Search results for: Algebraic Fractions

Authors: T. B. Karu Jayasundara

Abstract:

Regions of low gravity and gravity anomalies both influence heavy mineral concentrations on placer deposits. Economically imported heavy minerals are likely to have higher levels of deposition in low gravity regions of placer deposits. This can be found in coastal regions of Southern Asia, particularly in Sri Lanka and Peninsula India and areas located in the lowest gravity region of the world. The area about 70 kilometers of the east coast of Sri Lanka is covered by a high percentage of ilmenite deposits, and the southwest coast of the island consists of Monazite placer deposit. These deposits are one of the largest placer deposits in the world. In India, the heavy mineral industry has a good market. On the other hand, based on the coastal placer deposits recorded, the high gravity region located around Papua New Guinea, has no such heavy mineral deposits. In low gravity regions, with the help of other depositional environmental factors, the grains have more time and space to float in the sea, this helps bring high concentrations of heavy mineral deposits to the coast. The effect of low and high gravity can be demonstrated by using heavy mineral separation devices.  The Wilfley heavy mineral separating table is one of these; it is extensively used in industries and in laboratories for heavy mineral separation. The horizontally oscillating Wilfley table helps to separate heavy and light mineral grains in to deferent fractions, with the use of water. In this experiment, the low and high angle of the Wilfley table are representing low and high gravity respectively. A sample mixture of grain size <0.85 mm of heavy and light mineral grains has been used for this experiment. The high and low angle of the table was 6⁰ and 2⁰ respectively for this experiment. The separated fractions from the table are again separated into heavy and light minerals, with the use of heavy liquid, which consists of a specific gravity of 2.85. The fractions of separated heavy and light minerals have been used for drawing the two-dimensional graphs. The graphs show that the low gravity stage has a high percentage of heavy minerals collected in the upper area of the table than in the high gravity stage. The results of the experiment can be used for the comparison of regional low gravity and high gravity levels of heavy minerals. If there are any heavy mineral deposits in the high gravity regions, these deposits will take place far away from the coast, within the continental shelf.

Keywords: Anomaly, gravity, influence, mineral.

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Authors: Amanda M. Tadini, Houssam Hajjoul, Gustavo Nicolodelli, Stéphane Mounier, Célia R. Montes, Débora M. B. P. Milori

Abstract:

Soil organic matter (SOM) plays an important role in maintaining soil productivity and accounting for the promotion of biological diversity. The main components of the SOM are the humic substances which can be fractionated according to its solubility in humic acid (HA), fulvic acids (FA) and humin (HU). The determination of the chemical properties of organic matter as well as its interaction with metallic species is an important tool for understanding the structure of the humic fractions. Fluorescence spectroscopy has been studied as a source of information about what is happening at the molecular level in these compounds. Specially, soils of Amazon region are an important ecosystem of the planet. The aim of this study is to understand the molecular and structural composition of HA samples from Spodosol of Amazonia using the fluorescence Emission-Excitation Matrix (EEM) and Time Resolved Fluorescence Spectroscopy (TRFS). The results showed that the samples of HA showed two fluorescent components; one has a more complex structure and the other one has a simpler structure, which was also seen in TRFS through the evaluation of each sample lifetime. Thus, studies of this nature become important because it aims to evaluate the molecular and structural characteristics of the humic fractions in the region that is considered as one of the most important regions in the world, the Amazon.

Keywords: Amazonian soil, characterization, fluorescence, humic acid, lifetime.

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Authors: Chiung-Tsun Kuoa, Tzu-Hao Liu, Fang-Yi Lin, Tai-Hao Hsu, Hui-Yin Chen

Abstract:

Hyperglycemia-mediated accumulation of advanced glycation end-products (AGEs) play a pivotal role in the development of diabetic complications by inducing inflammation. In the present study, we evaluated the possible effects of water/ethanol (1/1, v/v) extracts (WEE) and its fractions from Canarium album Raeusch. (Chinese olive) which is a fruit used on AGEs-stimulated oxidative stress and inflammation in monocytes and vascular endothelial cells. Co-incubation of EA.hy926 endothelial cells with WEE and its fractions for 24h resulted in a significant decrease of monocyte–endothelial cell adhesion, the expression of ICAM-1, generation of intracellular ROS and depletion of GSH induced by AGEs. Chinese olive fruit extracts also reduced the expression of pro-inflammatory mediates, such as TNF-α, IL-1β and IL-6 in THP-1 cells. These findings suggested that Chinese olive fruit was able to protect vascular endothelium from dysfunction induced by AGEs. 

Keywords: Advanced glycation end-products (AGEs), Canarium album Raeusch, endothelial dysfunction, inflammation.

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Authors: M. Zarebnia, N. Aliniya

Abstract:

In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method

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Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

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In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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Authors: Melih Turgut, José Luis López-Bonilla, Süha Yılmaz

Abstract:

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated.

Keywords: Lorentzian 5-space, Frenet-Serret Invariants, Nonnull Curves

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Authors: Ahmet Tekcan

Abstract:

In this paper, we derive some algebraic identities on right and left neighbors R(F) and L(F) of an indefinite binary quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant Δ = b2 -4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F.

Keywords: Quadratic form, indefinite form, cycle, proper cycle, right neighbor, left neighbor.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

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In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: S. Shalaweh, P. Bouic, F. Weitz, R. Henkel

Abstract:

More than 3000 plants of notable phyto-therapeutic value grow in South Africa; these include Cissampelos capensis, commonly known in Afrikaans as dawidjie or dawidjiewortel. C. capensis is the most significant and popular medicinal plant used by the Khoisan as well as other rural groups in the Western region of South Africa. Its rhizomes are traditionally used to treat male fertility problems. Yet, no studies have investigated the effects of this plant or its extracts on human spermatozoa. Therefore, this study aimed at investigating the effects of C. capensis rhizome extract (CRE) fractions on ejaculated human spermatozoa in vitro. Spermatozoa from a total of 77 semen samples were washed with human tubular fluid medium supplemented with bovine serum albumin (HTF-BSA) and incubated for 2 hours with 20 μg/ml progesterone (P4) followed by incubation with different concentrations (0, 0.05, 0.5, 5, 50, 200 μg/ml) of fractionated CRE (F1=0% MeOH, F2=30% MeOH, F3=60% MeOH and F4=100% MeOH) for 1.5 hours at 37°C. A sample without addition of CRE fractions served as control. Samples were analyzed for sperm motility, reactive oxygen species (ROS), DNA-fragmentation, acrosome reaction and capacitation. Results showed that F1 resulted in significantly higher values for ROS, capacitation and hyper-activation compared to F2, F3, and F4 with P4-stimulated samples generally having higher values. No significant effect was found for the other parameters. In conclusion, alkaloids present in F1 of CRE appear to have triggered sperm intrinsic ROS production leading to sperm capacitation and acrosome reaction induced by P4.

Keywords: Capacitation, acrosome reaction, Cissampelos capensis, DNA fragmentation, ROS.

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Authors: Esra Yel, Tabriz Aslanov, Merve Sogancioglu, Suheyla Kocaman, Gulnare Ahmetli

Abstract:

The disposal of waste plastics has become a major worldwide environmental problem. Pyrolysis of waste plastics is one of the routes to waste minimization and recycling that has been gaining interest. In pyrolysis, the pyrolysed material is separated into gas, liquid (both are fuel) and solid (char) products. All fractions have utilities and economical value depending upon their characteristics. The first objective of this study is to determine the co-pyrolysis product fractions of waste HDPE- (high density polyethylene) and LDPE (low density polyethylene)-olive pomace (OP) and to determine the qualities of the solid product char. Chars obtained at 700 °C pyrolysis were used in biocomposite preparation as additive. As the second objective, the effects of char on biocomposite quality were investigated. Pyrolysis runs were performed at temperature 700 °C with heating rates of 5 °C/min. Biocomposites were prepared by mixing of chars with bisphenol-F type epoxy resin in various wt%. Biocomposite properties were determined by measuring electrical conductivity, surface hardness, Young’s modulus and tensile strength of the composites. The best electrical conductivity results were obtained with HDPE-OP char. For HDPE-OP char and LDPE-OP char, compared to neat epoxy, the tensile strength values of the composites increased by 102% and 78%, respectively, at 10% char dose. The hardness measurements showed similar results to the tensile tests, since there is a correlation between the hardness and the tensile strength.

Keywords: Pyrolysis, olive pomace, char, biocomposite, PE plastics.

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Authors: Shiping Wang, Peiyong Zhu, William Zhu

Abstract:

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

Keywords: Covering, poset, down-set, lattice, topological space, topological base.

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Authors: Padmanabhan Balasubramanian, C. Ardil

Abstract:

In this paper, we consider the problem of logic simplification for a special class of logic functions, namely complementary Boolean functions (CBF), targeting low power implementation using static CMOS logic style. The functions are uniquely characterized by the presence of terms, where for a canonical binary 2-tuple, D(mj) ∪ D(mk) = { } and therefore, we have | D(mj) ∪ D(mk) | = 0 [19]. Similarly, D(Mj) ∪ D(Mk) = { } and hence | D(Mj) ∪ D(Mk) | = 0. Here, 'mk' and 'Mk' represent a minterm and maxterm respectively. We compare the circuits minimized with our proposed method with those corresponding to factored Reed-Muller (f-RM) form, factored Pseudo Kronecker Reed-Muller (f-PKRM) form, and factored Generalized Reed-Muller (f-GRM) form. We have opted for algebraic factorization of the Reed-Muller (RM) form and its different variants, using the factorization rules of [1], as it is simple and requires much less CPU execution time compared to Boolean factorization operations. This technique has enabled us to greatly reduce the literal count as well as the gate count needed for such RM realizations, which are generally prone to consuming more cells and subsequently more power consumption. However, this leads to a drawback in terms of the design-for-test attribute associated with the various RM forms. Though we still preserve the definition of those forms viz. realizing such functionality with only select types of logic gates (AND gate and XOR gate), the structural integrity of the logic levels is not preserved. This would consequently alter the testability properties of such circuits i.e. it may increase/decrease/maintain the same number of test input vectors needed for their exhaustive testability, subsequently affecting their generalized test vector computation. We do not consider the issue of design-for-testability here, but, instead focus on the power consumption of the final logic implementation, after realization with a conventional CMOS process technology (0.35 micron TSMC process). The quality of the resulting circuits evaluated on the basis of an established cost metric viz., power consumption, demonstrate average savings by 26.79% for the samples considered in this work, besides reduction in number of gates and input literals by 39.66% and 12.98% respectively, in comparison with other factored RM forms.

Keywords: Reed-Muller forms, Logic function, Hammingdistance, Algebraic factorization, Low power design.

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

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In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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Authors: Michael Russelle S. Alvarez, Noel S. Quiming, Francisco M. Heralde

Abstract:

This study aims to: a) obtain ethanolic (95% EtOH) and aqueous extracts of Selaginella elmeri, Christella dentata, Elatostema sinnatum, Curculigo capitulata, Euphorbia hirta, Murraya koenigii, Alpinia speciosa, Cymbopogon citratus, Eucalyptus globulus, Jatropha curcas, Psidium guajava, Gliricidia sepium, Ixora coccinea and Capsicum frutescens and screen them for larvicidal activities against Aedes aegypti (Linn.) and Aedes albopictus (Skuse) larvae; b) to fractionate the most active extract and determine the most active fraction; c) to determine the larvicidal properties of the most active extract and fraction against by computing their percentage mortality, LC50, and LC90 after 24 and 48 hours of exposure; and d) to determine the nature of the components of the active extracts and fractions using phytochemical screening. Ethanolic (95% EtOH) and aqueous extracts of the selected plants will be screened for potential larvicidal activity against Ae. aegypti and Ae. albopictus using standard procedures and 1% malathion and a Piper nigrum based ovicide-larvicide by the Department of Science and Technology as positive controls. The results were analyzed using One-Way ANOVA with Tukey’s and Dunnett’s test. The most active extract will be subjected to partial fractionation using normal-phase column chromatography, and the fractions subsequently screened to determine the most active fraction. The most active extract and fraction were subjected to dose-response assay and probit analysis to determine the LC50 and LC90 after 24 and 48 hours of exposure. The active extracts and fractions will be screened for phytochemical content. The ethanolic extracts of C. citratus, E. hirta, I. coccinea, G. sepium, M. koenigii, E globulus, J. curcas and C. frutescens exhibited significant larvicidal activity, with C. frutescens being the most active. After fractionation, the ethyl acetate fraction was found to be the most active. Phytochemical screening of the extracts revealed the presence of alkaloids, tannins, indoles and steroids. A formulation using talcum powder–300 mg fraction per 1 g talcum powder–was made and again tested for larvicidal activity. At 2 g/L, the formulation proved effective in killing all of the test larvae after 24 hours.

Keywords: Larvicidal activity screening, partial purification, dose-response assay, Capsicum frutescens.

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Authors: Mohsen Zahraei

Abstract:

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for Є > 0, the notion of Birkhoff-James approximate orthogonality sets for Є−higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: Rank−k numerical range, isometry, numerical range, rectangular matrix polynomials.

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Authors: Risto Poykio, Kati Manskinen, Olli Dahl, Mikko Mäkelä, Hannu Nurmesniemi

Abstract:

When the results of the total element concentrations using USEPA method 3051A are compared to the sequential extraction analyses (i.e. the sum of fractions BCR1, BCR2 and BRC3), it can be calculated that the recovery values of elements varied between 56.8-% and 69.4-% in the bottom ash, and between 11.3-% and 70.9-% in the fly ash. This indicates that most of the elements in the ashes do not occur as readily soluble forms.

Keywords: Ash, BCR, leaching, solubility, waste

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Authors: F. Bayatbabolghani, K. Parand

Abstract:

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

Keywords: Collocation method, Hermite function, Semi-infinite, Thomas-Fermi equation.

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Authors: M. Faraji, F. Berroug

Abstract:

A one-dimensional mathematical model was developed in order to analyze and optimize the latent heat storage wall. The governing equations for energy transport were developed by using the enthalpy method and discretized with volume control scheme. The resulting algebraic equations were next solved iteratively by using TDMA algorithm. A series of numerical investigations were conducted in order to examine the effects of the thickness of the PCM layer on the thermal behavior of the proposed heating system. Results are obtained for thermal gain and temperature fluctuation. The charging discharging process was also presented and analyzed.

Keywords: Phase change material, Building, Concrete, Latent heat, Thermal control.

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Authors: Zdeňka Dostálová, David Matoušek, Bohumil Brtnik

Abstract:

As there are also graph methods of circuit analysis in addition to algebraic methods, it is, in theory, clearly possible to carry out an analysis of a whole switched circuit in two-phase switching exclusively by the graph method as well. This article deals with two methods of full-graph solving of switched circuits: by transformation graphs and by two-graphs. It deals with the circuit switched capacitors and the switched current, too. All methods are presented in an equally detailed steps to be able to compare.

Keywords: Switched capacitors of two phases, switched currents of two phases, transformation graph, two-graph, Mason's formula, voltage transfer, summary graph.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Mona Taheri

Abstract:

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.

Keywords: multiple algebras , universal algebras

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Authors: M. Khoshab, M. J. Sedigh

Abstract:

Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: Dynamic System, Lag on Supply Demand, Market Stability, Supply Demand Model.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Moghadazadeh Zahra, Towfighi Jafar, Mofarahi Masoud

Abstract:

This article is presented an experimental and modeling study of a four-bed pressure swing adsorption process using zeolite13X to provide oxygen-enriched air. The binary mixture N2/O2 (79/21 vol %) was used as a feed stream. The effects of purge/feed ratio (P/F), adsorption pressure, cyclic time and product flow rate on product purity and recovery under nonisothermal condition were studied. The adsorption dynamics of process were determined using a mathematical model incorporated mass and energy balances. A Mathlab code using finite difference method was developed to solve the set of coupled differential-algebraic equations, and the simulation results are agreed well with experimental results.

Keywords: Pressure swing adsorption (PSA), Oxygen, Zeolite 13X.

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Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML documents, Web pages, Machine learning, Fuzzy logic, Arabic Web pages.

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Authors: Jo˜ao Paulo Coelho, Wojciech Giernacki, Jos´e Boaventura-Cunha

Abstract:

The coefficient diagram method is primarily an algebraic control design method whose objective is to easily obtain a good controller with minimum user effort. As a matter of fact, if a system model, in the form of linear differential equations, is known, the user only need to define a time-constant and the controller order. The later can be established regarding the expected disturbance type via a lookup table first published by Koksal and Hamamci in 2004. However an inaccuracy in this table was detected and pointed-out in the present work. Moreover the above mentioned table was expanded in order to enclose any k order type disturbance.

Keywords: Coefficient diagram method, control system design, disturbance rejection.

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Authors: Karam Y. Maalawi

Abstract:

This paper presents a generalized formulation for the problem of buckling optimization of anisotropic, radially graded, thin-walled, long cylinders subject to external hydrostatic pressure. The main structure to be analyzed is built of multi-angle fibrous laminated composite lay-ups having different volume fractions of the constituent materials within the individual plies. This yield to a piecewise grading of the material in the radial direction; that is the physical and mechanical properties of the composite material are allowed to vary radially. The objective function is measured by maximizing the critical buckling pressure while preserving the total structural mass at a constant value equals to that of a baseline reference design. In the selection of the significant optimization variables, the fiber volume fractions adjoin the standard design variables including fiber orientation angles and ply thicknesses. The mathematical formulation employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately as well as the inclusion of the coupling stiffness terms is presented. The proposed model deals with dimensionless quantities in order to be valid for thin shells having arbitrary thickness-to-radius ratios. The critical buckling pressure level curves augmented with the mass equality constraint are given for several types of cylinders showing the functional dependence of the constrained objective function on the selected design variables. It was shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.

Keywords: Buckling instability, structural optimization, functionally graded material, laminated cylindrical shells, externalhydrostatic pressure.

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