Search results for: Closed form solution

Authors: Osama Al-Sehail

Abstract:

This paper argues for sustainability as a necessity in the evolution of tall architecture. It provides a different mode for dealing with sustainability in tall architecture, taking into consideration the speciality of its typology. To this end, the article develops a Biomimetic Structural Form as a paradigm to attain Vital Sustainability. A Biomimetic Structural Form, which is derived from the amalgamation of biomimicry as an approach for sustainability defining nature as source of knowledge and inspiration in solving humans’ problems and a Structural Form as a catalyst for evolving tall architecture, is a dynamic paradigm emerging from a conceptualizing and morphological process. A Biomimetic Structural Form is a flow system whose different forces and functions tend to be “better”, more "fit", to “survive”, and to be efficient. Through geometry and function—the two aspects of knowledge extracted from nature—the attributes of the Biomimetic Structural Form are formulated. Vital Sustainability is the survival level of sustainability in natural systems through which a system enhances the performance of its internal working and its interaction with the external environment. A Biomimetic Structural Form, in this context, is a medium for evolving tall architecture to emulate natural models in their ways of coexistence with the environment. As an integral part of this article, the sustainable super tall building 3Ts is discussed as a case study of applying Biomimetic Structural Form.   

Keywords: Biomimicry, design in nature, high-rise buildings, sustainability, structural form, tall architecture, vital sustainability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1522

Authors: Lili Wang, Meng Hu

Abstract:

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.

Keywords: Delayed BAM neural networks, Hull theorem, Mmatrix, Almost periodic solution, Global exponential stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1415

Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2001

Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: Temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 728

Authors: Dolapop Sribudda, Ura Pancharoen

Abstract:

The separation of Hg (II) from produced water by hollow fiber contactors (HFC) was investigation. This system included of two hollow fiber modules in the series connecting. The first module used for the extraction reaction and the second module for stripping reaction. Aliquat336 extractant was fed from the organic reservoirs into the shell side of the first hollow fiber module and continuous to the shell side of the second module. The organic liquid was continuously feed recirculate and back to the reservoirs. The feed solution was pumped into the lumen (tube side) of the first hollow fiber module. Simultaneously, the stripping solution was pumped in the same way in tube side of the second module. The feed and stripping solution was fed which had a countercurrent flow. Samples were kept in the outlet of feed and stripping solution at 1 hour and characterized concentration of Hg (II) by Inductively Couple Plasma Atomic Emission Spectroscopy (ICP-AES). Feed solution was produced water from natural gulf of Thailand. The extractant was Aliquat336 dissolved in kerosene diluent. Stripping solution used was nitric acid (HNO3) and thiourea (NH2CSNH2). The effect of carrier concentration and type of stripping solution were investigated. Results showed that the best condition were 10 % (v/v) Aliquat336 and 1.0 M NH2CSNH2. At the optimum condition, the extraction and stripping of Hg (II) were 98% and 44.2%, respectively.

Keywords: Hg (II), hollow fiber contactor, produced water, wastewater treatment.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1823

Authors: Tomáš Ludík, Josef Navrátil, Alena Langerová

Abstract:

Tackling emergency situations is performed based on emergency scenarios. These scenarios do not have a uniform form in the Czech Republic. They are unstructured and developed primarily in the text form. This does not allow solving emergency situations efficiently. For this reason, the paper aims at defining a Process Oriented Architecture to support and thus to improve tackling emergency situations in the Czech Republic. The innovative Process Oriented Architecture is based on the Workflow Reference Model while taking into account the options of Business Process Management Suites for the implementation of process oriented emergency scenarios. To verify the proposed architecture the Proof of Concept has been used which covers the reception of an emergency event at the district emergency operations centre. Within the particular implementation of the proposed architecture the Bonita Open Solution has been used. The architecture created in this way is suitable not only for emergency management, but also for educational purposes.

Keywords: Business Process Management Suite, Czech Republic, Emergency Scenarios, Process Execution, Process Oriented Architecture.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1826

Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: Analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3012

Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1856

Authors: Yong Li

Abstract:

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1604

Authors: Mamoun F. Al-Mistarihi, Rami Mohaisen

Abstract:

Cooperative diversity (CD) has been adopted in many communication systems because it helps in improving performance of the wireless communication systems with the help of the relays that emulate the multiple antenna terminals. This work aims to provide the derivation of the performance analysis expressions of the multiuser diversity (MUD) in the two-hop cooperative multi-relay wireless networks (TCMRNs). Considering the work analysis, we provide analytically the derivation of a closed form expression of the two most commonly used performance metrics namely, the outage probability and the symbol error probability (SEP) for the fixed decode-and-forward (FDF) protocol with MUD.

Keywords: Cooperative diversity (CD), fixed decode-andforward(FDF), multiuser diversity (MUD) , two - hop cooperative multi-relay wireless networks (TCMRN).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1538

Authors: A. Kurşun, E. Kara, E. Çetin, Ş. Aksoy, A. Kesimli

Abstract:

In this study, thermal elastic stress distribution occurred on long hollow cylinders made of functionally graded material (FGM) was analytically defined under thermal, mechanical and thermo mechanical loads. In closed form solutions for elastic stresses and displacements are obtained analytically by using the infinitesimal deformation theory of elasticity. It was assumed that elasticity modulus, thermal expansion coefficient and density of cylinder materials could change in terms of an exponential function as for that Poisson’s ratio was constant. A gradient parameter n is chosen between - 1 and 1. When n equals to zero, the disc becomes isotropic. Circumferential, radial and longitudinal stresses in the FGMs cylinders are depicted in the figures. As a result, the gradient parameters have great effects on the stress systems of FGMs cylinders.

Keywords: Functionally graded materials, hollow cylinder, thermoelasticity, thermomechanical load.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3083

Authors: C. C. Chen, C. M. Chu, C. J. Wang, C. Y. Chen, K. J. Huang

Abstract:

Cesiumiodide with Na doping (CsI(Na)) solution or melt is easily forming three- dimension dendrites on the free surface. The defects or bobbles form inside the CsI(Na) during the solution or melt solidification. The defects or bobbles can further effect the x-ray path in the CsI(Na) crystal and decrease the scintillation characteristics of CsI(Na). In order to enhance the CsI(Na) scintillated property we made single crystal of CsI(Na) column in the anodic aluminum oxide (AAO) template by hydraulic pressure injection method. It is interesting that when CsI(Na) melt is confined in the small AAO channels, the column grow as stable single column without any dendrites. The high aspect ratio (100~10000) of AAO and nano to sub-micron channel structure which is a suitable template for single of crystal CsI(Na) formation. In this work, a new low-cost approach to fabricate scintillator crystals using anodic aluminum oxide (AAO) rather than Si is reported, which can produce scintillator crystals with a wide range of controllable size to optimize their performance in X-ray detection.

Keywords: Cesiumiodide, AAO, scintillator, crystal, X-ray.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2064

Authors: V. Tanboonchuy, J.C. Hsu, N. Grisdanurak, C.H. Liao

Abstract:

This study focused on arsenate removal by nano zero-valent iron (NZVI) in the gas-bubbled aqueous solution. It appears that solution acidified by H2SO4 is far more favorable than by CO2-bubbled acidification. In addition, as dissolved oxygen was stripped out of solution by N2 gas bubbling, the arsenate removal dropped significantly. To take advantages of common practice of carbonation and oxic condition, pretreatment of CO2 and air bubbling in sequence are recommended for a better removal of arsenate.

Keywords: Arsenic, arsenate, zero-valent iron.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1708

Authors: Omaima Bamasak

Abstract:

This paper presents a novel method that allows an agent host to delegate its signing power to an anonymous mobile agent in such away that the mobile agent does not reveal any information about its host-s identity and, at the same time, can be authenticated by the service host, hence, ensuring fairness of service provision. The solution introduces a verification server to verify the signature generated by the mobile agent in such a way that even if colluding with the service host, both parties will not get more information than what they already have. The solution incorporates three methods: Agent Signature Key Generation method, Agent Signature Generation method, Agent Signature Verification method. The most notable feature of the solution is that, in addition to allowing secure and anonymous signature delegation, it enables tracking of malicious mobile agents when a service host is attacked. The security properties of the proposed solution are analyzed, and the solution is compared with the most related work.

Keywords: Anonymous signature delegation, collusion resistance, e-commerce fairness, mobile agent security.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1445

Authors: M.Eskandari-Ghadi, M.Mahmoodian

Abstract:

In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.

Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, Torsion

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1561

Authors: Andrey V. Timofeev

Abstract:

This paper introduces an original method for guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. Experiments have shown that if cardinality of the classifiers ensemble is increased then the cardinality of this set of hypothetical classes is reduced. The problem of the guaranteed estimation of the accuracy for an ensemble of Lipschitz classifiers is relevant in multichannel classification of target events in C-OTDR monitoring systems. Results of suggested approach practical usage to accuracy control in C-OTDR monitoring systems are present.

Keywords: Lipschitz classifiers, confidence set, C-OTDR monitoring, classifiers accuracy, classifiers ensemble.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1953

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1368

Authors: Seung-Yeon Kim

Abstract:

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.

Keywords: Phase transition, Ising magnet, Square lattice, Freeboundary conditions, Exact solution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1843

Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

Phase equilibria of AZ91D Mg alloys for nonflammable use, containing Ca and Y, were carried out by using FactSage® and FTLite database, which revealed that solid solution treatment could be performed at temperatures from 400 to 450oC. Solid solution treatment of AZ91D Mg alloy without Ca and Y was successfully conducted at 420oC and supersaturated microstructure with all beta phase resolved into matrix was obtained. In the case of AZ91D Mg alloy with some Ca and Y; however, a little amount of intermetallic particles were observed after solid solution treatment. After solid solution treatment, each alloy was annealed at temperatures of 180 and 200oC for time intervals from 1 min to 48 hrs and hardness of each condition was measured by micro-Vickers method. Peak aging conditions were deduced as at the temperature of 200oC for 10 hrs.

Keywords: Mg alloy, AZ91D, nonflammable alloy, phase equilibrium, peak aging.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2236

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1862

Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1994

Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1202

Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

Abstract:

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2373

Authors: S. Gupta, R. Chadha

Abstract:

Five crystal modifications of water insoluble artesunate were generated by recrystallizing it from various solvents with improved physicochemical properties. These generated crystal forms were characterized to select the most potent and soluble form. SEM of all the forms showed changes in external shape leading them to be different morphologically. DSC thermograms of Form III and Form V showed broad endotherm peaks at 83.04oC and 76.96oC prior to melting fusion of drug respectively. Calculated weight loss in TGA revealed that Form III and Form V are methanol and acetone solvates respectively. However, few additional peaks were appeared in XRPD pattern in these two solvate forms. All forms exhibit exothermic behavior in buffer and two solvates display maximum ease of molecular release from the lattice. Methanol and acetone solvates were found to be most soluble forms and exhibited higher antimalarial efficacy showing higher survival rate (83.3%) after 30 days.

Keywords: Artesunate, Crystal modifications, in vivo studies, Recrystallization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3323

Authors: Jian-Jun Shu

Abstract:

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.

Keywords: Flux, free impinging jet, solid-surface, uniform wall temperature.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1989

Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

Abstract:

The present study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. T0 validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: Inverse method, FLUENT, Plate-fin heat sink, Heat transfer characteristics.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2251

Authors: Vasana M. Don, Eldad J. Avital, Fariborz Motallebi

Abstract:

Supersonic open and closed cavity flows are investigated experimentally and computationally. Free stream Mach number of two is set. Schlieren imaging is used to visualise the flow behaviour showing stark differences between open and closed. Computational Fluid Dynamics (CFD) is used to simulate open cavity of flow with aspect ratio of 4. A rear wall treatment is implemented in order to pursue a simple passive control approach. Good qualitative agreement is achieved between the experimental flow visualisation and the CFD in terms of the expansion-shock waves system. The cavity oscillations are shown to be dominated by the first and third Rossister modes combining to high fluctuations of non-linear nature above the cavity rear edge. A simple rear wall treatment in terms of a hole shows mixed effect on the flow oscillations, RMS contours, and time history density fluctuations are given and analysed.

Keywords: Supersonic, Schlieren, open-cavity, flow simulation, passive control.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2395

Authors: Xiaoyan Dou, Yongkun Li

Abstract:

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Keywords: Almost periodic solution, food-limited population, feedback control, permanence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1959

Authors: Kanungnit Chawong, Panarat Rattanaphanee

Abstract:

Extraction of lactic acid from aqueous solution using n-butanol as an extractant was studied. Effect of mixing time, pH of the aqueous solution, initial lactic acid concentration, and volume ratio between the organic and the aqueous phase were investigated. Distribution coefficient and degree of lactic acid extraction was found to increase when the pH of aqueous solution was decreased. The pH Effect was substantially pronounced at pH of the aqueous solution less than 1. Initial lactic acid concentration and organic-toaqueous volume ratio appeared to have positive effect on the distribution coefficient and the degree of extraction. Due to the nature of n-butanol that is partially miscible in water, incorporation of aqueous solution into organic phase was observed in the extraction with large organic-to-aqueous volume ratio.

Keywords: Lactic acid, liquid-liquid extraction, n-Butanol, Solvating extractant.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3171

Authors: Yongxin Yuan, Hao Liu

Abstract:

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1647