Search results for: parametric function

Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

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Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: graphic parameterization, green building design, mathematical model, plane form

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Authors: Aya M. H. Eissa, Ayman H. A. Mahmoud

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When it comes to energy efficient thermal regulation system, natural systems do not only offer an inspirational source of innovative strategies but also sustainable and even regenerative ones. Using biomimetic design an energy efficient thermal regulation system can be developed. Although, conventional design process methods achieved fairly efficient systems, they still had limitations which can be overcome by using parametric design software. Accordingly, the main objective of this study is to apply and assess the efficiency of heat regulation strategies inspired from termite mounds in residential buildings’ thermal regulation system. Parametric design software is used to pave the way for further and more complex biomimetic design studies and implementations. A hot arid region is selected due to the deficiency of research in this climatic region. First, the analysis phase in which the stimuli, affecting, and the parameters, to be optimized, are set mimicking the natural system. Then, based on climatic data and using parametric design software Grasshopper, building form and openings height and areas are altered till settling on an optimized solution. Finally, an assessment of the efficiency of the optimized system, in comparison with a conventional system, is determined by firstly, indoors airflow and indoors temperature, by Ansys Fluent (CFD) simulation. Secondly by and total solar radiation falling on the building envelope, which was calculated using Ladybug, Grasshopper plugin. The results show an increase in the average indoor airflow speed from 0.5m/s to 1.5 m/s. Also, a slight decrease in temperature was noticed. And finally, the total radiation was decreased by 4%. In conclusion, despite the fact that applying a single bio-inspired heat regulation strategy might not be enough to achieve an optimum system, the concluded system is more energy efficient than the conventional ones as it aids achieving indoors comfort through passive techniques. Thus demonstrating the potential of parametric design software in biomimetic design.

Keywords: biomimicry, heat regulation systems, hot arid regions, parametric design, thermal comfort

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Authors: Pushpendra S. Bharti

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Process yield of electric discharge machining (EDM) is directly related to optimal combination(s) of process parameters. Optimization of process parameters of EDM is a multi-objective optimization problem owing to the contradictory behavior of performance measures. This paper employs Grey Relation Analysis (GRA) method as a multi-objective optimization technique for the optimal selection of process parameters combination. In GRA, multi-response optimization is converted into optimization of a single response grey relation grade which ultimately gives the optimal combination of process parameters. Experiments were carried out on die-sinking EDM by taking D2 steel as work piece and copper as electrode material. Taguchi's orthogonal array L36 was used for the design of experiments. On the experimental values, GRA was employed for the parametric optimization. A significant improvement has been observed and reported in the process yield by taking the parametric combination(s) obtained through GRA.

Keywords: electric discharge machining, grey relation analysis, material removal rate, optimization

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Philip Speranza

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As everyday transit options are shifting from autocentric to pedestrian and bicycle oriented modes for healthy living, downtown streets are becoming more attractive places to live. However, tools and methods to measure the natural environment at the small scale of streets do not exist. Fortunately, a combination of mobile data collection technology and parametric urban design software now allows an interface to relate urban ecological conditions. This paper describes creation of an interactive tool to measure urban phenomena of air, water, and heat/light at the scale of new three-by-three block pedestrianized areas in Barcelona called Superilles. Each Superilla limits transit to the exterior of the blocks and to create more walkable and bikeable interior streets for healthy living. The research will describe the integration of data collection, analysis, and design output via a live interface using parametric software Rhino Grasshopper and the Human User Interface (UI) plugin.

Keywords: transit, urban design, GIS, parametric design, Superilles, Barcelona, urban ecology

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

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The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

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Authors: Junaid Kameran Ahmed

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A laminated plate composite of graphite/epoxy has been analyzed dynamically in the present work by using a quadratic element (8-node diso-parametric), and by depending on 1^st order shear deformation theory, every node in this element has 6-degrees of freedom (displacement in x, y, and z axis and twist about x, y, and z axis). The dynamic analysis in the present work covered parametric studies on a composite laminated plate (square plate) to determine its effect on the natural frequency of the plate. The parametric study is represented by set of changes (plate thickness, number of layers, support conditions, layer orientation), and the plates have been simulated by using ANSYS package 12. The boundary conditions considered in this study, at all four edges of the plate, are simply supported and fixed boundary condition. The results obtained from ANSYS program show that the natural frequency for both fixed and simply supported increases with increasing the number of layers, but this increase in the natural frequency for the first five modes will be neglected after 10 layers. And it is observed that the natural frequency of a composite laminated plate will change with the change of ply orientation, the natural frequency increases and it will be at maximum with angle 45 of ply for simply supported laminated plate, and maximum natural frequency will be with cross-ply (0/90) for fixed laminated composite plate. It is also observed that the natural frequency increase is approximately doubled when the thickness is doubled.

Keywords: laminated plate, orthotropic plate, square plate, natural frequency (free vibration), composite (graphite / epoxy)

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Authors: Naga Velamakuri, Jyothi K. Reddy

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Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.

Keywords: quality function deployment, modular function deployment, house of quality, methodology

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Authors: Robert Pečenko, Karin Tomažič, Igor Planinc, Sabina Huč, Tomaž Hozjan

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Timber is favourable structural material due to high strength to weight ratio, recycling possibilities, and green credentials. Despite being flammable material, it has relatively high fire resistance. Everyday engineering practice around the word is based on an outdated design of timber structures considering standard fire exposure, while modern principles of performance-based design enable use of advanced non-standard fire curves. In Europe, standard for fire design of timber structures EN 1995-1-2 (Eurocode 5) gives two methods, reduced material properties method and reduced cross-section method. In the latter, fire resistance of structural elements depends on the effective cross-section that is a residual cross-section of uncharred timber reduced additionally by so called zero strength layer. In case of standard fire exposure, Eurocode 5 gives a fixed value of zero strength layer, i.e. 7 mm, while for non-standard parametric fires no additional comments or recommendations for zero strength layer are given. Thus designers often implement adopted 7 mm rule also for parametric fire exposure. Since the latest scientific evidence suggests that proposed value of zero strength layer can be on unsafe side for standard fire exposure, its use in the case of a parametric fire is also highly questionable and more numerical and experimental research in this field is needed. Therefore, the purpose of the presented study is to use advanced calculation methods to investigate the thickness of zero strength layer and parametric charring rates used in effective cross-section method in case of parametric fire. Parametric studies are carried out on a simple solid timber beam that is exposed to a larger number of parametric fire curves Zero strength layer and charring rates are determined based on the numerical simulations which are performed by the recently developed advanced two step computational model. The first step comprises of hygro-thermal model which predicts the temperature, moisture and char depth development and takes into account different initial moisture states of timber. In the second step, the response of timber beam simultaneously exposed to mechanical and fire load is determined. The mechanical model is based on the Reissner’s kinematically exact beam model and accounts for the membrane, shear and flexural deformations of the beam. Further on, material non-linear and temperature dependent behaviour is considered. In the two step model, the char front temperature is, according to Eurocode 5, assumed to have a fixed temperature of around 300°C. Based on performed study and observations, improved levels of charring rates and new thickness of zero strength layer in case of parametric fires are determined. Thus, the reduced cross section method is substantially improved to offer practical recommendations for designing fire resistance of timber structures. Furthermore, correlations between zero strength layer thickness and key input parameters of the parametric fire curve (for instance, opening factor, fire load, etc.) are given, representing a guideline for a more detailed numerical and also experimental research in the future.

Keywords: advanced numerical modelling, parametric fire exposure, timber structures, zero strength layer

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Authors: Alexander Marx

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Measuring and mitigating market risk is essential for the stability of enterprises, especially for major banking corporations and investment bank firms. To employ these risk measurement and mitigation processes, the Value at Risk (VaR) is the most commonly used risk metric by practitioners. In the past years, we have seen significant weaknesses in the predictive performance of the VaR in times of financial market crisis. To address this issue, the purpose of this study is to investigate the value-at-risk (VaR) estimation models and their predictive performance by applying a series of backtesting methods on the stock market indices of the G7 countries (Canada, France, Germany, Italy, Japan, UK, US, Europe). The study employs parametric, non-parametric, and semi-parametric VaR estimation models and is conducted during three different periods which cover the most recent financial market crisis: the overall period (2006–2022), the global financial crisis period (2008–2009), and COVID-19 period (2020–2022). Since the regulatory authorities have introduced and mandated the Conditional Value at Risk (Expected Shortfall) as an additional regulatory risk management metric, the study will analyze and compare both risk metrics on their predictive performance.

Keywords: value at risk, financial market risk, banking, quantitative risk management

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Authors: Apurv Kulkarni, Shreyas Badave, B. Rajiv

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Non-parametric reliability technique is useful for assessment of reliability of systems for which failure rates are not available. This is useful when detection of malfunctioning of any component is the key purpose during ongoing operation of the system. The main purpose of the Heat Exchanger Cycle discussed in this paper is to provide hot water at a constant temperature for longer periods of time. In such a cycle, certain components play a crucial role and this paper presents an effective way to predict the malfunctioning of the components by determination of system reliability. The method discussed in the paper is feasible and this is clarified with the help of various test cases.

Keywords: heat exchanger cycle, k-statistics, PID controller, system reliability

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Authors: Hamid Ahmadi, Neda Azari-Dodaran

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A total of 270 nonlinear steady-state finite element (FE) analyses were performed on 54 FE models of two-planar circular hollow section (CHS) KK-joints subjected to axial loading at five different temperatures (20 ºC, 200 ºC, 400 ºC, 550 ºC, and 700 ºC). The primary goal was to investigate the effects of temperature and geometrical characteristics on the ultimate strength, modes of failure, and initial stiffness of the KK-joints. Results indicated that on an average basis, the ultimate load of a two-planar tubular KK-joint at 200 ºC, 400 ºC, 550 ºC, and 700 ºC is 90%, 75%, 45%, and 16% of the joint’s ultimate load at ambient temperature, respectively. Outcomes of the parametric study showed that replacing the yield stress at ambient temperature with the corresponding value at elevated temperature to apply the EN 1993-1-8 equations for the calculation of the joint’s ultimate load at elevated temperatures may lead to highly unconservative results that might endanger the safety of the structure. Results of the parametric study were then used to develop a set of design formulas, through nonlinear regression analyses, to calculate the ultimate load of two-planar tubular KK-joints subjected to axial loading at elevated temperatures.

Keywords: ultimate load, two-planar tubular KK-joint, axial loading, elevated temperature, parametric equation

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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: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Ishith Seth, Lyndel Hewitt, Takako Yabe, James Wykes, Jonathan Clark, Bruce Ashford

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Background: Vastus lateralis (VL) can be used to reconstruct defects of the head and neck. Whilst the advantages are documented, donor-site morbidity is not well described. This study aimed to assess donor-site morbidity after VL flap harvest. The results will determine future directions for preventative and post-operative care to improve patient health outcomes. Methods: Ten participants (mean age 55 years) were assessed for the presence of donor-site morbidity after VL harvest. Musculoskeletal (pain, muscle strength, muscle length, tactile sensation), quality of life (SF-12), and lower limb function (lower extremity function, gait (function and speed), sit to stand were assessed using validated and standardized procedures. Outcomes were compared to age-matched healthy reference values or the non-operative side. Analyses were conducted using descriptive statistics and non-parametric tests. Results: There was no difference in muscle strength (knee extension), muscle length, ability to sit-to-stand, or gait function (all P > 0.05). Knee flexor muscle strength was significantly less on the operated leg compared to the non-operated leg (P=0.02) and walking speed was slower than age-matched healthy values (P<0.001). Thigh tactile sensation was impaired in 89% of participants. Quality of life was significantly less for the physical health component of the SF-12 (P<0.001). The mental health component of the SF-12 was similar to healthy controls (P=0.26). Conclusion: There was no effect on donor site morbidity with regards to knee extensor strength, pain, walking function, ability to sit-to-stand, and muscle length. VL harvest affected donor-site knee flexion strength, walking speed, tactile sensation, and physical health-related quality of life.

Keywords: vastus lateralis, morbidity, head and neck, surgery, donor-site morbidity

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Authors: Nahid Banihashemi

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An emerging important area of the life sciences is systems biology, which involves understanding the integrated behavior of large numbers of components interacting via non-linear reaction terms. A centrally important problem in this area is an understanding of the co-metabolism of protein and carbohydrate, as it has been clearly demonstrated that the ratio of these metabolites in diet is a major determinant of obesity and related chronic disease. In this regard, we have considered a systems biology model for the co-metabolism of carbon and nitrogen in colonies of the fungus Mucor mucedo. Oscillations are an important diagnostic of underlying dynamical processes of this model. The maintenance of specific patterns of oscillation and its relation to the robustness of this system are the important issues which have been targeted in this paper. In this regard, parametric sensitivity approach as a theoretical approach has been considered for the analysis of the robustness of this model. As a result, the parameters of the model which produce the largest sensitivities have been identified. Furthermore, the largest changes that can be made in each parameter of the model without losing the oscillations in biomass production have been computed. The results are obtained from the implementation of parametric sensitivity analysis in Matlab.

Keywords: system biology, parametric sensitivity analysis, robustness, carbon and nitrogen co-metabolism, Mucor mucedo

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Authors: Wi-Sun Ryu, Eun-Kee Bae

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Prior studies have shown that patients with right hemispheric stroke are likely to seek medical service compared with those with left hemispheric stroke. However, the underlying mechanism for this phenomenon is unknown. In the present study, we generated lesion probability maps in a patient with right and left middle cerebral artery infarct and statistically compared. We found that precentral gyrus-Brodmann area 44, a language area in the left hemisphere - involvement was significantly higher in patients with left hemispheric stroke. This finding suggests that a language dysfunction was more noticeable, thereby taking more patients to hospitals.

Keywords: cerebral infarct, brain MRI, statistical parametric mapping, middle cerebral infarct

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Hamid Ahmadi, Amirreza Ghaffari

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Fatigue life of tubular joints in offshore structures is not only dependent on the value of hot-spot stress, but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). The DoB exhibits considerable scatter calling for greater emphasis in accurate determination of its governing probability distribution which is a key input for the fatigue reliability analysis of a tubular joint. Although the tubular X-joints are commonly found in offshore jacket structures, as far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB in tubular X-joints. What has been used so far as the probability distribution of the DoB in reliability analyses is mainly based on assumptions and limited observations, especially in terms of distribution parameters. In the present paper, results of parametric equations available for the calculation of the DoB have been used to develop probability distribution models for the DoB in the chord member of tubular X-joints subjected to four types of bending loads. Based on a parametric study, a set of samples was prepared and density histograms were generated for these samples using Freedman-Diaconis method. Twelve different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood method was utilized to determine the parameters of fitted distributions. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs have been proposed for the DoB in tubular X-joints subjected to bending loads.

Keywords: tubular X-joint, degree of bending (DoB), probability density function (PDF), Kolmogorov-Smirnov goodness-of-fit test

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Authors: D. Sigirli

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The Receiver Operating Characteristic (ROC) curve is a commonly used statistical tool for evaluating the diagnostic performance of screening and diagnostic test with continuous or ordinal scale results which aims to predict the presence or absence probability of a condition, usually a disease. When the test results were measured as numeric values, sensitivity and specificity can be computed across all possible threshold values which discriminate the subjects as diseased and non-diseased. There are infinite numbers of possible decision thresholds along the continuum of the test results. The ROC curve presents the trade-off between sensitivity and the 1-specificity as the threshold changes. The empirical ROC curve which is a non-parametric estimator of the ROC curve is robust and it represents data accurately. However, especially for small sample sizes, it has a problem of variability and as it is a step function there can be different false positive rates for a true positive rate value and vice versa. Besides, the estimated ROC curve being in a jagged form, since the true ROC curve is a smooth curve, it underestimates the true ROC curve. Since the true ROC curve is assumed to be smooth, several smoothing methods have been explored to smooth a ROC curve. These include using kernel estimates, using log-concave densities, to fit parameters for the specified density function to the data with the maximum-likelihood fitting of univariate distributions or to create a probability distribution by fitting the specified distribution to the data nd using smooth versions of the empirical distribution functions. In the present paper, we aimed to propose a smooth ROC curve estimation based on the boundary corrected kernel function and to compare the performances of ROC curve smoothing methods for the diagnostic test results coming from different distributions in different sample sizes. We performed simulation study to compare the performances of different methods for different scenarios with 1000 repetitions. It is seen that the performance of the proposed method was typically better than that of the empirical ROC curve and only slightly worse compared to the binormal model when in fact the underlying samples were generated from the normal distribution.

Keywords: empirical estimator, kernel function, smoothing, receiver operating characteristic curve

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Authors: Nabaouia.Maktouf, Ali Ben Moussa, Saïd Turki

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This paper discusses the effect of an attached flexible membrane on the control of fluid around a circular cylinder. A parametric study has been investigated for different positions, sizes, modes as well as frequencies of oscillation of the flexible membrane. The numerical investigation was conducted for a Reynolds number equal to 150 using the commercial code Fluent 16.0 and parallel calculation into 4 processors. The motion of the flexible membrane was managed by the dynamic mesh and compiled into Fluent as a user-defined function. The first part of this paper discusses the effect of changing the position of a flexible membrane sized 8° as an angle of aperture on the aerodynamic coefficients. Results show that the flexible membrane placed at 110° from the stagnation point presents more non-linearity on the behavior of the drag coefficient compared to the drag behavior when placed at 180°, relative to the stagnation point. The effect of the size of the flexible surface was studied for the corresponding angles of aperture: 32° and 42°, respectively. The effect of modes (modes 1, 2, and 3) of vibrations has been investigated at a constant frequency of vibration f=2Hz for angles 32° and 42°. All the calculations have been done with a constant amplitude A =0.001m. A non-linearity of the drag coefficient was clearly observed for all the sizes, modes as well as frequencies of excitation. The Fast Fourier transformation shows the appearance of the natural shedding frequency and the multiples of the frequency of excitation. An increase in the modes of oscillation leads to a more linear behavior of the drag coefficient.

Keywords: fluid flow control, numerical simulation, dynamic mesh, aerodynamic forces, flexible membrane

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: Lanyan Peng, Ling Chen

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Leishan Miao New-Year is one of the grandest festivals in the southeastern of Guizhou Province in China. It was officially listed in the National Intangible Cultural Heritage List in 2008, as a traditional folk cultural activity organized by the local Miao people. With the rise of cultural tourism, after 19 years of exploration, the local government has successfully built Miao New-Year into a cultural card that is well-known at home and abroad. During the Miao New-Year period, it has attracted 3.8 million tourists and achieves a win-win situation in the economy and culture. However, tourism development has changed the living environment and living state of the local people. And it is accompanied by changes in the form of the festival, the content of the festival, and the local people’s needs and attitudes to the festival. This paper uses the field investigation method to achieve 410 questionnaires and 35 interviews, exploring the process and the reasons for changes of Leishan Miao New-Year’s cultural function. Among all the functions, the economic function, identity function, and entertainment function have been enhanced, and the marriage and love function has been extended. In the meanwhile, sacrificial function has been weakened. There are some trends in functions. The function of commemorating ancestor and self-entertainment has been changed to entertaining people and economic pursuit.

Keywords: Miao New-Year, Miao nationality, festival function, changes

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Authors: Nursel Koyuncu, Nihal Ata Tutkun

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Frailty model is a survival model that takes into account the unobserved heterogeneity for exploring the relationship between the survival of an individual and several covariates. In the recent years, proposed survival models become more complex and this feature causes convergence problems especially in large data sets. Therefore selection of sample from these big data sets is very important for estimation of parameters. In sampling literature, some authors have defined new sampling schemes to predict the parameters correctly. For this aim, we try to see the effect of sampling design in semi-parametric frailty model. We conducted a simulation study in R programme to estimate the parameters of semi-parametric frailty model for different sample sizes, censoring rates under classical simple random sampling and ranked set sampling schemes. In the simulation study, we used data set recording 17260 male Civil Servants aged 40–64 years with complete 10-year follow-up as population. Time to death from coronary heart disease is treated as a survival-time and age, systolic blood pressure are used as covariates. We select the 1000 samples from population using different sampling schemes and estimate the parameters. From the simulation study, we concluded that ranked set sampling design performs better than simple random sampling for each scenario.

Keywords: frailty model, ranked set sampling, efficiency, simple random sampling

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Mohammed A. Sakr, Tarek M. Khalifa, Walid N. Mansour

Abstract:

External bonding of fiber reinforced polymer (FRP) plates to reinforced concrete (RC) beams is an effective technique for flexural strengthening. This paper presents an analytical parametric study on the behavior of RC continuous beams flexurally strengthened with externally bonded FRP plates on the upper and lower fibers, conducted using simple uniaxial nonlinear finite element model (UNFEM). UNFEM is able to estimate the load-carrying capacity, different failure modes and the interfacial stresses of RC continuous beams flexurally strengthened with externally bonded FRP plates on the upper and lower fibers. The study investigated the effect of five key parameters on the behavior and moment redistribution of FRP-reinforced continuous beams. The investigated parameters were the length of the FRP plate, the width and the thickness of the FRP plate, the ratio between the area of the FRP plate to the concrete area, the cohesive shear strength of the adhesive layer, and the concrete compressive strength. The investigation resulted in a number of important conclusions reflecting the effects of the studied parameters on the behavior of RC continuous beams flexurally strengthened with externally bonded FRP plates.

Keywords: continuous beams, parametric study, finite element, fiber reinforced polymer

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