Search results for: generalized correlations

Authors: M. Tarawneh

Abstract:

This work is an experimental study on the heat transfer characteristics and pressure drop of different refrigerants during the condensation and evaporation processes in porous media. Four different refrigerants (R134a, R407C, 600a, R290), with different porosities were used to reach a real understanding of the actual heat transfer characteristics and pressure drop when using porous material inside the condenser and evaporator. Steel balls were used as porous media with different porosities (38%, 43%, 48%). The main goal of this project is to enhance the heat transfer coefficient during the condensation and evaporation processes when using different refrigerants and different porosities. Different correlations for the heat transfer coefficient and the pressure drop of the different refrigerants were developed. Also a generalized empirical correlation was developed for the different refrigerants. The experimental and predicted heat transfer coefficients and pressure drops were compared. It was found that, the Absolute standard deviation for the heat transfer coefficient and the pressure drop not exceeded values of 15% and 20%, respectively.

Keywords: condensation, evaporation, porous media, horizontal tubes, heat transfer coefficient, propane, butane

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Authors: Ines Elouedi, Atef Hammouda

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This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

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Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

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‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Wei Feilong

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In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

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Authors: Vinod Kumar Jaysaval, Prateek Agarwal

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Performance prediction of airborne radar is a challenging and cumbersome task in clutter scenario for different types of targets. A generalized model requires to predict the performance of Radar for air targets as well as ground moving targets. In this paper, we propose a generalized model to bring out the performance of airborne radar for different Pulsed Repetition Frequency (PRF) as well as different type of targets. The model provides a platform to bring out different subsystem parameters for different applications and performance requirements under different types of clutter terrain.

Keywords: airborne radar, blind zone, clutter, probability of detection

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Authors: Retius Chifurira

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Logistic regression model is the most used regression model to predict meteorological drought probabilities. When the dependent variable is extreme, the logistic model fails to adequately capture drought probabilities. In order to adequately predict drought probabilities, we use the generalized linear model (GLM) with the quantile function of the generalized extreme value distribution (GEVD) as the link function. The method maximum likelihood estimation is used to estimate the parameters of the generalized extreme value (GEV) regression model. We compare the performance of the logistic and the GEV regression models in predicting drought probabilities for Zimbabwe. The performance of the regression models are assessed using the goodness-of-fit tests, namely; relative root mean square error (RRMSE) and relative mean absolute error (RMAE). Results show that the GEV regression model performs better than the logistic model, thereby providing a good alternative candidate for predicting drought probabilities. This paper provides the first application of GLM derived from extreme value theory to predict drought probabilities for a drought-prone country such as Zimbabwe.

Keywords: generalized extreme value distribution, general linear model, mean annual rainfall, meteorological drought probabilities

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Authors: Wikanda Phaphan

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Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

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Authors: Muqaddas Javed, Muhammad Hanif

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The generalized multivariate ratio and regression type estimators for population mean are suggested under multi-phase stratified systematic sampling (MPSSS) using multi auxiliary information. Estimators are developed under the two different situations of availability of auxiliary information. The expressions of bias and mean square error (MSE) are developed. Special cases of suggested estimators are also discussed and simulation study is conducted to observe the performance of estimators.

Keywords: generalized estimators, multi-phase sampling, stratified random sampling, systematic sampling

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Authors: Shams Alyusof

Abstract:

This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Weisi Guo

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It is well established that there may be running correlations in sequential exam marks due to students sitting in the order of course registration patterns. As such, a random and non-sequential sampling of exam marks is a standard recommended practice. Here, the paper examines a large number of exam data stretching several years across different modules to see the degree to which it is true. Using the real mark distribution as a generative process, it was found that random simulated data had no more sequential randomness than the real data. That is to say, the running correlations that one often observes are statistically identical to chance. Digging deeper, it was found that some high running correlations have students that indeed share a common course history and make similar mistakes. However, at the statistical scale of a module question, the combined effect is statistically similar to the random shuffling of papers. As such, there may not be the need to take random samples for marks, but it still remains good practice to mark papers in a random sequence to reduce the repetitive marking bias and errors.

Keywords: data analysis, empirical study, exams, marking

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Authors: Weiwen Li, Hao Huang, Chengmao You, Jianji Liao, Lei Wang, Lina An

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Zooplankton are a central issue in the ecology which makes a great contribution to maintaining the balance of an ecosystem. It is critical in promoting the material cycle and energy flow within the ecosystems. A generalized additive model (GAM) was applied to analyze the relationships between the density (individuals per m³) of zooplankton and other variables in West Daya Bay. All data used in this analysis (the survey month, survey station (longitude and latitude), the depth of the water column, the superficial concentration of chlorophyll a, the benthonic concentration of chlorophyll a, the number of zooplankton species and the number of zooplankton species) were collected through monthly scientific surveys during January to December 2016. GLM model (generalized linear model) was used to choose the significant variables’ impact on the density of zooplankton, and the GAM was employed to analyze the relationship between the density of zooplankton and the significant variables. The results showed that the density of zooplankton increased with an increase of the benthonic concentration of chlorophyll a, but decreased with a decrease in the depth of the water column. Both high numbers of zooplankton species and the overall total number of zooplankton individuals led to a higher density of zooplankton.

Keywords: density, generalized linear model, generalized additive model, the West Daya Bay, zooplankton

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Authors: Hany Elsaid Fawaz Abdallah

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This study presents a new artificial neural network(ANN) model to predict the Nusselt Number and pressure drop for the turbulent flow in a triangular corrugated plate heat exchanger for forced air and turbulent water flow. An experimental investigation was performed to create a new dataset for the Nusselt Number and pressure drop values in the following range of dimensionless parameters: The plate corrugation angles (from 0° to 60°), the Reynolds number (from 10000 to 40000), pitch to height ratio (from 1 to 4), and Prandtl number (from 0.7 to 200). Based on the ANN performance graph, the three-layer structure with {12-8-6} hidden neurons has been chosen. The training procedure includes back-propagation with the biases and weight adjustment, the evaluation of the loss function for the training and validation dataset and feed-forward propagation of the input parameters. The linear function was used at the output layer as the activation function, while for the hidden layers, the rectified linear unit activation function was utilized. In order to accelerate the ANN training, the loss function minimization may be achieved by the adaptive moment estimation algorithm (ADAM). The ‘‘MinMax’’ normalization approach was utilized to avoid the increase in the training time due to drastic differences in the loss function gradients with respect to the values of weights. Since the test dataset is not being used for the ANN training, a cross-validation technique is applied to the ANN network using the new data. Such procedure was repeated until loss function convergence was achieved or for 4000 epochs with a batch size of 200 points. The program code was written in Python 3.0 using open-source ANN libraries such as Scikit learn, TensorFlow and Keras libraries. The mean average percent error values of 9.4% for the Nusselt number and 8.2% for pressure drop for the ANN model have been achieved. Therefore, higher accuracy compared to the generalized correlations was achieved. The performance validation of the obtained model was based on a comparison of predicted data with the experimental results yielding excellent accuracy.

Keywords: artificial neural networks, corrugated channel, heat transfer enhancement, Nusselt number, pressure drop, generalized correlations

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Authors: Oluwafunmibi Omotayo Fasanya, Augustine Kena Adjei

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Effective management of hypertension remains a critical public health challenge, particularly among racially and ethnically diverse populations. This study employs sophisticated statistical models to rigorously investigate the predictors of poor blood pressure (BP) control, with a specific focus on demographic, socioeconomic, and clinical risk factors. Leveraging a large sample of 19,253 adults drawn from the National Health and Nutrition Examination Survey (NHANES) across three distinct time periods (2013-2014, 2015-2016, and 2017-2020), we applied multivariable logistic regression and generalized estimating equations (GEE) to account for the clustered structure of the data and potential within-subject correlations. Our multivariable models identified significant associations between poor BP control and several key predictors, including race/ethnicity, age, gender, body mass index (BMI), prevalent diabetes, and chronic kidney disease (CKD). Non-Hispanic Black individuals consistently exhibited higher odds of poor BP control across all periods (OR = 1.99; 95% CI: 1.69, 2.36 for the overall sample; OR = 2.33; 95% CI: 1.79, 3.02 for 2017-2020). Younger age groups demonstrated substantially lower odds of poor BP control compared to individuals aged 75 and older (OR = 0.15; 95% CI: 0.11, 0.20 for ages 18-44). Men also had a higher likelihood of poor BP control relative to women (OR = 1.55; 95% CI: 1.31, 1.82), while BMI ≥35 kg/m² (OR = 1.76; 95% CI: 1.40, 2.20) and the presence of diabetes (OR = 2.20; 95% CI: 1.80, 2.68) were associated with increased odds of poor BP management. Further analysis using GEE models, accounting for temporal correlations and repeated measures, confirmed the robustness of these findings. Notably, individuals with chronic kidney disease displayed markedly elevated odds of poor BP control (OR = 3.72; 95% CI: 3.09, 4.48), with significant differences across the survey periods. Additionally, higher education levels and better self-reported diet quality were associated with improved BP control. College graduates exhibited a reduced likelihood of poor BP control (OR = 0.64; 95% CI: 0.46, 0.89), particularly in the 2015-2016 period (OR = 0.48; 95% CI: 0.28, 0.84). Similarly, excellent dietary habits were associated with significantly lower odds of poor BP control (OR = 0.64; 95% CI: 0.44, 0.94), underscoring the importance of lifestyle factors in hypertension management. In conclusion, our findings provide compelling evidence of the complex interplay between demographic, clinical, and socioeconomic factors in predicting poor BP control. The application of advanced statistical techniques such as GEE enhances the reliability of these results by addressing the correlated nature of repeated observations. This study highlights the need for targeted interventions that consider racial/ethnic disparities, clinical comorbidities, and lifestyle modifications in improving BP control outcomes.

Keywords: hypertension, blood pressure, NHANES, generalized estimating equations

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Yohei Saika

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On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, multiple interferograms, statistical mechanics

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Authors: Vladimir Mantsevich, Natalya Maslova, Petr Arseyev

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We investigated the tunneling current peculiarities in the system of two coupled by means of the external field quantum dots (QDs) weakly connected to the electrodes in the presence of Coulomb correlations between localized electrons by means of Heisenberg equations for pseudo operators with constraint. Special role of multi-electronic states was demonstrated. Various single-electron levels location relative to the sample Fermi level and to the applied bias value in symmetric tunneling contact were investigated. Rabi frequency tuning results in the single-electron energy levels spacing. We revealed the appearance of negative tunneling conductivity and demonstrated multiple switching "on" and "off" of the tunneling current depending on the Coulomb correlations value, Rabi frequency amplitude and energy levels spacing. We proved that Coulomb correlations strongly influence the system behavior. We demonstrated the presence of multi-stability in the coupled QDs with Coulomb correlations when single value of the tunneling current amplitude corresponds to the two values of Rabi frequency in the case when both single-electron energy levels are located slightly above eV and are close to each other. This effect disappears when the single-electron energy levels spacing increases.

Keywords: Coulomb correlations, negative tunneling conductivity, quantum dots, rabi frequency

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Khuram Shahzad, Omar Usman Khan

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Quantum bit string comparators (QBSC) operate on two sequences of n-qubits, enabling the determination of their relationships, such as equality, greater than, or less than. This is analogous to the way conditional statements are used in programming languages. Consequently, QBSCs play a crucial role in various algorithms that can be executed or adapted for quantum computers. The development of efficient and generalized comparators for any n-qubit length has long posed a challenge, as they have a high-cost footprint and lead to quantum delays. Comparators that are efficient are associated with inputs of fixed length. As a result, comparators without a generalized circuit cannot be employed at a higher level, though they are well-suited for problems with limited size requirements. In this paper, we introduce a generalized design for the comparison of two n-qubit logic states using just two ancillary bits. The design is examined on the basis of qubit requirements, ancillary bit usage, quantum cost, quantum delay, gate operations, and circuit complexity and is tested comprehensively on various input lengths. The work allows for sufficient flexibility in the design of quantum algorithms, which can accelerate quantum algorithm development.

Keywords: quantum comparator, quantum algorithm, space-efficient comparator, comparator

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Authors: Shiva Abdoli, Daniel T.Semere

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Several researches have been conducted to study consumption of energy in cutting process. Most of these researches are focusing to measure the consumption and propose consumption reduction methods. In this work, the relation between the cutting parameters and the consumption is investigated in order to establish a generalized energy consumption model that can be used for process and production planning in real production lines. Using the generalized model, the process planning will be carried out by taking into account the energy as a function of the selected process parameters. Similarly, the generalized model can be used in production planning to select the right operational parameters like batch sizes, routing, buffer size, etc. in a production line. The description and derivation of the model as well as a case study are given in this paper to illustrate the applicability and validity of the model.

Keywords: process parameters, cutting process, energy efficiency, Material Removal Rate (MRR)

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Authors: Imaneh Abbasi, Ladan Fata, Majid Sadeghi, Sara Banihashemi, Abolfazl Mohammadee

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Background: Dimensional and transdiagnostic approaches as a result of high comorbidity among mental disorders have captured researchers and clinicians interests for exploring the latent factors of development and maintenance of some psychological disorders. The goal of present study is to compare some of these common factors between generalized anxiety disorder and unipolar mood disorder. Methods: 27 patients with generalized anxiety disorder, 29 patients with depression disorder were recruited using SCID-I and 69 non-clinical population were selected using GHQ cut off point. MANCOVA was used for analyzing data. Results: The results show that worry, rumination, intolerance of uncertainty, maladaptive metacognitive beliefs, and experiential avoidance were all significantly different between GAD and unipolar mood disorder groups. However, there were not any significant differences in difficulties in emotion regulation and neuroticism between GAD and unipolar mood disorder groups. Discussion: Results indicate that although there are some transdiagnostic and common factors in GAD and unipolar mood disorder, there may be some specific vulnerability factors for each disorder. Further study is needed for answering these questions.

Keywords: transdiagnostic, depression, generalized anxiety disorder, emotion regulation

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Authors: Caroline E. Mendes, Alberto C. Badino

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Pneumatic reactors have been widely employed in various sectors of the chemical industry, especially where are required high heat and mass transfer rates. This study aimed to obtain correlations that allow the prediction of gas hold-up (Ԑ) and volumetric oxygen transfer coefficient (kLa), and compare these values, for three models of pneumatic reactors on two scales utilizing Newtonian fluids. Values of kLa were obtained using the dynamic pressure-step method, while  was used for a new proposed measure. Comparing the three models of reactors studied, it was observed that the mass transfer was superior to draft-tube airlift, reaching  of 0.173 and kLa of 0.00904s-1. All correlations showed good fit to the experimental data (R2≥94%), and comparisons with correlations from the literature demonstrate the need for further similar studies due to shortage of data available, mainly for airlift reactors and high viscosity fluids.

Keywords: bubble column, internal loop airlift, gas hold-up, kLa

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Authors: Nada Farhani, Naim Terbeh, Mounir Zrigui

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The recognition of the objects contained in images has always presented a challenge in the field of research because of several difficulties that the researcher can envisage because of the variability of shape, position, contrast of objects, etc. In this paper, we will be interested in the recognition of objects. The classical Hough Transform (HT) presented a tool for detecting straight line segments in images. The technique of HT has been generalized (GHT) for the detection of arbitrary forms. With GHT, the forms sought are not necessarily defined analytically but rather by a particular silhouette. For more precision, we proposed to combine the results from the GHT with the results from a calculation of similarity between the histograms and the spatiograms of the images. The main purpose of our work is to use the concepts from recognition to generate sentences in Arabic that summarize the content of the image.

Keywords: recognition of shape, generalized hough transformation, histogram, spatiogram, learning

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Authors: Amit Tribedi

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Genuine Quantumness present in Quantum Systems is the resource for implementing Quantum Information and Computation Protocols which can outperform the classical counterparts. These Quantumness measures encompass non-local ones known as quantum entanglement (QE) and quantum information theoretic (QIT) ones, e.g. Quantum Discord (QD). In this paper, some well-known measures of QE and QD in some wheel-like frustrated molecular magnetic systems have been studied. One of the systems has already been synthesized using coordination chemistry, and the other is hypothetical, where the dominant interaction is the spin-spin exchange interaction. Exact analytical methods and exact numerical diagonalization methods have been used. Some counter-intuitive non-trivial features, like non-monotonicity of quantum correlations with temperature, persistence of multipartite entanglement over bipartite ones etc. indicated by the behaviour of the correlations and the QIT measures have been found. The measures, being operational ones, can be used to realize the resource of Quantumness in experiments.

Keywords: 0D Magnets, discord, entanglement, frustration

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Authors: M. Guemmadi, A. Ouibrahim

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This numerical investigation aims to evaluate how a viscoelastic lubricant described by a generalized Maxwell model, affects the pressure distribution, the load capacity and thermal effect in a journal bearing lubrication. We use for the purpose the CFD package software completed by adapted user define functions (UDFs) to solve the coupled equations of momentum, of energy and of the viscoelastic model (generalized Maxwell model). Two parameters, viscosity and relaxation time are involved to show how viscoelasticity substantially affect the pressure distribution, the load capacity and the thermal transfer by comparison to Newtonian lubricant. These results were also compared with the available published results.

Keywords: journal bearing, lubrication, Maxwell model, viscoelastic fluids, computational modelling, load capacity

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Authors: O. Anan, D. Böhning, A. Maruotti

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The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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Authors: Kailash C. Madan

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We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times is compulsory and the second service with general service times is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server must take a vacation of random length of time with general vacation times. We obtain steady state probability generating functions for the queue size as well as the steady state mean queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.

Keywords: batch arrivals, compound Poisson process, generalized Coxian-2 service, steady state

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Authors: Rohan Erasala, Ian McCulloh

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The NFL Draft is a chance for every NFL team to select their next superstar. As a result, teams heavily invest in scouting, and millions of fans partake in the online discourse surrounding the draft. This paper investigates the potential correlations between positive sentiment in individual draft selection threads from the subreddit r/NFL and if this data can be used to make successful player recommendations. It is hypothesized that there will be limited correlations and nonviable recommendations made from these threads. The hypothesis is tested using sentiment analysis of draft thread comments and analyzing correlation and precision at k of top scores. The results indicate weak correlations between the percentage of positive comments in a draft selection thread and a player’s approximate value, but potentially viable recommendations from looking at players whose draft selection threads have the highest percentage of positive comments.

Keywords: national football league, NFL, NFL Draft, sentiment analysis, Reddit, social media, NLP

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Authors: Ahmed El-Banbi, Ahmed El-Maraghi

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PVT properties are needed as input data in all reservoir, production, and surface facilities engineering calculations. In the absence of PVT reports on valid reservoir fluid samples, engineers rely on PVT correlations to generate the required PVT data. The accuracy of PVT correlations varies, and no correlation group has been found to provide accurate results for all oil types. The effect of inaccurate PVT data can be significant in engineering calculations and is well documented in the literature. Bubble point pressure can sometimes be obtained from external sources. In this paper, we show how to utilize the known bubble point pressure to improve the accuracy of calculated PVT properties from correlations. We conducted a systematic study using around 250 reservoir oil samples to quantify the effect of pre-knowledge of bubble point pressure. The samples spanned a wide range of oils, from very volatile oils to black oils and all the way to low-GOR oils. A method for shifting both undersaturated and saturated sections of the PVT properties curves to the correct bubble point is explained. Seven PVT correlation families were used in this study. All PVT properties (e.g., solution gas-oil ratio, formation volume factor, density, viscosity, and compressibility) were calculated using the correct bubble point pressure and the correlation estimated bubble point pressure. Comparisons between the calculated PVT properties and actual laboratory-measured values were made. It was found that pre-knowledge of bubble point pressure and using the shifting technique presented in the paper improved the correlation-estimated values by 10% to more than 30%. The most improvement was seen in the solution gas-oil ratio and formation volume factor.

Keywords: PVT data, PVT properties, PVT correlations, bubble point pressure

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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