content, triethylene glycol

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Authors: Moussa Hamdan, Abdulati Abdullah

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This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.

Keywords: surface plasmons, optical waveguides, semiconductor lasers, refractive index, slab dialectical

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Amir Bahrami

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In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index or a descriptor index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper some descriptor index (descriptor index) of single-walled carbon nanotubes, is determined.

Keywords: chemical graph theory, molecular topology, molecular descriptor, single-walled carbon nanotubes

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Authors: Jean Pierre Ribeiro Daquila

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This paper aims to analyze the use of the Theory of Multiple Intelligences as a tool to facilitate students’ learning. This theory, proposed by the American psychologist and educator Howard Gardner, was first established in 1983 and advocates that human beings possess eight intelligence and not only one, as defended by psychologists prior to his theory. These intelligence are bodily-kinesthetic intelligence, musical, linguistic, logical-mathematical, spatial, interpersonal, intrapersonal, and naturalist. This paper will focus on bodily-kinesthetic intelligence. Spatial and bodily-kinesthetic intelligences are sensed by athletes, dancers, and others who use their bodies in ways that exceed normal abilities. These are intelligences that are closely related. A quarterback or a ballet dancer needs to have both an awareness of body motions and abilities as well as a sense of the space involved in the action. Nevertheless, there are many reasons which make classical ballet dance more integrated with other intelligences. Ballet dancers make it look effortless as they move across the stage, from the lifts to the toe points; therefore, there is acting both in the performance of the repertoire and in hiding the pain or physical stress. The ballet dancer has to have great mathematical intelligence to perform a fast allegro; for instance, each movement has to be executed in a specific millisecond. Flamenco dancers need to rely as well on their mathematic abilities, as the footwork requires the ability to make half, two, three, four or even six movements in just one beat. However, the precision of the arm movements is freer than in ballet dance; for this reason, ballet dancers need to be more holistically aware of their movements; therefore, our experiment will test whether this greater attention required by ballet dancers makes them acquire better results in the training sessions when compared to flamenco dancers. An experiment will be carried out in this study by training ballet dancers through dance (four years of experience dancing minimum – experimental group 1); a group of flamenco dancers (four years of experience dancing minimum – experimental group 2). Both experimental groups will be trained in two different domains – phonetics and chemistry – to examine whether there is a significant improvement in these areas compared to the control group (a group of regular students who will receive the same training through a traditional method). However, this paper will focus on phonetic training. Experimental group 1 will be trained with the aid of classical music plus bodily work. Experimental group 2 will be trained with flamenco rhythm and kinesthetic work. We would like to highlight that this study takes dance as an example of a possible area of strength; nonetheless, other types of arts can and should be used to support students, such as drama, creative writing, music and others. The main aim of this work is to suggest that other intelligences, in the case of this study, bodily-kinesthetic, can be used to help improve pronunciation.

Keywords: multiple intelligences, pronunciation, effective pronunciation trainings, short drills, musical intelligence, bodily-kinesthetic intelligence

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Authors: Lisa Kasmer

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Teachers’ instructional decisions shape the structure and content of mathematics lessons and influence the mathematics that students are given the opportunity to learn. Therefore, it is important to better understand how teachers make instructional decisions and thus find new ways to help practicing and future teachers give their students a more effective and robust learning experience. Understanding the relationship between teachers’ instructional decisions and their goals, resources, and orientations (beliefs) is important given the heightened focus on geometric transformations in the middle school mathematics curriculum. This work is significant as the development and support of current and future teachers need more effective ways to teach geometry to their students. The following research questions frame this study: (1) As middle school mathematics teachers plan and enact instruction related to teaching transformations, what thinking processes do they engage in to make decisions about teaching transformations with or without a coordinate system and (2) How do the goals, resources and orientations of these teachers impact their instructional decisions and reveal about their understanding of teaching transformations? Teachers and students alike struggle with understanding transformations; many teachers skip or hurriedly teach transformations at the end of the school year. However, transformations are an important mathematical topic as this topic supports students’ understanding of geometric and spatial reasoning. Geometric transformations are a foundational concept in mathematics, not only for understanding congruence and similarity but for proofs, algebraic functions, and calculus etc. Geometric transformations also underpin the secondary mathematics curriculum, as features of transformations transfer to other areas of mathematics. Teachers’ instructional decisions in terms of goals, orientations, and resources that support these instructional decisions were analyzed using open-coding. Open-coding is recognized as an initial first step in qualitative analysis, where comparisons are made, and preliminary categories are considered. Initial codes and categories from current research on teachers’ thinking processes that are related to the decisions they make while planning and reflecting on the lessons were also noted. Surfacing ideas and additional themes common across teachers while seeking patterns, were compared and analyzed. Finally, attributes of teachers’ goals, orientations and resources were identified in order to begin to build a picture of the reasoning behind their instructional decisions. These categories became the basis for the organization and conceptualization of the data. Preliminary results suggest that teachers often rely on their own orientations about teaching geometric transformations. These beliefs are underpinned by the teachers’ own mathematical knowledge related to teaching transformations. When a teacher does not have a robust understanding of transformations, they are limited by this lack of knowledge. These shortcomings impact students’ opportunities to learn, and thus disadvantage their own understanding of transformations. Teachers’ goals are also limited by their paucity of knowledge regarding transformations, as these goals do not fully represent the range of comprehension a teacher needs to teach this topic well.

Keywords: coordinate plane, geometric transformations, instructional decisions, middle school mathematics

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Authors: Razi Khalafi

Abstract:

Myocardial Infarction (MI) or acute Myocardial Infarction (AMI), commonly known as a heart attack, occurs when blood flow stops to part of the heart causing damage to the heart muscle. An ECG can often show evidence of a previous heart attack or one that's in progress. The patterns on the ECG may indicate which part of your heart has been damaged, as well as the extent of the damage. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. In this research by considering ECG signal as a random walk we work on forecasting the oncoming heart attack by analysing the ECG signals using the correlation dimension. In order to test the model a set of ECG signals for patients before and after heart attack was used and the strength of model for forecasting the behaviour of these signals were checked. Results show this methodology can forecast the ECG and accordingly heart attack with high accuracy.

Keywords: heart attack, ECG, random walk, correlation dimension, forecasting

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Authors: Armel Asongu Nkembi, Ahmad Fawad

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In this paper, we design a smart car parking system using the Node-Red interface, which enables the user to find the nearest parking area from his current location and gives the availability of parking slots in that respective parking area. The closest parking area is determined by sending an HTTP request to an API, and the shortest distance is computed using some mathematical formulations based on the coordinates retrieved. There is also the use of IR sensors to signal the availability or lack of available parking lots within any parking area. The aim is to reduce the time and effort needed to find empty parking lots and also avoid unnecessary traveling through filled parking lots in a parking area. Thus, it reduces fuel consumption, which in turn reduces carbon footprints in the atmosphere and, overall, makes the city much smarter.

Keywords: node-red, smart parking system, API, http request, IR sensors, Internet of Things, smart city, parking lots.

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Authors: George Hadjinicola, Andreas Soteriou

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This paper examines the relationship between the number of price promotions that a firm should conduct per year and the level of safety stocks that the firm should maintain. Price promotions result in temporary sales increases, which affect the operations function through (1) an increase in the quantities demanded and (2) an increase in safety stocks required to maintain the desired service level. We propose a modeling framework where both price promotions and improved service levels, operationalized through higher safety stocks, can affect sales. We treat the annual number of promotions as a decision variable. We identify market conditions where the operations function, through improved safety stocks, can complement price promotions or even play the leading role in sales increases.

Keywords: price promotions, safety stocks, marketing/operations interface, mathematical model

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Authors: B. Selma, S. Chouraqui

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The pancreas is an elongated organ that extends across the abdomen, below the stomach. In addition, it secretes certain enzymes that aid in food digestion. The pancreas also manufactures hormones responsible for regulating blood glucose levels. In the present paper, we propose a mathematical model to study the homeostasis of glucose and insulin in healthy human, and a simulation of this model, which depicts the physiological events after a meal, will be represented in ordinary humans. The aim of this paper is to design an algorithm which regulates the level of glucose in the blood. The algorithm applied the concept of expert system for performing an algorithm control in the form of an "active" used to prescribe the rate of insulin infusion. By decomposing the system into subsystems, we have developed parametric models of each subsystem by using a forcing function strategy. The results showed a performance of the control system.

Keywords: modeling, algorithm, regulation, glucose-insulin, blood, control system

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Authors: Rasha Waheeb, Bjorn Andersen, Rafa Shakir

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Purpose The purpose of this study is to avoid delays that occur in emergency reconstruction projects especially in post disaster circumstances whether if they were natural or manmade due to their particular national and humanitarian importance. We presented a theoretical and practical concepts for projects management in the field of construction industry that deal with a range of global and local trails. This study aimed to identify the factors of effective delay in construction projects in Iraq that affect the time and the specific quality cost, and find the best solutions to address delays and solve the problem by setting parameters to restore balance in this study. 30 projects were selected in different areas of construction were selected as a sample for this study. Design/methodology/approach This study discusses the reconstruction strategies and delay in time and cost caused by different delay factors in some selected projects in Iraq (Baghdad as a case study).A case study approach was adopted, with thirty construction projects selected from the Baghdad region, of different types and sizes. Project participants from the case projects provided data about the projects through a data collection instrument distributed through a survey. Mixed approach and methods were applied in this study. Mathematical data analysis was used to construct models to predict delay in time and cost of projects before they started. The artificial neural networks analysis was selected as a mathematical approach. These models were mainly to help decision makers in construction project to find solutions to these delays before they cause any inefficiency in the project being implemented and to strike the obstacles thoroughly to develop this industry in Iraq. This approach was practiced using the data collected through survey and questionnaire data collection as information form. Findings The most important delay factors identified leading to schedule overruns were contractor failure, redesigning of designs/plans and change orders, security issues, selection of low-price bids, weather factors, and owner failures. Some of these are quite in line with findings from similar studies in other countries/regions, but some are unique to the Iraqi project sample, such as security issues and low-price bid selection. Originality/value we selected ANN’s analysis first because ANN’s was rarely used in project management , and never been used in Iraq to finding solutions for problems in construction industry. Also, this methodology can be used in complicated problems when there is no interpretation or solution for a problem. In some cases statistical analysis was conducted and in some cases the problem is not following a linear equation or there was a weak correlation, thus we suggested using the ANN’s because it is used for nonlinear problems to find the relationship between input and output data and that was really supportive.

Keywords: construction projects, delay factors, emergency reconstruction, innovation ANN, post disasters, project management

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Authors: S. Wesebaum, S. Willeke

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Production companies are faced with an increasingly turbulent business environment, which demands very high production volumes- and delivery date flexibility. If a decoupling by storage stages is not possible (e.g. at a contract manufacturing company) or undesirable from a logistical point of view, load scattering effects the production processes. ‘Load’ characterizes timing and quantity incidence of production orders (e.g. in work content hours) to workstations in the production, which results in specific capacity requirements. Insufficient coordination between load (demand capacity) and capacity supply results in heavy load scattering, which can be described by deviations and uncertainties in the input behavior of a capacity unit. In order to respond to fluctuating loads, companies try to implement consistent and realizable input behavior using the capacity supply available. For example, a uniform and high level of equipment capacity utilization keeps production costs down. In contrast, strong load scattering at workstations leads to performance loss or disproportionately fluctuating WIP, whereby the logistics objectives are affected negatively. Options for reducing load scattering are e.g. shifting the start and end dates of orders, batch splitting and outsourcing of operations or shifting to other workstations. This leads to an adjustment of load to capacity supply, and thus to a reduction of load scattering. If the adaptation of load to capacity cannot be satisfied completely, possibly flexible capacity must be used to ensure that the performance of a workstation does not decrease for a given load. Where the use of flexible capacities normally raises costs, an adjustment of load to capacity supply reduces load scattering and, in consequence, costs. In the literature you mostly find qualitative statements for describing load scattering. Quantitative evaluation methods that describe load mathematically are rare. In this article the authors discuss existing approaches for calculating load scattering and their various disadvantages such as lack of opportunity for normalization. These approaches are the basis for the development of our mathematical quantification approach for describing load scattering that compensates the disadvantages of the current quantification approaches. After presenting our mathematical quantification approach, the method of batch splitting will be described. Batch splitting allows the adaptation of load to capacity to reduce load scattering. After describing the method, it will be explicitly analyzed in the context of the logistic curve theory by Nyhuis using the stretch factor α1 in order to evaluate the impact of the method of batch splitting on load scattering and on logistic curves. The conclusion of this article will be to show how the methods and approaches presented can help companies in a turbulent environment to quantify the occurring work load scattering accurately and apply an efficient method for adjusting work load to capacity supply. In this way, the achievements of the logistical objectives are increased without causing additional costs.

Keywords: batch splitting, production logistics, production planning and control, quantification, load scattering

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Authors: Waraporn Wimuktalop

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This research will select regions which are vulnerable to flooding in different level. Mathematical principles will be systematically and rationally utilized as a tool to solve problems of selection the regions. Therefore the method called Multiple Criteria Decision Making (MCDM) has been chosen by having two analysis standards, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and AHP (Analytic Hierarchy Process). There are three criterions that have been considered in this research. The first criterion is climate which is the rainfall. The second criterion is geography which is the height above mean sea level. The last criterion is the land utilization which both forest and agriculture use. The study found that the South has the highest risk of flooding, then the East, the Centre, the North-East, the West and the North, respectively.

Keywords: multiple criteria decision making, TOPSIS, analytic hierarchy process, flooding

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Authors: Olga V. Korotkaya

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This article is devoted to an important problem of calculation of deflected mode of the combustion chamber and the nozzle end of a new liquid-propellant rocket cruise engine. A special attention is given to the methodology of calculation. Three operating modes are considered. The analysis has been conducted in ANSYS software. The methods of conducted research are mathematical modelling, substructure method, cyclic symmetry, and finite element method. The calculation has been carried out to order of S. P. Korolev Rocket and Space Corporation «Energia». The main results are practical. Proposed methodology and created models would be able to use for a wide range of strength problems.

Keywords: combustion chamber, cyclic symmetry, finite element method, liquid-propellant rocket engine, nozzle end, substructure

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

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This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: distributed model, flexible manipulator, observer, robot control

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Authors: Dhruba Das

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In this article, the author has put forward the actual mathematical explanation of subnormal imprecise vector. Every subnormal imprecise vector has to be defined with reference to a membership surface. The membership surface of normal imprecise vector has already defined based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. A normal imprecise vector is a special case of subnormal imprecise vector. Nothing however is available in the literature about the membership surface when a subnormal imprecise vector is defined. The author has shown here how to construct the membership surface of a subnormal imprecise vector.

Keywords: imprecise vector, membership surface, subnormal imprecise number, subnormal imprecise vector

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Authors: H. Naderpour, R. C. Barros, S. M. Khatami

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Seismic excitation is naturally caused large horizontal relative displacements, which is able to provide collisions between two adjacent buildings due to insufficient separation distance and severe damages are occurred due to impact especially in tall buildings. In this paper, an impact is numerically simulated and two needed parameters are calculated, including impact force and energy absorption. In order to calculate mentioned parameters, mathematical study needs to model an unreal link element, which is logically assumed to be spring and dashpot to determine lateral displacement and damping ratio of impact. For the determination of dynamic response of impact, a new equation of motion is theoretically suggested to evaluate impact force and energy dissipation. In order to confirm the rendered equation, a series of parametric study are performed and the accuracy of formula is confirmed.

Keywords: pounding, impact, dissipated energy, coefficient of restitution

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