Search results for: general linear model

Authors: Ion Smeureanu, Adriana Reveiu, Marian Dardala, Titus Felix Furtuna, Roman Kanala

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This paper proposes a linear model for optimizing domestic energy consumption, in Romania. Both techno-economic and consumer behavior approaches have been considered, in order to develop the model. The proposed model aims to reduce the energy consumption, in households, by assembling in a unitary model, aspects concerning: residential lighting, space heating, hot water, and combined space heating – hot water, space cooling, and passenger transport. This paper focuses on space heating domestic energy consumption model, and quantify not only technical-economic issues, but also consumer behavior impact, related to people decision to envelope and insulate buildings, in order to minimize energy consumption.

Keywords: consumer behavior, open source energy modeling system (OSeMOSYS), MARKAL/TIMES Romanian energy model, virtual technologies

Procedia PDF Downloads 536

Authors: Sergio A. Carvalho, Jose Pinto-Gouveia, David Gillanders, Paula Castilho

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The role of psychological processes has long been recognized as crucial factors in depressive symptoms in chronic pain (CP). Although some studies have explored the negative impact of being entangled with internal experiences (e.g., thoughts, emotions, physical sensations) – cognitive fusion, it is not extensively explored 1) whether these are pain-related or rather general difficult experiences, and 2) how they relate to experiencing obstacles in committing to valued actions. The current study followed a cross-sectional design in a sample of 231 participants with CP, in which a mediational model was tested through path analyses in AMOS software. The model presented a very good model fit (Χ²/DF = 1.161; CFI = .999; TLI = .996; RMSEA = .026, PCLOSE = .550.), and results showed that pain intensity was not directly related to depressive symptoms (β = .055; p = .239) but was mediated by cognitive fusion with both general and pain-related internal experiences (β = .181, 95%CI [.097; .271]; p = .015). Additionally, results showed that only general cognitive fusion (but not pain-specific fusion) was associated with experiencing obstacles to living a meaningful life, which mediated its impact on depressive symptoms (β = .197, 95%CI [.102; .307]; p = .001). Overall, this study adds on current literature by suggesting that psychological interventions to pain management should not be focused only on management of pain-related experiences, but also on developing more effective ways of relating to overall internal experiences.

Keywords: cognitive fusion, chronic pain, depressive symptoms, valued living

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Authors: Chad Brown

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This paper establishes general conditions for the convergence rates of nonparametric sieve estimators with dependent data. We present two key results: one for nonstationary data and another for stationary mixing data. Previous theoretical results often lack practical applicability to deep neural networks (DNNs). Using these conditions, we derive convergence rates for DNN sieve estimators in nonparametric regression settings with both nonstationary and stationary mixing data. The DNN architectures considered adhere to current industry standards, featuring fully connected feedforward networks with rectified linear unit activation functions, unbounded weights, and a width and depth that grows with sample size.

Keywords: sieve extremum estimates, nonparametric estimation, deep learning, neural networks, rectified linear unit, nonstationary processes

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Authors: Rahal Nacer, Beghdad Houda, Tehami Mohamed, Souici Abdelaziz

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Although the shrinkage of the concrete causes undesirable parasitic effects to the structure, it can then harm the resistance and the good appearance of the structure. Long term behaviourmodelling of steel-concrete composite beams requires the use of the time variable and the taking into account of all the sustained stress history of the concrete slab constituting the cross section. The work introduced in this article is a theoretical study of the behaviour of composite beams with respect to the phenomenon of concrete shrinkage. While using the theory of the linear viscoelasticity of the concrete, and on the basis of the rate of creep method, in proposing an analytical model, made up by a system of two linear differential equations, emphasizing the effects caused by shrinkage on the resistance of a steel-concrete composite beams. Results obtained from the application of the suggested model to a steel-concrete composite beam are satisfactory.

Keywords: composite beams, shrinkage, time, rate of creep method, viscoelasticity theory

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Authors: Shahriyar Keshtgar, Mahmoud Reza Heyhat, Sasan Bagheri, Ebrahim Gholami, Seyed Naser Raiisosadat

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Various tectonic interpretations have been presented by different researchers to explain the geological evolution of eastern Iran, but there are still many ambiguities and many disagreements about the geodynamic nature of the Paleogene mountain range of eastern Iran. The purpose of this research is to clarify and discuss the tectonic position of the foreland and hinterland regions of eastern Iran from the tectonic perspective of sedimentary basins. In the tectonic model of oceanic subduction crust under the Afghan block, the hinterland is located to the east and on the Afghan block, and the foreland is located on the passive margin of the Sistan open ocean in the west. After the collision of the two microcontinents, the foreland basin must be located somewhere on the passive margin of the Lut block. This basin can deposit thick Paleocene to Oligocene sediments on the Cretaceous and older sediments. Thrust faults here will move towards the west. If we accept the subduction model of the Sistan Ocean under the Lut Block, the hinterland is located to the west towards the Lut Block, and the foreland basin is located towards the Sistan Ocean in the east. After the collision of the two microcontinents, the foreland basin with Paleogene sediments should expand on the Sefidaba basin. Thrust faults here will move towards the east. If we consider the two-sided subduction model of the ocean crust under both Lut and Afghan continental blocks, the tectonic position of the foreland and hinterland basins will not change and will be similar to the one-sided subduction models. After the collision of two microcontinents, the foreland basin should develop in the central part of the eastern Iranian orogen. In the oroclinic buckling model, the foreland basin will continue not only in the east and west but continuously in the north as well. In this model, since there is practically no collision, the foreland basin is not developed, and the remnants of the Sistan Ocean ophiolites and their deep turbidite sediments appear in the axial part of the mountain range, where the Neh and Khash complexes are located. The structural data from this research in the northern border of the Sistan belt and the Lut block indicate the convergence of the tectonic vergence directions towards the interior of the Sistan belt (in the Ahangaran area towards the southwest, in the north of Birjand towards the south-southeast, in the Sechengi area to the southeast). According to this research, not only the general movement of thrust sheets do not follow the linear orogeny models, but the expected active foreland basins have not been formed in the mentioned places in eastern Iran. Therefore, these results do not follow previous tectonic models for eastern Iran (i.e., rifting of eastern Iran continental crust and subsequent linear collision of the Lut and Afghan blocks), but it seems that was caused by buckling model in the Late Eocene-Oligocene.

Keywords: foreland, hinterland, tectonic vergence, orocline buckling, eastern Iran

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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: A. L. Qureshi, A. A. Mahessar, A. Baloch

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Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. However, it is difficult to find analytical solution of these complex non-linear equations. Hence, verification of the numerical model should be carried out against field data and numerical predictions. This paper presents the verification of developed finite element model applying for unsteady flow in the open channels. The results of a proposed model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29 km at both sites (15 km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400 km downstream from Sukkur barrage, which demonstrates accurate model predictions with observed daily discharges. Hence, this model may be utilized for predicting and issuing flood warnings about flood hazardous in advance.

Keywords: finite element method, Preissmann scheme, HEC-RAS, flood forecasting, Indus river

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Authors: David Alejandro Lazo-Vasquez, Jorge Luis Balino

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In the petroleum industry, multiphase flow occurs when oil, gas, and water are transported in the same pipe through large pipeline systems. The flow can take different patterns depending on parameters like fluid velocities, pipe diameter, pipe inclination, and fluid properties. Mainly, intermittent flow is produced by the natural propagation of short and long waves, according to the Kelvin-Helmholtz Stability Theory. To model stratified flow and the onset of intermittent flow, it is crucial to have knowledge of short and long waves behavior. The two-fluid model, frequently employed for characterizing multiphase systems, becomes ill-posed for high liquid and gas velocities and large inclination angles, for short waves can develop infinite growth rates. We are interested in focusing attention on long-wave instability, which leads to the production of roll waves that may grow and result in the transition from stratified flow to intermittent flow. In this study, global and local linear stability analyses for dynamic and kinematic stability criteria predict the regions of stability of the flow for different pipe inclinations and fluid velocities in regularized and non-regularized systems, concurrently. It was possible to distinguish when: wave growth rates are absolutely bounded (stable stratified smooth flow), waves have finite growth rates (unstable stratified wavy flow), and when the equation system becomes elliptic and hyperbolization is needed. In order to bound short wave growth rates and regularize the equation system, we incorporated some lower and higher-order terms like interfacial drag and surface tension, respectively.

Keywords: linear stability analysis, multiphase flow, onset of slugging, two-fluid model regularization

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: P. S. Jagadeesh Kumar, S. Meenakshi Sundaram, Wenli Hu, Yang Yung

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In 3D video games, the dominance of production is unceasingly growing with a protruding level of affordability in terms of budget. Afterward, the automation of speech-lip synchronization technique is customarily onerous and has advanced a critical research subject in virtual reality based 3D video games. This paper presents one of these automatic tools, precisely riveted on the synchronization of the speech and the lip movement of the game characters. A robust and precise speech recognition segment that systematized with Algebraic Code Excited Linear Prediction method is developed which unconventionally delivers lip sync results. The Algebraic Code Excited Linear Prediction algorithm is constructed on that used in code-excited linear prediction, but Algebraic Code Excited Linear Prediction codebooks have an explicit algebraic structure levied upon them. This affords a quicker substitute to the software enactments of lip sync algorithms and thus advances the superiority of service factors abridged production cost.

Keywords: algebraic code excited linear prediction, speech-lip synchronization, video games, virtual reality

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Authors: Seyedehsomayeh Hosseini

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Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: D. Prangchumpol

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This research presents a forecasting method of requisition document demands for Military units by using Exponential Smoothing methods to analyze data. The data used in the forecast is an actual data requisition document of The Adjutant General Department. The results of the forecasting model to forecast the requisition of the document found that Holt–Winters’ trend and seasonality method of α=0.1, β=0, γ=0 is appropriate and matches for requisition of documents. In addition, the researcher has developed a requisition online system to improve the performance of requisition documents of The Adjutant General Department, and also ensuring that the operation can be checked.

Keywords: requisition, holt–winters, time series, royal thai army

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Authors: Muhammad Naveed Tahir, Wang Yingkuan, Huang Wenjiang, Raheel Osman

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Numerous models used in prediction and decision-making process but most of them are linear in natural environment, and linear models reach their limitations with non-linearity in data. Therefore accurate estimation is difficult. Artificial Neural Networks (ANN) found extensive acceptance to address the modeling of the complex real world for the non-linear environment. ANN’s have more general and flexible functional forms than traditional statistical methods can effectively deal with. The link between information technology and agriculture will become more firm in the near future. Monitoring crop biophysical properties non-destructively can provide a rapid and accurate understanding of its response to various environmental influences. Crop chlorophyll content is an important indicator of crop health and therefore the estimation of crop yield. In recent years, remote sensing has been accepted as a robust tool for site-specific management by detecting crop parameters at both local and large scales. The present research combined the ANN model with satellite-derived chlorophyll indices from LANDSAT 8 imagery for predicting real-time wheat chlorophyll estimation. The cloud-free scenes of LANDSAT 8 were acquired (Feb-March 2016-17) at the same time when ground-truthing campaign was performed for chlorophyll estimation by using SPAD-502. Different vegetation indices were derived from LANDSAT 8 imagery using ERADAS Imagine (v.2014) software for chlorophyll determination. The vegetation indices were including Normalized Difference Vegetation Index (NDVI), Green Normalized Difference Vegetation Index (GNDVI), Chlorophyll Absorbed Ratio Index (CARI), Modified Chlorophyll Absorbed Ratio Index (MCARI) and Transformed Chlorophyll Absorbed Ratio index (TCARI). For ANN modeling, MATLAB and SPSS (ANN) tools were used. Multilayer Perceptron (MLP) in MATLAB provided very satisfactory results. For training purpose of MLP 61.7% of the data, for validation purpose 28.3% of data and rest 10% of data were used to evaluate and validate the ANN model results. For error evaluation, sum of squares error and relative error were used. ANN model summery showed that sum of squares error of 10.786, the average overall relative error was .099. The MCARI and NDVI were revealed to be more sensitive indices for assessing wheat chlorophyll content with the highest coefficient of determination R²=0.93 and 0.90 respectively. The results suggested that use of high spatial resolution satellite imagery for the retrieval of crop chlorophyll content by using ANN model provides accurate, reliable assessment of crop health status at a larger scale which can help in managing crop nutrition requirement in real time.

Keywords: ANN, chlorophyll content, chlorophyll indices, satellite images, wheat

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Authors: Tomas Berhanu Bekele

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Traffic congestion is one of the main problems related to transportation in developed as well as developing countries. Traffic control systems are based on the idea of avoiding traffic instabilities and homogenizing traffic flow in such a way that the risk of accidents is minimized and traffic flow is maximized. Lately, Intelligent Transport Systems (ITS) has become an important area of research to solve such road traffic-related issues for making smart decisions. It links people, roads and vehicles together using communication technologies to increase safety and mobility. Moreover, accurate prediction of road traffic is important to manage traffic congestion. The aim of this study is to develop an ANN model for the prediction of traffic flow and to compare the ANN model with the linear regression model of traffic flow predictions. Data extraction was carried out in intervals of 15 minutes from the video player. Video of mixed traffic flow was taken and then counted during office work in order to determine the traffic volume. Vehicles were classified into six categories, namely Car, Motorcycle, Minibus, mid-bus, Bus, and Truck vehicles. The average time taken by each vehicle type to travel the trap length was measured by time displayed on a video screen.

Keywords: intelligent transport system (ITS), traffic flow prediction, artificial neural network (ANN), linear regression

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: identification, Hammerstein-Wiener, optimization, quantization

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Authors: Tareq Oshan

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Facility location and size decisions are important to any company because they affect profitability and success. However, warehouses are exposed to various risks of failure that affect their activity. This paper presents a mixed-integer non-linear mathematical model that can be used to determine optimal warehouse locations and sizes, which warehouses to fortify, and which branches should be assigned to specific warehouses when there is a risk of warehouse failure. Every branch is assigned to a fortified primary warehouse or a nonfortified primary warehouse and a fortified backup warehouse. The standard method and an introduced method, based on the average probabilities, for linearizing this mathematical model were used. A Canadian case study was used to demonstrate the developed mathematical model, followed by some sensitivity analysis.

Keywords: supply chain network design, fortified warehouse, mixed-integer mathematical model, warehouse failure risk

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Authors: Kazuyoshi Mori

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In this paper, we consider the parametrization of Anantharam’s model within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters of Anantharam’s model. We consider single-input single-output systems in this paper. By the investigation, we find three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: linear systems, parametrization, coprime factorization, number of parameters

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Authors: D. Srinivasacharya, Nidhi Humnekar

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The goal of this research is to numerically investigate the convection of nanofluid flow in an inclined porous channel. Brownian motion and thermophoresis effects are accounted for by nanofluid. In addition, the flow in the porous region governs Brinkman’s equation. The perturbed state of the generalized eigenvalue problem is obtained using normal mode analysis, and Chebyshev spectral collocation was used to solve this problem. For various values of the governing parameters, the critical wavenumber and critical Rayleigh number are calculated, and preferred modes are identified.

Keywords: Brinkman model, inclined channel, nanofluid, linear stability, porous media

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Authors: Jamal Fayazi, Farhad Anoosheh, Mohammad R. Ghorbani, Ali R. Paydar

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In this study, to determine the best non-linear regression model describing the growth curve of native poultry, 9657 chicks of generations 18, 19, and 20 raised in Mazandaran breeding center were used. Fowls and roosters of this center distributed in south of Caspian Sea region. To estimate the genetic variability of none linear regression parameter of growth traits, a Gibbs sampling of Bayesian analysis was used. The average body weight traits in the first day (BW1), eighth week (BW8) and twelfth week (BW12) were respectively estimated as 36.05, 763.03, and 1194.98 grams. Based on the coefficient of determination, mean squares of error and Akaike information criteria, Gompertz model was selected as the best growth descriptive function. In Gompertz model, the estimated values for the parameters of maturity weight (A), integration constant (B) and maturity rate (K) were estimated to be 1734.4, 3.986, and 0.282, respectively. The direct heritability of BW1, BW8 and BW12 were respectively reported to be as 0.378, 0.3709, 0.316, 0.389, 0.43, 0.09 and 0.07. With regard to estimated parameters, the results of this study indicated that there is a possibility to improve some property of growth curve using appropriate selection programs.

Keywords: direct heritability, Gompertz, growth traits, maturity weight, native poultry

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Authors: Sherry Ann Ganase, Sandra Sookram

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This study examines adaptation measures and factors that influence adaptation decisions in Bequia by using multiple linear regression and a structural equation model. Using survey data, the results suggest that households are knowledgeable and concerned about climate change but lack knowledge about the measures needed to adapt. The findings from the SEM suggest that a positive relationship exist between vulnerability and adaptation, vulnerability and perception, along with a negative relationship between perception and adaptation. This suggests that being aware of the terms associated with climate change and knowledge about climate change is insufficient for implementing adaptation measures; instead the risk and importance placed on climate change, vulnerability experienced with household flooding, drainage and expected threat of future sea level are the main factors that influence the adaptation decision. The results obtained in this study are beneficial to all as adaptation requires a collective effort by stakeholders.

Keywords: adaptation, Bequia, multiple linear regression, structural equation model

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Authors: S. Nandagopalan, N. Pradeep

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The aim of this paper is to propose a general framework for storing, analyzing, and extracting knowledge from two-dimensional echocardiographic images, color Doppler images, non-medical images, and general data sets. A number of high performance data mining algorithms have been used to carry out this task. Our framework encompasses four layers namely physical storage, object identification, knowledge discovery, user level. Techniques such as active contour model to identify the cardiac chambers, pixel classification to segment the color Doppler echo image, universal model for image retrieval, Bayesian method for classification, parallel algorithms for image segmentation, etc., were employed. Using the feature vector database that have been efficiently constructed, one can perform various data mining tasks like clustering, classification, etc. with efficient algorithms along with image mining given a query image. All these facilities are included in the framework that is supported by state-of-the-art user interface (UI). The algorithms were tested with actual patient data and Coral image database and the results show that their performance is better than the results reported already.

Keywords: active contour, Bayesian, echocardiographic image, feature vector

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

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This paper aims to analysis the behaviour of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Current-voltage curves are particularly analysed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: electrostatic precipitator, current-voltage characteristics, least squares method, electric field, magnetic field

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Mohammad Pourmohammadi Fallah, Maziar Salahi

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In the literature, a mixed-integer linear programming model for the integrated production planning and warehouse layout problem is proposed. To solve the model, the authors proposed a Lagrangian relax-and-fix heuristic that takes a significant amount of time to stop with gaps above 5$\%$ for large-scale instances. Here, we present two heuristic algorithms to solve the problem. In the first one, we use a greedy approach by allocating warehouse locations with less reservation costs and also less transportation costs from the production area to locations and from locations to the output point to items with higher demands. Then a smaller model is solved. In the second heuristic, first, we sort items in descending order according to the fraction of the sum of the demands for that item in the time horizon plus the maximum demand for that item in the time horizon and the sum of all its demands in the time horizon. Then we categorize the sorted items into groups of 3, 4, or 5 and solve a small-scale optimization problem for each group, hoping to improve the solution of the first heuristic. Our preliminary numerical results show the effectiveness of the proposed heuristics.

Keywords: capacitated lot-sizing, warehouse layout, mixed-integer linear programming, heuristics algorithm

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Authors: Huazhen Lin, Ruihua Xu, Zhibin Jiang

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In this real-world case, timetabling the LRT network as a whole is rather challenging for the operator: they are supposed to create a timetable to avoid various route conflicts manually while satisfying a given interval and the number of rolling stocks, but the outcome is not satisfying. Therefore, the operator adopts a computerised timetabling tool, the Train Plan Maker (TPM), to cope with this problem. However, with various constraints in the dual-line network, it is still difficult to find an adequate pairing of turnback time, interval and rolling stocks’ number, which requires extra manual intervention. Aiming at current problems, a one-off model for timetabling is presented in this paper to simplify the procedure of timetabling. Before the timetabling procedure starts, this paper presents how the dual-line system with a ring and several branches is turned into a simpler structure. Then, a non-linear programming model is presented in two stages. In the first stage, the model sets a series of constraints aiming to calculate a proper timing for coordinating two lines by adjusting the turnback time at termini. Then, based on the result of the first stage, the model introduces a series of inequality constraints to avoid various route conflicts. With this model, an analysis is conducted to reveal the relation between the ratio of trains in different directions and the possible minimum interval, observing that the more imbalance the ratio is, the less possible to provide frequent service under such strict constraints.

Keywords: light rail transit (LRT), non-linear programming, railway timetabling, timetable coordination

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Authors: Obaid Algahtani

Abstract:

An interval may be defined as a convex combination as follows: I=[a,b]={x_α=(1-α)a+αb: α∈[0,1]}. Consequently, we may adopt interval operations by applying the scalar operation point-wise to the corresponding interval points: I ∙J={x_α∙y_α ∶ αϵ[0,1],x_α ϵI ,y_α ϵJ}, With the usual restriction 0∉J if ∙ = ÷. These operations are associative: I+( J+K)=(I+J)+ K, I*( J*K)=( I*J )* K. These two properties, which are missing in the usual interval operations, will enable the extension of the usual linear system concepts to the interval setting in a seamless manner. The arithmetic introduced here avoids such vague terms as ”interval extension”, ”inclusion function”, determinants which we encounter in the engineering literature that deal with interval linear systems. On the other hand, these definitions were motivated by our attempt to arrive at a definition of interval random variables and investigate the corresponding statistical properties. We feel that they are the natural ones to handle interval systems. We will enable the extension of many results from usual state space models to interval state space models. The interval state space model we will consider here is one of the form X_((t+1) )=AX_t+ W_t, Y_t=HX_t+ V_t, t≥0, where A∈ 〖IR〗^(k×k), H ∈ 〖IR〗^(p×k) are interval matrices and 〖W 〗_t ∈ 〖IR〗^k,V_t ∈〖IR〗^p are zero – mean Gaussian white-noise interval processes. This feeling is reassured by the numerical results we obtained in a simulation examples.

Keywords: interval analysis, interval matrices, state space model, Kalman Filter

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Authors: Manojkumar Sabanayagam

Abstract:

The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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Authors: Paschal A. Ochang, Emmanuel C. Oji

Abstract:

The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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