Search results for: radial function

Authors: Mahmoud Samkan

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Dispersed Generation (DG) is a promising solution to many power system problems such as voltage regulation and power loss. This paper proposes a heuristic two-step method to optimize the location and size of DG for reducing active power losses and, therefore, improve the voltage profile in radial distribution networks. In addition to a DG placed at the system load gravity center, this method consists in assigning a DG to each lateral of the network. After having determined the central DG placement, the location and size of each lateral DG are predetermined in the first step. The results are then refined in the second step. This method is tested for 33-bus system for 100% DG penetration. The results obtained are compared with those of other methods found in the literature.

Keywords: optimal location, optimal size, dispersed generation (DG), radial distribution networks, reducing losses

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

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

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

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Authors: Srikanta Tagore Sarkar, Prasanta Kumar Mandal, Dibakar Roy

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The association of a capitate fracture with a scaphoid fracture has been termed as the naviculocapitate syndrome. The existence of some nondisplaced fractures of scaphoid and capitate with or without the fracture of lunate or radius suggests that there is a spectrum of these injuries, and this confuses the terminology. With our case; we report an unusual variety of this naviculocapitate syndrome with distal radial Colles fracture in addition to the nondisplaced fractures of the scaphoid, capitate and the dorsal lip of radial fracture. When we looked at the literature there is no another Colles fracture reported together with undisplaced scapho-capitate syndrome. The coronal and sagittal images that obtained from the MDCT (Multidetector computed tomography) is useful and effective imaging modality to diagnose complex wrist fractures with more details that are not detected in X-rays.

Keywords: scaphoid, capitate, Colles’ fracture, syndrome, MDCT, unusual

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Authors: Mohammad Reza Rahimi Khoygani, Reza Ghasemi

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In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results.

Keywords: adaptive control, pendulum dynamical system, nonlinear control, adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Naga Velamakuri, Jyothi K. Reddy

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

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

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Authors: Ali Kadir, S. R. Mishra, M. Shamshuddin, O. Anwar Beg

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Motivation- Rotating disk bio-reactors are fundamental to numerous medical/biochemical engineering processes including oxygen transfer, chromatography, purification and swirl-assisted pumping. The modern upsurge in biologically-enhanced engineering devices has embraced new phenomena including bioconvection of micro-organisms (photo-tactic, oxy-tactic, gyrotactic etc). The proven thermal performance superiority of nanofluids i.e. base fluids doped with engineered nanoparticles has also stimulated immense implementation in biomedical designs. Motivated by these emerging applications, we present a numerical thermofluid dynamic simulation of the transport phenomena in bioconvection nanofluid rotating disk bioreactor flow. Methodology- We study analytically and computationally the time-dependent three-dimensional viscous gyrotactic bioconvection in swirling nanofluid flow from a rotating disk configuration. The disk is also deformable i.e. able to extend (stretch) in the radial direction. Stefan blowing is included. The Buongiorno dilute nanofluid model is adopted wherein Brownian motion and thermophoresis are the dominant nanoscale effects. The primitive conservation equations for mass, radial, tangential and axial momentum, heat (energy), nanoparticle concentration and micro-organism density function are formulated in a cylindrical polar coordinate system with appropriate wall and free stream boundary conditions. A mass convective condition is also incorporated at the disk surface. Forced convection is considered i.e. buoyancy forces are neglected. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Karman and other transformations to render the boundary value problem (BVP) into an ordinary differential system which is solved with the efficient Adomian decomposition method (ADM). Validation with earlier Runge-Kutta shooting computations in the literature is also conducted. Extensive computations are presented (with the aid of MATLAB symbolic software) for radial and circumferential velocity components, temperature, nanoparticle concentration, micro-organism density number and gradients of these functions at the disk surface (radial local skin friction, local circumferential skin friction, Local Nusselt number, Local Sherwood number, motile microorganism mass transfer rate). Main Findings- Increasing radial stretching parameter decreases radial velocity and radial skin friction, reduces azimuthal velocity and skin friction, decreases local Nusselt number and motile micro-organism mass wall flux whereas it increases nano-particle local Sherwood number. Disk deceleration accelerates the radial flow, damps the azimuthal flow, decreases temperatures and thermal boundary layer thickness, depletes the nano-particle concentration magnitudes (and associated nano-particle species boundary layer thickness) and furthermore decreases the micro-organism density number and gyrotactic micro-organism species boundary layer thickness. Increasing Stefan blowing accelerates the radial flow and azimuthal (circumferential flow), elevates temperatures of the nanofluid, boosts nano-particle concentration (volume fraction) and gyrotactic micro-organism density number magnitudes whereas suction generates the reverse effects. Increasing suction effect reduces radial skin friction and azimuthal skin friction, local Nusselt number, and motile micro-organism wall mass flux whereas it enhances the nano-particle species local Sherwood number. Conclusions - Important transport characteristics are identified of relevance to real bioreactor nanotechnological systems not discussed in previous works. ADM is shown to achieve very rapid convergence and highly accurate solutions and shows excellent promise in simulating swirling multi-physical nano-bioconvection fluid dynamics problems. Furthermore, it provides an excellent complement to more general commercial computational fluid dynamics simulations.

Keywords: bio-nanofluids, rotating disk bioreactors, Von Karman swirling flow, numerical solutions

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Authors: Mohammad Hossain Mohammadi, Saif Al Ameri, Sana Ziaei, Jinane Mounsef

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Automated enumeration of the number of hand fingers is widely used in several motion gaming and distance control applications, and is discussed in several published papers as a starting block for hand recognition systems. The automated finger enumeration technique should not only be accurate, but also must have a fast response for a moving-picture input. The high performance of video in motion games or distance control will inhibit the program’s overall speed, for image processing software such as Matlab need to produce results at high computation speeds. Since an automated finger enumeration with minimum error and processing time is desired, a comparative study between two finger enumeration techniques is presented and analyzed in this paper. In the pre-processing stage, various image processing functions were applied on a real-time video input to obtain the final cleaned auto-cropped image of the hand to be used for the two techniques. The first technique uses the known morphological tool of skeletonization to count the number of skeleton’s endpoints for fingers. The second technique uses a radial distance method to enumerate the number of fingers in order to obtain a one dimensional hand representation. For both discussed methods, the different steps of the algorithms are explained. Then, a comparative study analyzes the accuracy and speed of both techniques. Through experimental testing in different background conditions, it was observed that the radial distance method was more accurate and responsive to a real-time video input compared to the skeletonization method. All test results were generated in Matlab and were based on displaying a human hand for three different orientations on top of a plain color background. Finally, the limitations surrounding the enumeration techniques are presented.

Keywords: comparative study, hand recognition, fingertip detection, skeletonization, radial distance, Matlab

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: H. Aissa, L. Mouzai, M. Bouhadef

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The effects of down slope steepness on soil splash distribution under a water drop impact have been investigated in this study. The equipment used are the burette to simulate a water drop, a splash cup filled with sandy soil which forms the source area and a splash board to collect the ejected particles. The results found in this study have shown that the apparent mass increased with increasing downslope angle following a linear regression equation with high coefficient of determination. In the same way, the radial soil splash distribution over the distance has been analyzed statistically, and an exponential function was the best fit of the relationship for the different slope angles. The curves and the regressions equations validate the well known FSDF and extend the theory of Van Dijk.

Keywords: splash distribution, water drop, slope steepness, soil detachment

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Authors: Alireza Lavaei, Alireza Lohrasbi, Mohammadali M. Shahlaei

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To reduce the overall time of structural optimization for earthquake loads two strategies are adopted. In the first strategy, a neural system consisting self-organizing map and radial basis function neural networks, is utilized to predict the time history responses. In this case, the input space is classified by employing a self-organizing map neural network. Then a distinct RBF neural network is trained in each class. In the second strategy, an improved genetic algorithm is employed to find the optimum design. A 72-bar space truss is designed for optimal weight using exact and approximate analysis for the El Centro (S-E 1940) earthquake loading. The numerical results demonstrate the computational advantages and effectiveness of the proposed method.

Keywords: optimization, genetic algorithm, neural networks, self-organizing map

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: Anubhav Shrivastava, Lakshya Bhat, Shivarudraswamy

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Distributed Generation is the need of the hour. With current advancements in the DG technology, there are some major issues that need to be tackled in order to make this method of generation of energy more efficient and feasible. Among other problems, the control in voltage is the major issue that needs to be addressed. This paper focuses on control of voltage using reactive power control of DGs with the help of fuzzy logic. The membership functions have been defined accordingly and the control of the system is achieved. Finally, with the help of simulation results in Matlab, the control of voltage within the tolerance limit set (+/- 5%) is achieved. The voltage waveform graphs for the IEEE 14 bus system are obtained by using simple algorithm with MATLAB and then with fuzzy logic for 14 bus system. The goal of this project was to control the voltage within limits by controlling the reactive power of the DG using fuzzy logic.

Keywords: distributed generation, fuzzy logic, matlab, newton raphson, IEEE 14 bus, voltage regulation, radial network

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Authors: İbrahim Aktaş, Árpád Baricz

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

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

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Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: Christian Lavault

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

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

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Authors: Jatinder Kaur, Pankaj Thakur

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The effect of pressure and temperature in non-homogeneous circular cylinder by taking non-homogeneity of material in terms of compressibility c=c₀r⁻ᵏ has been observed. From the results, it could be seen that for K<0, high pressure is required in the initial yielding state than for the case K >0. Under thermal conditions for value K<0, lesser amount of pressure is required for initial yielding, and further, the amount keeps on decreasing with an increase in temperature. Curves are drawn between pressure and radii ratio for initial and fully plastic state with and without temperature conditions. Further graphs between stresses (hoop and radial) and radii ratio for fully plastic state with and without temperature conditions are also drawn and concluded that hoop stresses become minimum with the increase in temperature as compared to radial stresses.

Keywords: cylinder, elastic, plastic, copper, steel, stresses, pressure, load

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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

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

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Authors: Rubaiyea Uddin

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The hippocampus, located in the limbic system, is most commonly known for its role in memory and spatial navigation (as cited in Brain Reward and Pathways). It maintains an especially important role in specifically episodic and declarative memory. The hippocampus has also recently been linked to dopamine, the reward pathway’s primary neurotransmitter. Since research has found that dopamine also contributes to memory consolidation and hippocampal plasticity, this neurotransmitter is potentially responsible for contributing to the hippocampus’s role in memory formation. In this experiment we tested to see the effect of tactile cues on spatial navigation for eight different mice. We used a radial arm that had one designated 'reward' arm containing sucrose. The presence or absence of bedding was our tactile cue. We attempted to see if the memory of that cue would enhance the mice’s memory of having received the reward in that arm. The results from our study showed there was no significant response from the use of tactile cues on spatial navigation on our 129 mice. Tactile cues therefore do not influence spatial navigation.

Keywords: mice, radial arm maze, memory, spatial navigation, tactile cues, hippocampus, reward, sensory skills, Alzheimer’s, neurodegnerative disease

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Authors: Alexandru Achim, Tamás Szűcsborus, Viktor Sasi, Ferenc Nagy, Zoltán Jambrik, Attila Nemes, Albert Varga, Călin Homorodean, Olivier F. Bertrand, Zoltán Ruzsa

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Aim: Our study aimed to establish the safety and the technical success of distal radial access for balloon aortic valvuloplasty (DR-BAV). The secondary objective was to determine the effectiveness and appropriate role of DR-BAV within half year follow-up. Methods: Clinical and angiographic data from 32 consecutive patients with symptomatic aortic stenosis were evaluated in a prospective pilot single-center study. Between 2020 and 2021, the patients were treated utilizing dual distal radial access with 6-10F compatible balloons. The efficacy endpoint was divided into technical success (successful valvuloplasty balloon inflation at the aortic valve and absence of intra- or periprocedural major complications), hemodynamic success (a reduction of the mean invasive gradient >30%), and clinical success (an improvement of at least one clinical category in the NYHA classification). The safety endpoints were vascular complications (major and minor Valve Academic Research Consortium (VARC)-2 bleeding, diminished or lost arterial pulse or the presence of any pseudo-aneurysm or arteriovenous fistula during the clinical follow-up) and major adverse events, MAEs (the composite of death, stroke, myocardial infarction, and urgent major aortic valve replacement or implantation during the hospital stay and or at one-month follow-up). Results: 32 patients (40 % male, mean age 80 ± 8,5) with severe aortic valve stenosis were included in the study and 4 patients were excluded. Technical success was achieved in all patients (100%). Hemodynamic success was achieved in 30 patients (93,75%). Invasive max and mean gradients were reduced from 73±22 mm Hg and 49±22 mm Hg to 49±19 mm Hg and 20±13 mm Hg, respectively (p = <.001). Clinical success was achieved in 29 patients (90,6%). In total, no major adverse cardiac or cerebrovascular event nor vascular complications (according to VARC 2 criteria) occurred during the intervention. All-cause death at 6 months was 12%. Conclusion: According to our study, dual distal radial artery access is a safe and effective option for balloon aortic valvuloplasty in patients with severe aortic valve stenosis and can be performed in all patients with sufficient lumen diameter. Future randomized studies are warranted to investigate whether this technique is superior to other approaches.

Keywords: mean invasive gradient, distal radial access for balloon aortic valvuloplasty (DR-BAV), aortic valve stenosis, pseudo-aneurysm, arteriovenous fistula, valve academic research consortium (VARC)-2

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Authors: Vladimir S. Timofeev

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

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

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Authors: Rogelio Luck, Yucheng Liu

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

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

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Authors: Nattachote Rugthaicharoencheep

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This paper presents a feeder reconfiguration problem in distribution systems. The objective is to minimize the system power loss and to improve bus voltage profile. The optimization problem is subjected to system constraints consisting of load-point voltage limits, radial configuration format, no load-point interruption, and feeder capability limits. A method based on genetic algorithm, a search algorithm based on the mechanics of natural selection and natural genetics, is proposed to determine the optimal pattern of configuration. The developed methodology is demonstrated by a 33-bus radial distribution system with distributed generations and feeder capacitors. The study results show that the optimal on/off patterns of the switches can be identified to give the minimum power loss while respecting all the constraints.

Keywords: network reconfiguration, distributed generation capacitor placement, loss reduction, genetic algorithm

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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

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

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Authors: Lanyan Peng, Ling Chen

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

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

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Authors: Irina Peterburgsky

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

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

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Authors: J. K. Alhassan, B. Attah, S. Misra

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Human beings have the ability to make logical decisions. Although human decision - making is often optimal, it is insufficient when huge amount of data is to be classified. medical dataset is a vital ingredient used in predicting patients health condition. In other to have the best prediction, there calls for most suitable machine learning algorithms. This work compared the performance of Artificial Neural Network (ANN) and Decision Tree Algorithms (DTA) as regards to some performance metrics using diabetes data. The evaluations was done using weka software and found out that DTA performed better than ANN. Multilayer Perceptron (MLP) and Radial Basis Function (RBF) were the two algorithms used for ANN, while RegTree and LADTree algorithms were the DTA models used. The Root Mean Squared Error (RMSE) of MLP is 0.3913,that of RBF is 0.3625, that of RepTree is 0.3174 and that of LADTree is 0.3206 respectively.

Keywords: artificial neural network, classification, decision tree algorithms, diabetes mellitus

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Authors: Zuhier Altawallbeh

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

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

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Authors: Magdi. M. Nabi, Ding-Li Yu

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Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward, feedback control

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Authors: Nosheen Zareen Khan, Abdul Majeed Siddiqui, Muhammad Afzal Rana

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The steady flow of a second order fluid through constricted tube with slip velocity at wall is modeled and analyzed theoretically. The governing equations are simplified by implying no slip in radial direction. Based on Karman Pohlhausen procedure polynomial solution for axial velocity profile is presented. An expressions for pressure gradient, shear stress, separation and reattachment points and radial velocity are also calculated. The effect of slip and no slip velocity on velocity, shear stress, pressure gradient are discussed and depicted graphically. It is noted that when Reynolds number increases velocity of the fluid decreases in both slip and no slip conditions. It is also found that the wall shear stress, separation and reattachment points are strongly effected by Reynolds number.

Keywords: approximate solution, constricted tube, non-Newtonian fluids, Reynolds number

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Authors: N. Beit Saeid

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Cyclones are used in the field of air industrial gases pollution and control the pollution with centrifugal forces that is generated with spatial geometry of the cyclone. Their simple design, low capital and maintenance costs and adaptability to a wide range of operating conditions have made cyclones one of the most widely used industrial dust collectors. Their cost of operation is proportional to the fan energy required to overcome their pressure drop. Optimized geometry of outlet diffuser of the cyclones potentially could reduce exit pressure losses without affecting collection efficiency. Three rectangular outlets and a radial outlet with a variable opening had been analyzed on two cyclones. Pressure drop was investigated for inlet velocities from about 10 to 20 m s−1. The radial outlet reduced cyclone pressure drop by between 8.7 and 11.9 percent when its exit area was equal to the flow area of the cyclone vortex finder or gas exit. A simple payback based on avoided energy costs was estimated to be between 3600 and 5000 h, not including installation cost.

Keywords: cyclone, CFD, optimization, genetic algorithm

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