Search results for: generalized estimating equations

Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Muhammad Sameer Ahmed, Piotr Remlein, Tansal Gucluoglu

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The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

Keywords: free space optics, generalized frequency division multiplexing, weather conditions, gamma gamma distribution

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Alireza Abbasi Moshaii, Shaghayegh Nasiri, Mehdi Tale Masouleh

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The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3-RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. Mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, their CAD model has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: robotic, static analysis, 3-RCC, 3-RRS

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Authors: A. Ishag Mohamed, A. A. Rabah

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The objective of this research is to develop a generalized correlation for the prediction of thermal conductivity of n-Alkanes and Alkenes. There is a minority of research and lack of correlation for thermal conductivity of liquids in the open literature. The available experimental data are collected covering the groups of n-Alkanes and Alkenes.The data were assumed to correlate to temperature using Filippov correlation. Nonparametric regression of Grace Algorithm was used to develop the generalized correlation model. A spread sheet program based on Microsoft Excel was used to plot and calculate the value of the coefficients. The results obtained were compared with the data that found in Perry's Chemical Engineering Hand Book. The experimental data correlated to the temperature ranged "between" 273.15 to 673.15 K, with R2 = 0.99.The developed correlation reproduced experimental data that which were not included in regression with absolute average percent deviation (AAPD) of less than 7 %. Thus the spread sheet was quite accurate which produces reliable data.

Keywords: N-Alkanes, N-Alkenes, nonparametric, regression

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Authors: Lizhou Chen, Abdelhamid Belgaid, Assem Elsayed, Xiaoming Yang

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Compression index is essential in foundation settlement calculation. The traditional method for determining compression index is consolidation test which is expensive and time consuming. Many researchers have used regression methods to develop empirical equations for predicting compression index from soil properties. Based on a large number of compression index data collected from consolidation tests, the accuracy of some popularly empirical equations were assessed. It was found that primary compression index is significantly overestimated in some equations while it is underestimated in others. The sensitivity analyses of soil parameters including water content, liquid limit and void ratio were performed. The results indicate that the compression index obtained from void ratio is most accurate. The ANOVA (analysis of variance) demonstrates that the equations with multiple soil parameters cannot provide better predictions than the equations with single soil parameter. In other words, it is not necessary to develop the relationships between compression index and multiple soil parameters. Meanwhile, it was noted that secondary compression index is approximately 0.7-5.0% of primary compression index with an average of 2.0%. In the end, the proposed prediction equations using power regression technique were provided that can provide more accurate predictions than those from existing equations.

Keywords: compression index, clay, settlement, consolidation, secondary compression index, soil parameter

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Authors: Wajdi Mohamed Ratemi

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The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Abdullah Alhomidan

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This study is conducted to identify the main factors affecting accuracy of pretender cost estimate in building construction projects in Saudi Arabia from owners’ perspective. 44 factors affecting pretender cost estimate were identified through literature review and discussion with some construction experts. The results show that the top important factors affecting pretender cost estimate accuracy are: level of competitors in the tendering, material price changes, communications with suppliers, communications with client, and estimating method used.

Keywords: cost estimate, accuracy, pretender, estimating, bid estimate

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: H. R. Fazlollahi

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Dark Energy origin is unknown and so describing this mysterious component in large scale structure needs to manipulate our theories in general relativity. Although in most models, dark energy arises from extra terms through modifying Einstein-Hilbert action, maybe its origin traces back to fundamental aspects of ground energy of space-time given in quantum mechanics. Hence, diluting space-time in general relativity with quantum mechanics properties leads to the Karolyhazy relation corresponding energy density of quantum fluctuations of space-time. Through generalized uncertainty principle and an eye to Karolyhazy approach in this study we extend energy density of quantum fluctuations of space-time. Also, the application of this idea is considered in late time evolution and we have shown how extra term in generalized uncertainty principle plays as a plausible interaction term role in suggested model.

Keywords: generalized uncertainty principle, karolyhazy approach, agegraphic dark energy, cosmology

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Authors: Davood Yazdani Cherati, Ali Pak, Mehrdad Jafarzadeh

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This research contains the formulation of a two-dimensional analytical solution to transient heat, and moisture flow in a semi-infinite unsaturated soil environment under the influence of daily temperature changes. For this purpose, coupled energy conservation and mass fluid continuity equations governing hydrothermal behavior of unsaturated soil media are presented in terms of temperature and volumetric moisture content. In consideration of the soil environment as an infinite half-space and by linearization of the governing equations, Laplace–Fourier transformation is conducted to convert differential equations with partial derivatives (PDEs) to ordinary differential equations (ODEs). The obtained ODEs are solved, and the inverse transformations are calculated to determine the solution to the system of equations. Results indicate that heat variation induces moisture transport in both horizontal and vertical directions.

Keywords: analytical solution, heat conduction, hydrothermal analysis, laplace–fourier transformation, two-dimensional

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Jyh Sheen, Yong-Lin Wang

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This research dedicates to find a different measurement procedure of microwave dielectric properties of ceramic materials with high dielectric constants. For the composite of ceramic dispersed in the polymer matrix, the dielectric constants of the composites with different concentrations can be obtained by various mixture equations. The other development of mixture rule is to calculate the permittivity of ceramic from measurements on composite. To do this, the analysis method and theoretical accuracy on six basic mixture laws derived from three basic particle shapes of ceramic fillers have been reported for dielectric constants of ceramic less than 40 at microwave frequency. Similar researches have been done for other well-known mixture rules. They have shown that both the physical curve matching with experimental results and low potential theory error are important to promote the calculation accuracy. Recently, a modified of mixture equation for high dielectric constant ceramics at microwave frequency has also been presented for strontium titanate (SrTiO3) which was selected from five more well known mixing rules and has shown a good accuracy for high dielectric constant measurements. However, it is still not clear the accuracy of this modified equation for other high dielectric constant materials. Therefore, the five more well known mixing rules are selected again to understand their application to other high dielectric constant ceramics. The other high dielectric constant ceramic, TiO2 with dielectric constant 100, was then chosen for this research. Their theoretical error equations are derived. In addition to the theoretical research, experimental measurements are always required. Titanium dioxide is an interesting ceramic for microwave applications. In this research, its powder is adopted as the filler material and polyethylene powder is like the matrix material. The dielectric constants of those ceramic-polyethylene composites with various compositions were measured at 10 GHz. The theoretical curves of the five published mixture equations are shown together with the measured results to understand the curve matching condition of each rule. Finally, based on the experimental observation and theoretical analysis, one of the five rules was selected and modified to a new powder mixture equation. This modified rule has show very good curve matching with the measurement data and low theoretical error. We can then calculate the dielectric constant of pure filler medium (titanium dioxide) by those mixing equations from the measured dielectric constants of composites. The accuracy on the estimating dielectric constant of pure ceramic by various mixture rules will be compared. This modified mixture rule has also shown good measurement accuracy on the dielectric constant of titanium dioxide ceramic. This study can be applied to the microwave dielectric properties measurements of other high dielectric constant ceramic materials in the future.

Keywords: microwave measurement, dielectric constant, mixture rules, composites

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Authors: Babak Safaei, A. M. Fattahi

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Polymer/carbon nanotube nanocomposites have a wide range of promising applications Due to their enhanced properties. In this work, free vibration analysis of single-walled carbon nanotube-reinforced composite plates is conducted in which carbon nanotubes are embedded in an amorphous polyethylene. The rule of mixture based on various types of plate model namely classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT) was employed to obtain fundamental frequencies of the nanocomposite plates. Generalized differential quadrature (GDQ) method was used to discretize the governing differential equations along with the simply supported and clamped boundary conditions. The material properties of the nanocomposite plates were evaluated using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites. Then the results obtained directly from MD simulations were fitted with those calculated by the rule of mixture to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results are presented to address the influences of nanotube volume fraction and edge supports on the value of fundamental frequency of carbon nanotube-reinforced composite plates corresponding to both long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, free vibration, generalized, differential quadrature (GDQ) method

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Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

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In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

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Authors: Adewoyin O. Olusegun, Emmanuel O. Joshua, Marvel L. Akinyemi

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The heterogeneous nature of the subsurface requires the use of factual information to deal with rather than assumptions or generalized equations. Therefore, there is need to determine the actual rate of settlement possible in the soil before structures are built on it. This information will help in determining the type of foundation design and the kind of reinforcement that will be necessary in constructions. This paper presents a simplified and a faster approach for determining foundation settlement in any type of soil using real field data acquired from seismic refraction techniques and cone penetration tests. This approach was also able to determine the depth of settlement of each strata of soil. The results obtained revealed the different settlement time and depth of settlement possible.

Keywords: heterogeneous, settlement, foundation, seismic, technique

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations

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Authors: Jose Francisco Ferreira Ribeiro, Alexandre Bevilacqua Leoneti, Andre Lucirton Costa

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This paper presents a mathematical model in binary variables 0/1 to make the assignment of surgical procedures to the operating rooms in a hospital. The proposed mathematical model is based on the generalized assignment problem, which maximizes the sum of preferences for the use of the operating rooms by doctors, respecting the time available in each room. The corresponding program was written in Visual Basic of Microsoft Excel, and tested to schedule surgeries at St. Lydia Hospital in Ribeirao Preto, Brazil.

Keywords: generalized assignment problem, logistics, optimization, scheduling

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, temperature extremes are forecast by employing the block maxima method of the generalized extreme value (GEV) distribution to analyse temperature data from the Cameroon Development Corporation (CDC). By considering two sets of data (raw data and simulated data) and two (stationary and non-stationary) models of the GEV distribution, return levels analysis is carried out and it was found that in the stationary model, the return values are constant over time with the raw data, while in the simulated data the return values show an increasing trend with an upper bound. In the non-stationary model, the return levels of both the raw data and simulated data show an increasing trend with an upper bound. This clearly shows that although temperatures in the tropics show a sign of increase in the future, there is a maximum temperature at which there is no exceedance. The results of this paper are very vital in agricultural and environmental research.

Keywords: forecasting, generalized extreme value (GEV), meteorology, return level

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