Search results for: Quadratic objective function.

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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Authors: Hsuan-Chu Li

Abstract:

We demonstrate a way to count the number of Young tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding Schur function. This result gives an answer to the question that was put out by Jenny Buontempo and Brian Hopkins.

Keywords: Young tableau, Schur function.

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Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

Abstract:

In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Marko A. Rodriguez

Abstract:

There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

Abstract:

For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: Differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization.

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Authors: Moataz M. Naguib, Hatem Khater, A. Baith Mohamed

Abstract:

MARS is a shared-key (symmetric) block cipher algorithm supporting 128-bit block size and a variable key size of between 128 and 448 bits. MARS has a several rounds of cryptographic core that is designed to take advantage of the powerful results for improving security/performance tradeoff over existing ciphers. In this work, a new function added to improve the ciphering process it is called, Meta-Morphic function. This function use XOR, Rotating, Inverting and No-Operation logical operations before and after encryption process. The aim of these operations is to improve MARS cipher process and makes a high confusion criterion for the Ciphertext.

Keywords: AES, MARS, Metamorphic, Cryptography, Block Cipher.

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Authors: Rishabh Garg

Abstract:

Blockchain technology can allow remote, untrusted parties in the banking and financial sector to reach consensus on the state of databases without the involvement of gatekeepers. Like a bookkeeper, it can manage all financial transactions including payments, settlements, fundraising, securities management, loans, credits and trade finance. It can outperform existing systems in terms of identity verification, asset transfers, peer-to-peer transfers, hedge funds, security and auditability. Blockchain-based decentralized finance (DeFi) is a new financial protocol. Being open and programmable, it enables various DeFi use-cases, including asset management, tokenization, tokenized derivatives, decentralized autonomous organizations, data analysis and valuation, payments, lending and borrowing, insurance, margin trading, prediction market, gambling and yield-farming, etc. In addition, it can ease financial transactions, cash-flow, use of programmable currency, no-loss lotteries, etc. This paper aims to assess the potential of decentralized finance by leveraging the blockchain-enabled Ethereum platform as an alternative to traditional finance. The study also aims to find out the impact of decentralized finance on prediction markets, quadratic funding and crowd-funding, together with the potential challenges and solutions associated with its implementation.

Keywords: Advance trading, crowd funding, exchange tokens, fund aggregation, margin trading, quadratic funding, smart contracts, streaming money, token derivatives.

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Authors: Satyasen Panda, Urmila Bhanja

Abstract:

In this paper, we have presented and analyzed three-dimensional (3-D) matrices of wavelength/time/space code for optical code division multiple access (OCDMA) networks with NAND subtraction detection technique. The 3-D codes are constructed by integrating a two-dimensional modified quadratic congruence (MQC) code with one-dimensional modified prime (MP) code. The respective encoders and decoders were designed using fiber Bragg gratings and optical delay lines to minimize the bit error rate (BER). The performance analysis of the 3D-OCDMA system is based on measurement of signal to noise ratio (SNR), BER and eye diagram for a different number of simultaneous users. Also, in the analysis, various types of noises and multiple access interference (MAI) effects were considered. The results obtained with NAND detection technique were compared with those obtained with OR and AND subtraction techniques. The comparison results proved that the NAND detection technique with 3-D MQC\MP code can accommodate more number of simultaneous users for longer distances of fiber with minimum BER as compared to OR and AND subtraction techniques. The received optical power is also measured at various levels of BER to analyze the effect of attenuation.

Keywords: Cross correlation, three-dimensional optical code division multiple access, spectral amplitude coding optical code division multiple access, multiple access interference, phase induced intensity noise, three-dimensional modified quadratic congruence/modified prime code.

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Authors: Mehmet Bozca

Abstract:

Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.

Keywords: Singular value, optimisation, gearbox, torsional vibration.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

Abstract:

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: Francisco Aparisi, Marco A. de Luna

Abstract:

In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.

Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.

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Authors: R. Uthayakumar, G. Arockia Prabakar

Abstract:

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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Authors: Hamid Abdi, Abolfazl Salami, Abolfazl Ahmadi

Abstract:

Programmable logic controllers are the main controllers in the today's industries; they are used for several applications in industrial control systems and there are lots of examples exist from the PLC applications in industries especially in big companies and plants such as refineries, power plants, petrochemical companies, steel companies, and food and production companies. In the PLCs there are some functions in the function library in software that can be used in PLC programs as basic program elements. The aim of this project are introducing and implementing a new function block of a neural network to the function library of PLC. This block can be applied for some control applications or nonlinear functions calculations after it has been trained for these applications. The implemented neural network is a Perceptron neural network with three layers, three input nodes and one output node. The block can be used in manual or automatic mode. In this paper the structure of the implemented function block, the parameters and the training method of the network are presented by considering the especial method of PLC programming and its complexities. Finally the application of the new block is compared with a classic simulated block and the results are presented.

Keywords: Programmable Logic Controller, PLC Programming, Neural Networks, Perception Network, Intelligent Control.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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Authors: A. H. Fatah, A. H. Ahmed

Abstract:

Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Keywords: Gamma-Ray, Spectrum analysis, Non-linear leastsquare fitting.

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Authors: Shun Horikoshi, Tohru Kawabe

Abstract:

This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: Sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis.

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Authors: Manoochehr Gholipoor

Abstract:

The response of growth and yield of rainfed-chickpea to population density should be evaluated based on long-term experiments to include the climate variability. This is achievable just by simulation. In this simulation study, this evaluation was done by running the CYRUS model for long-term daily weather data of five locations in Iran. The tested population densities were 7 to 59 (with interval of 2) stands per square meter. Various functions, including quadratic, segmented, beta, broken linear, and dent-like functions, were tested. Considering root mean square of deviations and linear regression statistics [intercept (a), slope (b), and correlation coefficient (r)] for predicted versus observed variables, the quadratic and broken linear functions appeared to be appropriate for describing the changes in biomass and grain yield, and in harvest index, respectively. Results indicated that in all locations, grain yield tends to show increasing trend with crowding the population, but subsequently decreases. This was also true for biomass in five locations. The harvest index appeared to have plateau state across low population densities, but decreasing trend with more increasing density. The turning point (optimum population density) for grain yield was 30.68 stands per square meter in Isfahan, 30.54 in Shiraz, 31.47 in Kermanshah, 34.85 in Tabriz, and 32.00 in Mashhad. The optimum population density for biomass ranged from 24.6 (in Tabriz) to 35.3 stands per square meter (Mashhad). For harvest index it varied between 35.87 and 40.12 stands per square meter.

Keywords: Rainfed-chickpea, biomass, harvest index, grain yield, simulation.

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Authors: Ahmed A. A. Radwan, Bahgat A. Abdel Latef, Abdel Mgeid A. Ali, Osman A. Sadek

Abstract:

This study investigates the use of genetic algorithms in information retrieval. The method is shown to be applicable to three well-known documents collections, where more relevant documents are presented to users in the genetic modification. In this paper we present a new fitness function for approximate information retrieval which is very fast and very flexible, than cosine similarity fitness function.

Keywords: Cosine similarity, Fitness function, Genetic Algorithm, Information Retrieval, Query learning.

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Authors: Seyed Habib A. Rahmati

Abstract:

During last decades, developing multi-objective evolutionary algorithms for optimization problems has found considerable attention. Flexible job shop scheduling problem, as an important scheduling optimization problem, has found this attention too. However, most of the multi-objective algorithms that are developed for this problem use nonprofessional approaches. In another words, most of them combine their objectives and then solve multi-objective problem through single objective approaches. Of course, except some scarce researches that uses Pareto-based algorithms. Therefore, in this paper, a new Pareto-based algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our considered objectives are makespan, critical machine work load, and total work load of machines. The proposed algorithm is also compared with one the best Pareto-based algorithms of the literature on some multi-objective criteria, statistically.

Keywords: Scheduling, Flexible job shop scheduling problem, controlled elitism non-dominated sorting genetic algorithm

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Authors: Nurcan Tuncbag, Turkan Haliloglu, Ozlem Keskin

Abstract:

Understanding the cell's large-scale organization is an interesting task in computational biology. Thus, protein-protein interactions can reveal important organization and function of the cell. Here, we investigated the correspondence between protein interactions and function for the yeast. We obtained the correlations among the set of proteins. Then these correlations are clustered using both the hierarchical and biclustering methods. The detailed analyses of proteins in each cluster were carried out by making use of their functional annotations. As a result, we found that some functional classes appear together in almost all biclusters. On the other hand, in hierarchical clustering, the dominancy of one functional class is observed. In the light of the clustering data, we have verified some interactions which were not identified as core interactions in DIP and also, we have characterized some functionally unknown proteins according to the interaction data and functional correlation. In brief, from interaction data to function, some correlated results are noticed about the relationship between interaction and function which might give clues about the organization of the proteins, also to predict new interactions and to characterize functions of unknown proteins.

Keywords: Pair-wise protein interactions, DIP database, functional correlations, biclustering.

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Authors: Komeil Jahanifar, Zahra Abedi, Yaghob Zeraatkish

Abstract:

This research was conducted for the first time at the southeastern coasts of the Caspian Sea in order to evaluate the performance of osteichthyes cooperatives through production (catch) function. Using one of the indirect valuation methods in this research, contributory factors in catch were identified and were inserted into the function as independent variables. In order to carry out this research, the performance of 25 Osteichthyes catching cooperatives in the utilization year of 2009 which were involved in fishing in Miankale wildlife refuge region. The contributory factors in catch were divided into groups of economic, ecological and biological factors. In the mentioned function, catch rate of the cooperative were inserted into as the dependant variable and fourteen partial variables in terms of nine general variables as independent variables. Finally, after function estimation, seven variables were rendered significant at 99 percent reliably level. The results of the function estimation indicated that human resource (fisherman quantity) had the greatest positive effect on catch rate with an influence coefficient of 1.7 while weather conditions had the greatest negative effect on the catch rate of cooperatives with an influence coefficient of -2.07. Moreover, factors like member's share, experience and fisherman training and fishing effort played the main roles in the catch rate of cooperative with influence coefficients of 0.81, 0.5 and 0.21, respectively.

Keywords: Production Function, Coefficient, Variable, Osteichthyes, Caspian Sea

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Authors: H. Hosseini, M. Javadi, M. Moghiman, M. H. Ghodsi Rad

Abstract:

Carbon disulfide is widely used for the production of viscose rayon, rubber, and other organic materials and it is a feedstock for the synthesis of sulfuric acid. The objective of this paper is to analyze possibilities for efficient production of CS2 from sour natural gas reformation (H2SMR) (2H2S+CH4 =CS2 +4H2) . Also, the effect of H2S to CH4 feed ratio and reaction temperature on carbon disulfide production is investigated numerically in a reforming reactor. The chemical reaction model is based on an assumed Probability Density Function (PDF) parameterized by the mean and variance of mixture fraction and β-PDF shape. The results show that the major factors influencing CS2 production are reactor temperature. The yield of carbon disulfide increases with increasing H2S to CH4 feed gas ratio (H2S/CH4≤4). Also the yield of C(s) increases with increasing temperature until the temperature reaches to 1000°K, and then due to increase of CS2 production and consumption of C(s), yield of C(s) drops with further increase in the temperature. The predicted CH4 and H2S conversion and yield of carbon disulfide are in good agreement with result of Huang and TRaissi.

Keywords: Carbon disulfide, sour natural gas, H2SMR, probability density function.

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Authors: Ruhugül Özge Ocak, Banu Öztürk Kurtaslan

Abstract:

Botanical gardens are very significant organizations which protect the environment against the increasing environmental problems, provide environmental education for people, offer recreation possibilities, etc. This article describes botanical gardens and their functions. The most important function of botanical garden is to provide environmental education for people and improve environmental awareness. Considering this function, some botanical gardens were examined and opinions were suggested about the subject.

Keywords: Botanical garden, environment, environmental education, recreation.

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Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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Authors: Rafik Medjoudj, Rabah Medjoudj, D. Aissani

Abstract:

The electrical substation components are often subject to degradation due to over-voltage or over-current, caused by a short circuit or a lightning. A particular interest is given to the circuit breaker, regarding the importance of its function and its dangerous failure. This component degrades gradually due to the use, and it is also subject to the shock process resulted from the stress of isolating the fault when a short circuit occurs in the system. In this paper, based on failure mechanisms developments, the wear out of the circuit breaker contacts is modeled. The aim of this work is to evaluate its reliability and consequently its residual lifetime. The shock process is based on two random variables such as: the arrival of shocks and their magnitudes. The arrival of shocks was modeled using homogeneous Poisson process (HPP). By simulation, the dates of short-circuit arrivals were generated accompanied with their magnitudes. The same principle of simulation is applied to the amount of cumulative wear out contacts. The objective reached is to find the formulation of the wear function depending on the number of solicitations of the circuit breaker.

Keywords: reliability, short-circuit, models of shocks.

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Authors: Mahmood Reza Shakarami, Reza Sedaghati

Abstract:

Recently, distributed generation technologies have received much attention for the potential energy savings and reliability assurances that might be achieved as a result of their widespread adoption. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering wind turbines. The main objective of the DFR is to minimize the deviation of the bus voltage. Since the DFR is a nonlinear optimization problem, we apply the Adaptive Modified Firefly Optimization (AMFO) approach to solve it. As a result of the conflicting behavior of the single- objective function, a fuzzy based clustering technique is employed to reach the set of optimal solutions called Pareto solutions. The approach is tested on the IEEE 32-bus standard test system.

Keywords: Adaptive Modified Firefly Optimization (AMFO), Pareto solutions, feeder reconfiguration, wind turbines, bus voltage.

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Authors: F. Sarhaddi, S. Farahat, M .A. Alavi, F. Sobhnamayan

Abstract:

In this paper, an attempt has been made to obtain nonsensitive solutions in the multi-objective optimization of a photovoltaic/thermal (PV/T) air collector. The selected objective functions are overall energy efficiency and exergy efficiency. Improved thermal, electrical and exergy models are used to calculate the thermal and electrical parameters, overall energy efficiency, exergy components and exergy efficiency of a typical PV/T air collector. A computer simulation program is also developed. The results of numerical simulation are in good agreement with the experimental measurements noted in the previous literature. Finally, multi-objective optimization has been carried out under given climatic, operating and design parameters. The optimized ranges of inlet air velocity, duct depth and the objective functions in optimal Pareto front have been obtained. Furthermore, non-sensitive solutions from energy or exergy point of view in the results of multi-objective optimization have been shown.

Keywords: Solar photovoltaic thermal (PV/T) air collector, Overall energy efficiency, Exergy efficiency, Multi-objectiveoptimization, Sensitivity analysis.

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Authors: N. Tuncbag, T. Haliloglu, O. Keskin

Abstract:

Understanding the cell's large-scale organization is an interesting task in computational biology. Thus, protein-protein interactions can reveal important organization and function of the cell. Here, we investigated the correspondence between protein interactions and function for the yeast. We obtained the correlations among the set of proteins. Then these correlations are clustered using both the hierarchical and biclustering methods. The detailed analyses of proteins in each cluster were carried out by making use of their functional annotations. As a result, we found that some functional classes appear together in almost all biclusters. On the other hand, in hierarchical clustering, the dominancy of one functional class is observed. In brief, from interaction data to function, some correlated results are noticed about the relationship between interaction and function which might give clues about the organization of the proteins.

Keywords: Pair-wise protein interactions, DIP database, functional correlations, biclustering.

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Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: Channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow.

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