Search results for: linear eigenvalue analysis

Authors: Christos Lampropoulos, Maria Konsta, Ifigenia Apostolou, Vicky Dradaki, Tamta Sirbilatze, Irini Dri, Christina Kordali, Vaggelis Lambas, Kostas Argyros, Georgios Mavras

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Objectives: Mediterranean diet has been associated with lower incidence of cardiovascular disease and cancer. The purpose of our study was to examine the hypothesis that Mediterranean diet may protect against mortality and reduce admission duration in elderly, hospitalized patients. Methods: Sample population included 150 patients (78 men, 72 women, mean age 80±8.2). The following data were taken into account in analysis: anthropometric and laboratory data, dietary habits (MedDiet score), patients’ nutritional status [Mini Nutritional Assessment (MNA) score], physical activity (International Physical Activity Questionnaires, IPAQ), smoking status, cause and duration of current admission, medical history (co-morbidities, previous admissions). Primary endpoints were mortality (from admission until 6 months afterwards) and duration of admission, compared to national guidelines for closed consolidated medical expenses. Logistic regression and linear regression analysis were performed in order to identify independent predictors for mortality and admission duration difference respectively. Results: According to MNA, nutrition was normal in 54/150 (36%) of patients, 46/150 (30.7%) of them were at risk of malnutrition and the rest 50/150 (33.3%) were malnourished. After performing multivariate logistic regression analysis we found that the odds of death decreased 30% per each unit increase of MedDiet score (OR=0.7, 95% CI:0.6-0.8, p < 0.0001). Patients with cancer-related admission were 37.7 times more likely to die, compared to those with infection (OR=37.7, 95% CI:4.4-325, p=0.001). According to multivariate linear regression analysis, admission duration was inversely related to Mediterranean diet, since it is decreased 0.18 days on average for each unit increase of MedDiet score (b:-0.18, 95% CI:-0.33 - -0.035, p=0.02). Additionally, the duration of current admission increased on average 0.83 days for each previous hospital admission (b:0.83, 95% CI:0.5-1.16, p<0.0001). The admission duration of patients with cancer was on average 4.5 days higher than the patients who admitted due to infection (b:4.5, 95% CI:0.9-8, p=0.015). Conclusion: Mediterranean diet adequately protects elderly, hospitalized patients against mortality and reduces the duration of hospitalization.

Keywords: Mediterranean diet, malnutrition, nutritional status, prognostic factors for mortality

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Authors: G. Çelik Gül, F. Kurtuluş

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Rare earths containing complex metal oxides have drawn much attention due to physical, chemical and optical properties which make them feasible in so many areas such as non-linear optical materials and ion exchanger. We have researched a systematic study to obtain rare earth containing zirconium molybdate compound, characterization, investigation of crystal system and calculation of unit cell parameters.  After a successful synthesis of Nd₂Zr₃(MoO₄)₉ which is a member of rare earth metal containing complex oxides family, X-ray diffraction (XRD), High Score Plus/Rietveld refinement analysis, and Fourier Transform Infrared Spectroscopy (FTIR) were completed to determine the crystal structure. Morphological properties and elemental composition were determined by scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis. Thermal properties were observed via Thermogravimetric-differential thermal analysis (TG/DTA).

Keywords: Nd₂Zr₃(MoO₄)₉, powder x-ray diffraction, solid state synthesis, zirconium molybdates

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Authors: Brahim Fares Zaidi

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Our work aims to improve our Automatic Recognition System for Dysarthria Speech based on the Hidden Models of Markov and the Hidden Markov Model Toolkit to help people who are sick. With pronunciation problems, we applied two techniques of speech parameterization based on Mel Frequency Cepstral Coefficients and Perceptual Linear Prediction and concatenated them with JITTER and SHIMMER coefficients in order to increase the recognition rate of a dysarthria speech. For our tests, we used the NEMOURS database that represents speakers with dysarthria and normal speakers.

Keywords: ARSDS, HTK, HMM, MFCC, PLP

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: D. S. Naumann, B. J. Evans, O. Hassan

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This paper outlines the development of an automated aerodynamic optimisation algorithm using a novel method of parameterising a computational mesh by employing user–defined control nodes. The shape boundary movement is coupled to the movement of the novel concept of the control nodes via a quasi-1D-linear deformation. Additionally, a second order smoothing step has been integrated to act on the boundary during the mesh movement based on the change in its second derivative. This allows for both linear and non-linear shape transformations dependent on the preference of the user. The domain mesh movement is then coupled to the shape boundary movement via a Delaunay graph mapping. A Modified Cuckoo Search (MCS) algorithm is used for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible NavierStokes solver is used for aerodynamic modelling to predict aerodynamic design fitness. The resulting coupled algorithm is applied to a range of test cases in two dimensions including the design of a subsonic, transonic and supersonic intake and the optimisation approach is compared with more conventional optimisation strategies. Ultimately, the algorithm is tested on a three dimensional wing optimisation case.

Keywords: mesh movement, aerodynamic shape optimization, cuckoo search, shape parameterisation

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Authors: Tahani Salman Alangari

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Student success can be impacted by internal factors such as their emotional well-being and external factors such as organizational support and instructional support in the classroom. This study is to identify at least one factor that forecasts student engagement. It is a cross-sectional, conducted on 6206 teachers and encompassed three years of data collection and observations of math instruction in approximately 50 schools and 300 classrooms. A multiple linear regression revealed that a model predicting student engagement from emotional support, classroom organization, and instructional support was significant. Four linear regression models were tested using hierarchical regression to examine the effects of independent variables: emotional support was the highest predictor of student engagement while instructional support was the lowest.

Keywords: student engagement, emotional support, organizational support, instructional support, well-being

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Authors: Sorin Oancea

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More than half a century after Ivan Sutherland’s seminal essay, ‘The Ultimate Display’ (1965), 3D Virtual Reality is still an emergent and exploratory medium in terms of its narrative potential, production methodology, and market penetration. Traditionally positioned in front of the screen/canvas as a ‘window-on-the-world’, the storyboarder and animation director transcend the medium and its narrative reality entirely while designing a linear cinematic sequence. This paper proposes a gradual transition from the traditional linear sequence design process based on a transcendent position of the storyboarder and animation director to an increasingly immersed one characterized by a sense of unmediated presence and immanence. Employing a quaitative analysis of the current exploratory storyboarding processes for 3D VR, this research uses a practice-based methodology based on producing a short-form 3D VR narrative experience to derive its findings. The original contribution to knowledge is charting an empirically derived conceptual framework for VR storyboarding and animation directing, with the documented reflective and reflexive process as a map for directorial transitioning between converging mediums by articulating the new VR lexical categories and expounding links to allied performative arts, such as film and theatre.

Keywords: storyboarding, immersive, virtual reality, transitioning

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Authors: Ehsan Sakhaei, Ali Taherabadi

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In this study, an aft sweep wing with specific characteristic feature was analysis with CFD method in Fluent software. In this analysis wings aerodynamic coefficient was calculated in different rake angle and wing lift curve slope to rake angle was achieved. Wing section was selected among NACA airfoils version 6. The sweep angle of wing is 15 degree, aspect ratio 8 and taper ratios 0.4. Designing and modeling this wing was done in CATIA software. This model was meshed in Gambit software and its three dimensional analysis was done in Fluent software. CFD methods used here were based on pressure base algorithm. SIMPLE technique was used for solving Navier-Stokes equation and Spalart-Allmaras model was utilized to simulate three dimensional wing in air. Roskam method is one of the common and most used methods for determining aerodynamics parameters in the field of airplane designing. In this study besides CFD analysis, an advanced aircraft analysis was used for calculating aerodynamic coefficient using Roskam method. The results of CFD were compared with measured data acquired from Roskam method and authenticity of relation was evaluated. The results and comparison showed that in linear region of lift curve there is a minor difference between aerodynamics parameter acquired from CFD to relation present by Roskam.

Keywords: aft sweep wing, CFD method, fluent, Roskam, Spalart-Allmaras model

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Authors: Ibrahim Ali, Adamu Danlami Ahmed

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This study examines the impact of depreciation on taxable income and financial performance of consumer goods companies quoted on the Nigerian stock exchange. The study adopts ex-post factor research design. Data were collected using a secondary source. The findings of the study suggest that, method of depreciation adopted in any organization influence the taxable profit. Depreciation techniques can either be: depressive, accelerative and linear depreciation. It was also recommended that consumer goods should adjust their method of depreciation to make sure an appropriate method is adopted. This will go a long way to revitalize their taxable profit.

Keywords: accelerated, linear, depressive, depreciation

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Authors: Tayyab Hassan, Talha Rehman, Qasim Abdul Aziz, Ahmad Salman

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The constant monitoring of blood glucose level is necessary for maintaining health of patients and to alert medical specialists to take preemptive measures before the onset of any complication as a result of diabetes. The current clinical monitoring of blood glucose uses invasive methods repeatedly which are uncomfortable and may result in infections in diabetic patients. Several attempts have been made to develop non-invasive techniques for blood glucose measurement. In this regard, the existing methods are not reliable and are less accurate. Other approaches claiming high accuracy have not been tested on extended dataset, and thus, results are not statistically significant. It is a well-known fact that acetone concentration in breath has a direct relation with blood glucose level. In this paper, we have developed the first of its kind, reliable and high accuracy breath analyzer for non-invasive blood glucose measurement. The acetone concentration in breath was measured using MQ 138 sensor in the samples collected from local hospitals in Pakistan involving one hundred patients. The blood glucose levels of these patients are determined using conventional invasive clinical method. We propose a linear regression classifier that is trained to map breath acetone level to the collected blood glucose level achieving high accuracy.

Keywords: blood glucose level, breath acetone concentration, diabetes, linear regression

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

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This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges

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Authors: Prasannakumar Palaniappan, Dong Ho Shin, Chul Gyu Song

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The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.

Keywords: contour filtering, linear array, photoacoustic tomography, universal back projection

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Authors: Strahinja Kovačević, Sanja Podunavac-Kuzmanović, Lidija Jevrić, Milica Karadžić

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The present study is based on the quantitative structure-activity relationship (QSAR) analysis of eighteen compounds with anti-prion activity. The structures and anti-prion activities (expressed in response units, RU%) of the analyzed compounds are taken from CHEMBL database. In the first step of analysis 85 molecular descriptors were calculated and based on them the hierarchical cluster analysis (HCA) and principal component analysis (PCA) were carried out in order to detect potential significant similarities or dissimilarities among the studied compounds. The calculated molecular descriptors were physicochemical, lipophilicity and ADMET (absorption, distribution, metabolism, excretion and toxicity) descriptors. The first stage of the QSAR analysis was simple linear regression modeling. It resulted in one acceptable model that correlates Henry's law constant with RU% units. The obtained 2D-QSAR model was validated by cross-validation as an internal validation method. The validation procedure confirmed the model’s quality and therefore it can be used for prediction of anti-prion activity. The next stage of the analysis of anti-prion activity will include 3D-QSAR and molecular docking approaches in order to select the most promising compounds in treatment of prion diseases. These results are the part of the project No. 114-451-268/2016-02 financially supported by the Provincial Secretariat for Science and Technological Development of AP Vojvodina.

Keywords: anti-prion activity, chemometrics, molecular modeling, QSAR

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Authors: Mehdi Ghatei, Masoomeh Lorestani

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Upstream Tailings Storage Facilities (TSFs) may experience slope instabilities due to soil liquefaction, especially in regions known to be seismically active. In this study, liquefaction susceptibility of an upstream-raised TSF in Western Australia was assessed using two different approaches. The first approach assessed liquefaction susceptibility using Cone Penetration Tests with pore pressure measurement (CPTu) as described by the National Centre for Earthquake Engineering Research (NCEER). This assessment was based on the four CPTu tests that were conducted on the perimeter embankment of the TSF. The second approach used the Finite Element (FE) method with application of an equivalent linear model to predict the undrained cyclic behavior, the pore water pressure and the liquefaction of the materials. The tailings parameters were estimated from the CPTu profiles and from the laboratory tests. The cyclic parameters were estimated from the literature where test results of similar material were available. The results showed that there was a good agreement, in the liquefaction susceptibility of the tailings material, between the NCEER and FE methods with equivalent linear model.

Keywords: liquefaction , CPTU, NCEER, finite element method, equivalent linear model

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Authors: Khair Al-Deen Bsisu, Osama Mahmoud Abuzeid

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Significant technological advances have been achieved in the design and building construction of steel and glass in the last two decades. The metal glass support frame has been replaced by further sophisticated technological solutions, for example, the point fixed glazing systems. The minimization of the visual mass has reached extensive possibilities through the evolution of technology in glass production and the better understanding of the structural potential of glass itself, the technological development of bolted fixings, the introduction of the glazing support attachments of the glass suspension systems and the use for structural stabilization of cables that reduce to a minimum the amount of metal used. The variability of solutions of tension structures, allied to the difficulties related to geometric and material non-linear behavior, usually overrules the use of analytical solutions, letting numerical analysis as the only general approach to the design and analysis of tension structures. With the characteristics of low stiffness, lightweight, and small damping, tension structures are obviously geometrically nonlinear. In fact, analysis of cable truss is not only one of the most difficult nonlinear analyses because the analysis path may have rigid-body modes, but also a time consuming procedure. Non-linear theory allowing for large deflections is used. The flexibility of supporting members was observed to influence the stresses in the pane considerably in some cases. No other class of architectural structural systems is as dependent upon the use of digital computers as are tensile structures. Besides complexity, the process of design and analysis of tension structures presents a series of specificities, which usually lead to the use of special purpose programs, instead of general purpose programs (GPPs), such as ANSYS. In a special purpose program, part of the design know how is embedded in program routines. It is very probable that this type of program will be the option of the final user, in design offices. GPPs offer a range of types of analyses and modeling options. Besides, traditional GPPs are constantly being tested by a large number of users, and are updated according to their actual demands. This work discusses the use of ANSYS for the analysis and design of tension structures, such as cable truss structures under wind and gravity loadings. A model to describe the glass panels working in coordination with the cable truss was proposed. Under the proposed model, a FEM model of the glass panels working in coordination with the cable truss was established.

Keywords: Glass Construction material, Facades, Finite Element, Pre-Tensioned Cable Truss

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Nadia Sghaier

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In this paper, we aim to identify the determinants of the life and non-life insurance premiums of different lines for the case of the Tunisian insurance market over a recent period from 1997 to 2019. The empirical analysis is conducted using the linear cointegration techniques in the panel data framework, which allow both long and short-run relationships. The obtained results show evidence of long-run relationship between premiums, losses, and financial variables (stock market indices and interest rate). Furthermore, we find that the short-run effect of explanatory variables differs across lines. This finding has important implications for insurance tarification and regulation.

Keywords: insurance premiums, lines, Tunisian insurance market, cointegration approach in panel data

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Authors: Fawwaz Eniola Fajingbesi, Nur Shahida Midia, Elsheikh M. A. Elsheikh, Siti Hajar Yusoff

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Empirical analysis of lightning related phenomena in real time is extremely dangerous due to the relatively high electric discharge involved. Hence, design and optimization of efficient grounding systems depending on real time empirical methods are impeded. Using numerical methods, the dynamics of complex systems could be modeled hence solved as sets of linear and non-linear systems . In this work, the induced current distribution as lightning strike traverses the soil have been numerically modeled in a 2D axial-symmetry and solved using finite element method (FEM) in COMSOL Multiphysics 5.2 AC/DC module. Stratified and non- stratified electrode system were considered in the solved model and soil conductivity (σ) varied between 10 – 58 mS/m. The result discussed therein were the electric field distribution, current distribution and soil ionization phenomena. It can be concluded that the electric field and current distribution is influenced by the injected electric potential and the non-linearity in soil conductivity. The result from numerical calculation also agrees with previously laboratory scale empirical results.

Keywords: current distribution, grounding systems, lightning discharge, numerical model, soil conductivity, soil ionization

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Majid Farsadrouh Rashti, Parisa Jahani, Amir Shafiee, Mehrdad Mofidi

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The dihydroxybenzene isomers, hydroquinone (HQ), catechol (CC) and resorcinol (RS) have been widely recognized as important environmental pollutants due to their toxicity and low degradability in the ecological environment. Speciation of HQ, CC and RS is very important for environmental analysis because they co-exist of these isomers in environmental samples and are too difficult to degrade as an environmental contaminant with high toxicity. There are many analytical methods have been reported for detecting these isomers, such as spectrophotometry, fluorescence, High-performance liquid chromatography (HPLC) and electrochemical methods. These methods have attractive advantages such as simple and fast response, low maintenance costs, wide linear analysis range, high efficiency, excellent selectivity and high sensitivity. A novel modified glassy carbon electrode (GCE) with Pd@ Cu/CNTs core−shell nanowires for the simultaneous determination of hydroquinone (HQ), catechol (CC) and resorcinol (RS) is described. A detailed investigation by field emission scanning electron microscopy and electrochemistry was performed in order to elucidate the preparation process and properties of the GCE/ Pd/CuNWs-CNTs. The electrochemical response characteristic of the modified GPE/LFOR toward HQ, CC and RS were investigated by cyclic voltammetry, differential pulse voltammetry (DPV) and Chronoamperometry. Under optimum conditions, the calibrations curves were linear up to 228 µM for each with detection limits of 0.4, 0.6 and 0.8 µM for HQ, CC and RS, respectively. The diffusion coefficient for the oxidation of HQ, CC and RS at the modified electrode was calculated as 6.5×10⁻⁵, 1.6 ×10⁻⁵ and 8.5 ×10⁻⁵ cm² s⁻¹, respectively. DPV was used for the simultaneous determination of HQ, CC and RS at the modified electrode and the relative standard deviations were 2.1%, 1.9% and 1.7% for HQ, CC and RS, respectively. Moreover, GCE/Pd/CuNWs-CNTs was successfully used for determination of HQ, CC and RS in real samples.

Keywords: dihydroxybenzene isomers, galvanized copper nanowires, electrochemical sensor, Palladium, speciation

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Authors: Victoria Siriaki Jorry, I. S. Mbalawata, Hayong Shin

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The main objective in a change detection problem is to develop algorithms for efficient detection of gradual and/or abrupt changes in the parameter distribution of a process or time series data. In this paper, we present a modified cumulative (MCUSUM) algorithm to detect the start and end of a time-varying linear drift in mean value of a time series data based on likelihood ratio test procedure. The design, implementation and performance of the proposed algorithm for a linear drift detection is evaluated and compared to the existing CUSUM algorithm using different performance measures. An approach to accurately approximate the threshold of the MCUSUM is also provided. Performance of the MCUSUM for gradual change-point detection is compared to that of standard cumulative sum (CUSUM) control chart designed for abrupt shift detection using Monte Carlo Simulations. In terms of the expected time for detection, the MCUSUM procedure is found to have a better performance than a standard CUSUM chart for detection of the gradual change in mean. The algorithm is then applied and tested to a randomly generated time series data with a gradual linear trend in mean to demonstrate its usefulness.

Keywords: average run length, CUSUM control chart, gradual change detection, likelihood ratio test

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Authors: Riadh Zorgati, Thomas Triboulet

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In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.

Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix

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Authors: A. Danbaba

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Samurai Sudoku consists of five Sudoku square designs each having nine treatments in each row (column or sub-block) only once such the five Sudoku designs overlaps. Two or more Samurai designs can be joint together to give an extended Samurai design. In addition, two Samurai designs, each containing five Sudoku square designs, are mutually orthogonal (Graeco). If we superimpose two Samurai designs and obtained a pair of Latin and Greek letters in each row (column or sub-block) of the five Sudoku designs only once, then we have Graeco Samurai design. In this paper, simple method of constructing Samurai designs and mutually orthogonal Samurai design are proposed. In addition, linear models and methods of data analysis for the designs are proposed.

Keywords: samurai design, graeco samurai design, sudoku design, row or column swap

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Authors: Emilienne Lardy, Eric Ballot, Mariam Lafkihi

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Efficient urban logistics requires a comprehensive understanding of traffic dynamics, particularly as it pertains to kinetic parameters influencing energy consumption and trip duration estimations. While real-time traffic information is increasingly accessible, current high-precision forecasting services embedded in route planning often function as opaque 'black boxes' for users. These services, typically relying on AI-processed counting data, fall short in accommodating open design parameters essential for management studies, notably within Supply Chain Management. This work revisits the modelling of traffic conditions in the context of city logistics, emphasizing its significance from the user’s point of view, with two focuses. Firstly, the focus is not on the vehicle flow but on the vehicles themselves and the impact of the traffic conditions on their driving behaviour. This means opening the range of studied indicators beyond vehicle speed, to describe extensively the kinetic and dynamic aspects of the driving behaviour. To achieve this, we leverage the Art. Kinema parameters are designed to characterize driving cycles. Secondly, this study examines how the driving context (i.e., exogenous factors to the traffic flow) determines the mentioned driving behaviour. Specifically, we explore how accurately the kinetic behaviour of a vehicle can be predicted based on a limited set of exogenous factors, such as time, day, road type, orientation, slope, and weather conditions. To answer this question, statistical analysis was conducted on real-world driving data, which includes high-frequency measurements of vehicle speed. A Factor Analysis and a Generalized Linear Model have been established to link kinetic parameters with independent categorical contextual variables. The results include an assessment of the adjustment quality and the robustness of the models, as well as an overview of the model’s outputs.

Keywords: factor analysis, generalised linear model, real world driving data, traffic congestion, urban logistics, vehicle kinematics

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Authors: J. V. Gonzalez Fernandez, T. Mozume, S. Gozu, A. Lastras Martinez, L. F. Lastras Martinez, J. Ortega Gallegos, R. E. Balderas Navarro

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We report on a theoretical-experimental study of photoreflectance anisotropy (PRA) spectroscopy of coupled double quantum wells. By probing the in-plane interfacial optical anisotropies, we demonstrate that PRA spectroscopy has the capacity to detect and distinguish layers with quantum dimensions. In order to account for the experimental PRA spectra, we have used a theoretical model at k=0 based on a linear electro-optic effect through a piezoelectric shear strain.

Keywords: coupled double quantum well (CDQW), linear electro-optic (LEO) effect, photoreflectance anisotropy (PRA), piezoelectric shear strain

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Authors: Bharti Gupta, V. K. Kukreja

Abstract:

A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

Procedia PDF Downloads 224

Authors: F. Maass, P. Martin, J. Olivares

Abstract:

The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

Procedia PDF Downloads 245

Authors: Fatma Abidi, Taoufik Harizi, Slah Msahli, Faouzi Sakli

Abstract:

Nine different Tunisian handmade carpets were used for the investigation. The raw material of the carpet pile yarns was wool. The influence of the different structure parameters (linear density and pile height) on the carpet compression was investigated. Carpets were tested under dynamic loading in order to evaluate and observe the thickness loss and carpet behavior under dynamic loads. To determine the loss of pile height under dynamic loading, the pile height carpets were measured. The test method was treated according to the Tunisian standard NT 12.165 (corresponds to the standard ISO 2094). The pile height measurements are taken and recorded at intervals up to 1000 impacts (measures of this study were made after 50, 100, 200, 500, and 1000 impacts). The loss of pile height is calculated using the variation between the initial height and those measured after the number of reported impacts. The experimental results were statistically evaluated using Design Expert Analysis of Variance (ANOVA) software. As regards the deformation, results showed that both of the structure parameters of the pile yarn and the pile height have an influence. The carpet with the higher pile and the less linear density of pile yarn showed the worst performance. Results of a polynomial regression analysis are highlighted. There is a good correlation between the loss of pile height and the impacts number of dynamic loads. These equations are in good agreement with measured data. Because the prediction is reasonably accurate for all samples, these equations can also be taken into account when calculating the theoretical loss of pile height for the considered carpet samples. Statistical evaluations of the experimen¬tal data showed that the pile material and number of impacts have a significant effect on mean thickness and thickness loss variations.

Keywords: Tunisian handmade carpet, loss of pile height, dynamic loads, performance

Procedia PDF Downloads 321