Search results for: non linear function

Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand

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Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models on two different realworld electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.

Keywords: EHR, machine learning, imputation, laboratory variables, algorithmic bias

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Authors: Tunjo Perič, Marin Fatović

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In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology is tested on the example of flour purchase for a bakery with two decision makers.

Keywords: cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection

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Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

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Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

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Authors: Taha Zakaraia Abdel Wahid

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The behavior of the unsteady non-equilibrium distribution function for a dilute gas under the effect of non-linear thermal radiation field is presented. For the best of our knowledge this is done for the first time at all. The distinction and comparisons between the unsteady perturbed and the unsteady equilibrium velocity distribution functions are illustrated. The equilibrium time for the dilute gas is determined for the first time. The non-equilibrium thermodynamic properties of the system (gas+the heated plate) are investigated. The results are applied to the Argon gas, for various values of radiation field intensity. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior. The results are discussed.

Keywords: dilute gas, radiation field, exact solutions, travelling wave method, unsteady BGK model, irreversible thermodynamics, unsteady non-equilibrium distribution functions

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Authors: Alev Atak

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We study the endogeneity in the cryptocurrency market over the branching ratio of the Hawkes process and evaluate the movement of self-excitability in the financial markets. We consider a semi-parametric self-exciting point process regression model where the excitation function is assumed to be smooth and decreasing but otherwise unspecified, and the baseline intensity is assumed to be a linear function of the regressors. We apply the empirical analysis to the three largest crypto assets, i.e. Bitcoin - Ethereum - Ripple, and provide a comparison with other financial assets such as SP500, Gold, and the volatility index VIX observed from January 2015 to December 2020. The results depict variable and high levels of endogeneity in the basket of cryptocurrencies under investigation, underlining the evidence of a significant role of endogenous feedback mechanisms in the price formation process.

Keywords: hawkes process, cryptocurrency, endogeneity, reflexivity

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Authors: Zunaira Asif, Zhi Chen

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The sustainable measures on air quality management are recognized as one of the most serious environmental concerns in the mining region. The mining operations emit various types of pollutants which have significant impacts on the environment. This study presents a stochastic control strategy by developing the air pollution control model to achieve a cost-effective solution. The optimization method is formulated to predict the cost of treatment using linear programming with an objective function and multi-constraints. The constraints mainly focus on two factors which are: production of metal should not exceed the available resources, and air quality should meet the standard criteria of the pollutant. The applicability of this model is explored through a case study of an open pit metal mine, Utah, USA. This method simultaneously uses meteorological data as a dispersion transfer function to support the practical local conditions. The probabilistic analysis and the uncertainties in the meteorological conditions are accomplished by Monte Carlo simulation. Reasonable results have been obtained to select the optimized treatment technology for PM_2.5, PM₁₀, NO_x, and SO₂. Additional comparison analysis shows that baghouse is the least cost option as compared to electrostatic precipitator and wet scrubbers for particulate matter, whereas non-selective catalytical reduction and dry-flue gas desulfurization are suitable for NO_x and SO₂ reduction respectively. Thus, this model can aid planners to reduce these pollutants at a marginal cost by suggesting control pollution devices, while accounting for dynamic meteorological conditions and mining activities.

Keywords: air pollution, linear programming, mining, optimization, treatment technologies

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor

Procedia PDF Downloads 113

Authors: D. Glamowska, K. Szymkowska, K. Mojsiewicz- Pieńkowska, K. Cal, Z. Jankowski

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Introduction: The integrity of the outermost layer of skin (stratum corneum) is vital to the penetration of various compounds, including toxic substances. Barrier function of skin depends of its structure. The barrier function of the stratum corneum is provided by patterned lipid lamellae (binlayer). However, a lot of substances, including the low molecular methyl siloxanes (volatile methyl siloxanes, VMS) have an impact on alteration the skin barrier due to damage of stratum corneum structure. VMS belong to silicones. They are widely used in the pharmaceutical as well as cosmetic industry. Silicones fulfill the role of ingredient or excipient in medicinal products and the excipient in personal care products. Due to the significant human exposure to this group of compounds, an important aspect is toxicology of the compounds and safety assessment of products. Silicones in general opinion are considered as a non-toxic substances, but there are some data about their negative effect on living organisms through the inhaled or oral application. However, the transdermal route has not been described in the literature as a possible alternative route of penetration. The aim of the study was to verify the possibility of penetration of the stratum corneum, further permeation into the deeper layers of the skin (epidermis and dermis) as well as to the fluid acceptor by VMS. Methods: Research methodology was developed based on the OECD and WHO guidelines. In ex-vivo study, the fluorescence microscope and ATR FT-IR spectroscopy was used. The Franz- type diffusion cells were used to application of the VMS on the sample of human skin (A=0.65 cm) for 24h. The stratum corneum at the application site was tape-stripped. After separation of epidermis, relevant dyes: fluorescein, sulforhodamine B, rhodamine B hexyl ester were put on and observations were carried in the microscope. To confirm the penetration and permeation of the cyclic or linear VMS and thus the presence of silicone in the individual layers of the skin, spectra ATR FT-IR of the sample after application of silicone and H2O (control sample) were recorded. The research included comparison of the intesity of bands in characteristic positions for silicones (1263 cm-1, 1052 cm-1 and 800 cm-1). Results: and Conclusions The results present that cyclic and linear VMS are able to overcome the barrier of the skin. Influence of them on damage of corneocytes of the stratum corneum was observed. This phenomenon was due to distinct disturbances in the lipid structure of the stratum corneum. The presence of cyclic and linear VMS were identified in the stratum corneum, epidermis as well as in the dermis by both fluorescence microscope and ATR FT-IR spectroscopy. This confirms that the cyclic and linear VMS can penetrate to stratum corneum and permeate through the human skin layers. Apart from this they cause changes in the structure of the skin. Results show to possible absorption into the blood and lymphathic vessels by the VMS with linear and cyclic structure.

Keywords: low molecular methyl siloxanes, volatile methyl siloxanes, linear and cyclic siloxanes, skin penetration, skin permeation

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Authors: Guermache Ahmed Chafik, Khelfellah Ismail, Ait-Ali Takfarines

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The Savonius vertical axis wind turbine is characterized by sufficient starting torque at low wind speeds, simple design and does not require orientation to the wind direction; however, the developed power is lower than other types of wind turbines such as Darrieus. To increase these performances several studies and researches have been developed, such as optimizing blades shape, using passive controls and also minimizing power losses sources like the resisting torque due to friction. This work aims to estimate the performance of a Savonius wind turbine introducing a User Defined Function to the CFD model analyzing resisting torque. This User Defined Function is developed to simulate the action of the wind speed on the rotor; it receives the moment coefficient as an input to compute the rotational velocity that should be imposed on computational domain rotating regions. The rotational velocity depends on the aerodynamic moment applied on the turbine and the resisting torque, which is considered a linear function. Linking the implemented User Defined Function with the CFD solver allows simulating the real functioning of the Savonius turbine exposed to wind. It is noticed that the wind turbine takes a while to reach the stationary regime where the rotational velocity becomes invariable; at that moment, the tip speed ratio, the moment and power coefficients are computed. To validate this approach, the power coefficient versus tip speed ratio curve is compared with the experimental one. The obtained results are in agreement with the available experimental results.

Keywords: resistant torque modeling, Savonius wind turbine, user-defined function, vertical axis wind turbine performances

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Authors: Nureni O. Adeboye, Dawud A. Agunbiade

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This research attempts to investigate the effects of heteroscedasticity and periodicity in a Panel Data Regression Model (PDRM) by extending previous works on balanced panel data estimation within the context of fitting PDRM for Banks audit fee. The estimation of such model was achieved through the derivation of Joint Lagrange Multiplier (LM) test for homoscedasticity and zero-serial correlation, a conditional LM test for zero serial correlation given heteroscedasticity of varying degrees as well as conditional LM test for homoscedasticity given first order positive serial correlation via a two-way error component model. Monte Carlo simulations were carried out for 81 different variations, of which its design assumed a uniform distribution under a linear heteroscedasticity function. Each of the variation was iterated 1000 times and the assessment of the three estimators considered are based on Variance, Absolute bias (ABIAS), Mean square error (MSE) and the Root Mean Square (RMSE) of parameters estimates. Eighteen different models at different specified conditions were fitted, and the best-fitted model is that of within estimator when heteroscedasticity is severe at either zero or positive serial correlation value. LM test results showed that the tests have good size and power as all the three tests are significant at 5% for the specified linear form of heteroscedasticity function which established the facts that Banks operations are severely heteroscedastic in nature with little or no periodicity effects.

Keywords: audit fee lagrange multiplier test, heteroscedasticity, lagrange multiplier test, Monte-Carlo scheme, periodicity

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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: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Tarek Sayed Taha Ali

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The dependence of the axial-vector coupling constant gA on the quark masses has been investigated in the frame work of the extended linear sigma model. The field equations have been solved in the mean-field approximation. Our study shows a better fitting to the experimental data compared with the existing models.

Keywords: extended linear sigma model, nucleon properties, axial coupling constant, physic

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Authors: Yanisa Chaiya, Jintana Sanwong

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Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: Marin Mandić, Elis Sutlović, Tonći Modrić, Luka Stanić

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With the restructuring and deregulation of the power system, storage owners, generation companies or private producers can offer their multiple services on various power markets and earn income in different types of markets, such as the day-ahead, real-time, ancillary services market, etc. During the COVID-19 pandemic, electricity prices, as well as ancillary services prices, increased significantly. The optimization of the energy storage operation was performed using a suitable model for simulating the operation of a pumped storage hydropower plant under market conditions. The objective function maximizes the income earned through energy arbitration, regulation-up, regulation-down and spinning reserve services. The optimization technique used for solving the objective function is mixed integer linear programming (MILP). In numerical examples, the pumped storage hydropower plant operation has been optimized considering the already achieved hourly electricity market prices from Nord Pool for the pre-pandemic (2019) and the pandemic (2020 and 2021) years. The impact of the electricity market prices during the COVID-19 pandemic on energy storage operation is shown through the analysis of income, operating hours, reserved capacity and consumed energy for each service. The results indicate the role of energy storage during a significant fluctuation in electricity and services prices.

Keywords: electrical market prices, electricity market, energy storage optimization, mixed integer linear programming (MILP) optimization

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Authors: Manlika Ratchagit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, Lyapunov functional, linear matrix inequalities

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Authors: Manlika Rajchakit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, lyapunov functional, linear matrix inequalities

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Authors: Saeed Otarod

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

Keywords: explicit, linear, differential, closed form

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Authors: 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: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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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: Joseph Thomas Eghwerido, Julian I. Mbegbu

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In modelling environment processes, we apply multidisciplinary knowledge to explain, explore and predict the Earth's response to natural human-induced environmental changes. Thus, the analysis of spatial-time ecological and environmental studies, the spatial parameters of interest are always heterogeneous. This often negates the assumption of stationarity. Hence, the dispersion of the transportation of atmospheric pollutants, landscape or topographic effect, weather patterns depends on a good estimate of spatial covariance. The generalized linear mixed model, although linear in the expected value parameters, its likelihood varies nonlinearly as a function of the covariance parameters. As a consequence, computing estimates for a linear mixed model requires the iterative solution of a system of simultaneous nonlinear equations. In other to predict the variables at unsampled locations, we need to know the estimate of the present sampled variables. The geostatistical methods for solving this spatial problem assume covariance stationarity (locally defined covariance) and uniform in space; which is not apparently valid because spatial processes often exhibit nonstationary covariance. Hence, they have globally defined covariance. We shall consider different existing methods of solutions of spatial covariance of a space-time processes at unsampled locations. This stationary covariance changes with locations for multiple time set with some asymptotic properties.

Keywords: parametric, nonstationary, Kernel, Kriging

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Authors: Ksenija Dumičić, Anita Čeh Časni, Irena Palić

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This paper examines economic and Information and Communication Technology (ICT) development influence on recently increasing Internet purchases by individuals for European Union member states. After a growing trend for Internet purchases in EU27 was noticed, all possible regression analysis was applied using nine independent variables in 2011. Finally, two linear regression models were studied in detail. Conducted simple linear regression analysis confirmed the research hypothesis that the Internet purchases in analysed EU countries is positively correlated with statistically significant variable Gross Domestic Product per capita (GDPpc). Also, analysed multiple linear regression model with four regressors, showing ICT development level, indicates that ICT development is crucial for explaining the Internet purchases by individuals, confirming the research hypothesis.

Keywords: European union, Internet purchases, multiple linear regression model, outlier

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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: Stojan Kravanja, Andrej Ivanič, Tomaž Žula

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This contribution focuses on structural optimization in civil engineering using mixed integer non-linear programming (MINLP). MINLP is characterized as a versatile method that can handle both continuous and discrete optimization variables simultaneously. Continuous variables are used to optimize parameters such as dimensions, stresses, masses, or costs, while discrete variables represent binary decisions to determine the presence or absence of structural elements within a structure while also calculating discrete materials and standard sections. The optimization process is divided into three main steps. First, a mechanical superstructure with a variety of different topology-, material- and dimensional alternatives. Next, a MINLP model is formulated to encapsulate the optimization problem. Finally, an optimal solution is searched in the direction of the defined objective function while respecting the structural constraints. The economic or mass objective function of the material and labor costs of a structure is subjected to the constraints known from structural analysis. These constraints include equations for the calculation of internal forces and deflections, as well as equations for the dimensioning of structural components (in accordance with the Eurocode standards). Given the complex, non-convex and highly non-linear nature of optimization problems in civil engineering, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is applied. This algorithm alternately solves subproblems of non-linear programming (NLP) and main problems of mixed-integer linear programming (MILP), in this way gradually refines the solution space up to the optimal solution. The NLP corresponds to the continuous optimization of parameters (with fixed topology, discrete materials and standard dimensions, all determined in the previous MILP), while the MILP involves a global approximation to the superstructure of alternatives, where a new topology, materials, standard dimensions are determined. The optimization of a convex problem is stopped when the MILP solution becomes better than the best NLP solution. Otherwise, it is terminated when the NLP solution can no longer be improved. While the OA/ER algorithm, like all other algorithms, does not guarantee global optimality due to the presence of non-convex functions, various modifications, including convexity tests, are implemented in OA/ER to mitigate these difficulties. The effectiveness of the proposed MINLP approach is demonstrated by its application to various structural optimization tasks, such as mass optimization of steel buildings, cost optimization of timber halls, composite floor systems, etc. Special optimization models have been developed for the optimization of these structures. The MINLP optimizations, facilitated by the user-friendly software package MIPSYN, provide insights into a mass or cost-optimal solutions, optimal structural topologies, optimal material and standard cross-section choices, confirming MINLP as a valuable method for the optimization of structures in civil engineering.

Keywords: MINLP, mixed-integer non-linear programming, optimization, structures

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Authors: Glenda Marie D. Balitaan

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The branch of business management that deals with inventory planning and control is known as inventory management. It comprises keeping track of supply levels and forecasting demand, as well as scheduling when and how to plan. Keeping excess inventory results in a loss of money, takes up physical space, and raises the risk of damage, spoilage, and loss. On the other hand, too little inventory frequently causes operations to be disrupted and raises the possibility of low customer satisfaction, both of which can be detrimental to a company's reputation. The United Victorious Feed mill Corporation's present inventory management practices were assessed in terms of inventory level, warehouse allocation, ordering frequency, shelf life, and production requirement. To help the company achieve their optimal level of inventory, a mathematical model was created using Integer Linear Programming. Due to the season, the goal function was to reduce the cost of purchasing US Soya and Yellow Corn. Warehouse space, annual production requirements, and shelf life were all considered. To ensure that the user only uses one application to record all relevant information, like production output and delivery, the researcher built a Visual Basic system. Additionally, the technology allows management to change the model's parameters.

Keywords: inventory management, integer linear programming, inventory management system, feed mill

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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: 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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