Search results for: self-consistent field theory.

Authors: Ondřej Nowak

Abstract:

This paper presents an exploration into the structure of the corporate governance network and interlocking directorates in the Czech Republic. First a literature overview and a basic terminology of the network theory is presented. Further in the text, statistics and other calculations relevant to corporate governance networks are presented. For this purpose an empirical data set consisting of 2 906 joint stock companies in the Czech Republic was examined. Industries with the highest average number of interlocks per company were healthcare, and energy and utilities. There is no observable link between the financial performance of the company and the number of its interlocks. Also interlocks with financial companies are very rare.

Keywords: Corporate Governance, Interlocking Directorates, Network Theory, Czech Republic.

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Authors: Marcin Perzyk, Artur Soroczynski

Abstract:

General requirements for knowledge representation in the form of logic rules, applicable to design and control of industrial processes, are formulated. Characteristic behavior of decision trees (DTs) and rough sets theory (RST) in rules extraction from recorded data is discussed and illustrated with simple examples. The significance of the models- drawbacks was evaluated, using simulated and industrial data sets. It is concluded that performance of DTs may be considerably poorer in several important aspects, compared to RST, particularly when not only a characterization of a problem is required, but also detailed and precise rules are needed, according to actual, specific problems to be solved.

Keywords: Knowledge extraction, decision trees, rough setstheory, industrial processes.

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Authors: Francesco Venuti, Simona Alfiero

Abstract:

The aim of this paper is to develop an empirical research on the nature and consequences of corporate governance on Eurozone Insurance Industry risk taking attitude. More particularly, we analyzed the effect of public ownership on risk taking with respect to privately held Insurance Companies. We also analyzed the effects on risk taking attitude of different degrees of ownership concentration, directors compensation, and the dimension/diversity of the Board of Directors. Our results provide quite strong evidence that, coherently with the Agency Theory, publicly traded insurance companies with more concentrated ownership are less risky than the corresponding privately held.

Keywords: Agency theory, corporate governance, insurance companies, risk taking.

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Authors: A. Tagar, F. A. Chandio, I. A. Mari, B. Wagan

Abstract:

An experiment was conducted on the comparative study of drip and furrow irrigation methods at the farmer-s field in Umar Kot. The total area under experiment about 4000m2 was divided into two equal portions. One portion about 40m X 50m was occupied by drip and the other portion about 40m X 50m by furrow irrigation method. Soil at the experimental site was clay loam in texture for 0-60cm depth; average dry bulk density and field capacity was 1.16g/cm3 and 28.5% respectively. The results reveal that the drip irrigation method saved 56.4% water and gave 22% more yield as compared to that of furrow irrigation method. Higher water use efficiency about 4.87 was obtained in drip irrigation method; whereas lower water used efficiency about 1.66 was obtained in furrow irrigation method. The present study suggests farming community to adopt drip irrigation method instead of old traditional flooding methods.

Keywords: Drip and furrow irrigations methods, water saving, yield of tomato crop.

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Authors: L. Dagilienė

Abstract:

The article explores the impact of normative institutional factors on the development of sustainability reporting. The vast majority of research in the scientific literature focuses on mandatory institutional factors, i.e. how public institutions and market regulators affect sustainability reporting. Meanwhile, there is lack of empirical data for the impact of normative institutional factors. The effect of normative factors in this paper is based on the role of non-governmental organizations (NGO) and institutional theory. The case of Global Compact Local Network in the developing country was examined. The research results revealed that in the absence of regulated factors, companies were not active with regard to social disclosures; they presented non-systemized social information of a descriptive nature. Only 10% of sustainability reports were prepared using the GRI methodology. None of the reports were assured by third parties.

Keywords: Institutional theory, normative, sustainability reporting.

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Authors: M. Yilmaz, I. Yilmaz, M. Uysal

Abstract:

The Earth system generates different phenomena that are observable at the surface of the Earth such as mass deformations and displacements leading to plate tectonics, earthquakes, and volcanism. The dynamic processes associated with the interior, surface, and atmosphere of the Earth affect the three pillars of geodesy: shape of the Earth, its gravity field, and its rotation. Geodesy establishes a characteristic structure in order to define, monitor, and predict of the whole Earth system. The traditional and new instruments, observables, and techniques in geodesy are related to the gravity field. Therefore, the geodesy monitors the gravity field and its temporal variability in order to transform the geodetic observations made on the physical surface of the Earth into the geometrical surface in which positions are mathematically defined. In this paper, the main components of the gravity field modeling, (Free-air and Bouguer) gravity anomalies are calculated via recent global models (EGM2008, EIGEN6C4, and GECO) over a selected study area. The model-based gravity anomalies are compared with the corresponding terrestrial gravity data in terms of standard deviation (SD) and root mean square error (RMSE) for determining the best fit global model in the study area at a regional scale in Turkey. The least SD (13.63 mGal) and RMSE (15.71 mGal) were obtained by EGM2008 for the Free-air gravity anomaly residuals. For the Bouguer gravity anomaly residuals, EIGEN6C4 provides the least SD (8.05 mGal) and RMSE (8.12 mGal). The results indicated that EIGEN6C4 can be a useful tool for modeling the gravity field of the Earth over the study area.

Keywords: Free-air gravity anomaly, Bouguer gravity anomaly, global model, land gravity.

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Authors: Imran Siddique

Abstract:

This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state solutions.

Keywords: Newtonian fluids, Velocity field, Exact solutions, Shear stress, Cylindrical domains.

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Authors: S. Parida, S. C. Mohanty

Abstract:

The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C⁰ finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.

Keywords: FGM, pretwisted plate, thermal environment, HOST, simple power law.

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Authors: C. Temaneh-Nyah, J. Makiche, J. Nujoma

Abstract:

This paper considers the characterization of a complex electromagnetic environment due to multiple sources of electromagnetic radiation as a five-dimensional surface which can be described by a set of several surface sections including: instant EM field intensity distribution maps at a given frequency and altitude, instantaneous spectrum at a given location in space and the time evolution of the electromagnetic field spectrum at a given point in space. This characterization if done over time can enable the exposure levels of Radio Frequency Radiation at every point in the analysis area to be determined and results interpreted based on comparison of the determined RFR exposure level with the safe guidelines for general public exposure given by recognized body such as the International commission on non-ionizing radiation protection (ICNIRP), Institute of Electrical and Electronic Engineers (IEEE), the National Radiation Protection Authority (NRPA).

Keywords: Electromagnetic Environment, Electric Field Strength, Mathematical Models.

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Authors: Majid A. AlSayari

Abstract:

The study reported here investigated social cognitive theory (SCT) in the context of Vocational Rehab (VR) for people with disabilities. The prime purpose was to increase knowledge of VR phenomena and make recommendations for improving VR services. The sample consisted of 242 persons with Spinal Cord Injuries (SCI) who completed questionnaires. A further 32 participants were Trainers. Analysis of questionnaire data was carried out using factor analysis, multiple regression analysis, and thematic analysis. The analysis suggested that, in motivational terms, and consistent with research carried out in other academic contexts, self-efficacy was the best predictor of VR performance. The author concludes that that VR self-efficacy predicted VR training performance.

Keywords: Social cognitive theory, vocational rehab, self-efficacy, proxy efficacy, people with disabilities.

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Authors: Fred Lacy

Abstract:

A superconductor has the ability to conduct electricity perfectly and exclude magnetic fields from its interior. In order to understand electromagnetic characteristics of superconductors, their material properties need to be examined. To facilitate this understanding, a theoretical model based on concepts of electromagnetics is presented to explain the electrical and magnetic properties of superconductors. The permittivity response is the key aspect of the model and it describes the electrical resistance response and why it vanishes at the material’s critical temperature. The model also explains the behavior of magnetic fields and why they cannot exist inside superconducting materials. The theoretical concepts and equations associated with this model are used to demonstrate that they are sufficient in describing the behavior of both type I and type II (or high temperature) superconductors. This model is also able to explain why superconductors behave differently than perfect conductors. As a result, examining the permittivity response and understanding electromagnetic field theory provides insight into the major aspects associated with superconducting materials.

Keywords: Ampere’s law, permittivity, permeability, resistivity, Schrödinger wave equation.

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Authors: A. Nachour, L. Ouzizi, Y. Aoura

Abstract:

Recent developments on multi-agent system have brought a new research field on image processing. Several algorithms are used simultaneously and improved in deferent applications while new methods are investigated. This paper presents a new automatic method for edge detection using several agents and many different actions. The proposed multi-agent system is based on parallel agents that locally perceive their environment, that is to say, pixels and additional environmental information. This environment is built using Vector Field Convolution that attract free agent to the edges. Problems of partial, hidden or edges linking are solved with the cooperation between agents. The presented method was implemented and evaluated using several examples on different synthetic and medical images. The obtained experimental results suggest that this approach confirm the efficiency and accuracy of detected edge.

Keywords: Edge detection, medical MR images, multi-agent systems, vector field convolution.

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Authors: Kariyappa B. S., Hariprasad S. A., R. Nagaraj

Abstract:

In this paper, a new method of controlling position of AC Servomotor using Field Programmable Gate Array (FPGA). FPGA controller is used to generate direction and the number of pulses required to rotate for a given angle. Pulses are sent as a square wave, the number of pulses determines the angle of rotation and frequency of square wave determines the speed of rotation. The proposed control scheme has been realized using XILINX FPGA SPARTAN XC3S400 and tested using MUMA012PIS model Alternating Current (AC) servomotor. Experimental results show that the position of the AC Servo motor can be controlled effectively. KeywordsAlternating Current (AC), Field Programmable Gate Array (FPGA), Liquid Crystal Display (LCD).

Keywords: Alternating Current (AC), Field Programmable Gate Array (FPGA), Liquid Crystal Display (LCD).

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Authors: Rahim Jafari, Tuba Okutucu-Özyurt

Abstract:

The hydrodynamics and heat transfer characteristics of a vaporized elongated bubble in a rectangular microchannel have been simulated based on Cahn-Hilliard phase-field method. In the simulations, the initially nucleated bubble starts growing as it comes in contact with superheated water. The growing shape of the bubble compared well with the available experimental data in the literature.

Keywords: Microchannel, boiling, Cahn-Hilliard method, Two-phase flow, Simulation.

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Authors: A.C. Duarte, C.I.L. Justino, K. Duarte, A.C. Freitas, R. Pereira, P. Chaves, P. Bettencourt, S. Cardoso, T.A.P. Rocha-Santos

Abstract:

This paper aims at overviewing the topics of a research project (CARDIOSENSOR) on the field of health sciences (biomaterials and biomedical engineering). The project has focused on the development of a nanosensor for the assessment of the risk of cardiovascular diseases by the monitoring of C-reactive protein (CRP), which has been currently considered as the best validated inflammatory biomarker associated to cardiovascular diseases. The project involves tasks such as: 1) the development of sensor devices based on field effect transistors (FET): assembly, optimization and validation; 2) application of sensors to the detection of CRP in standard solutions and comparison with enzyme-linked immunosorbent assay (ELISA); and 3) application of sensors to real samples such as blood and saliva and evaluation of their ability to predict the risk of cardiovascular disease.

Keywords: Carbon nanotubes field effect transistors, cardiovascular diseases, C-reactive protein, sensor.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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Authors: K. Kamalanand, P. Mannar Jawahar

Abstract:

Methods of contemporary mathematical physics such as chaos theory are useful for analyzing and understanding the behavior of complex biological and physiological systems. The three dimensional model of HIV/AIDS is the basis of active research since it provides a complete characterization of disease dynamics and the interaction of HIV-1 with the immune system. In this work, the behavior of the HIV system is analyzed using the three dimensional HIV model and a chaotic measure known as the Hurst exponent. Results demonstrate that Hurst exponents of CD4, CD8 cells and viral load vary nonlinearly with respect to variations in system parameters. Further, it was observed that the three dimensional HIV model can accommodate both persistent (H>0.5) and anti-persistent (H<0.5) dynamics of HIV states. In this paper, the objectives of the study, methodology and significant observations are presented in detail.

Keywords: HIV/AIDS, mathematical model, chaos theory, Hurst exponent

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Authors: Z. Nougrara

Abstract:

In this paper we propose a novel methodology for extracting a road network and its nodes from satellite images of Algeria country. This developed technique is a progress of our previous research works. It is founded on the information theory and the mathematical morphology; the information theory and the mathematical morphology are combined together to extract and link the road segments to form a road network and its nodes. We therefore have to define objects as sets of pixels and to study the shape of these objects and the relations that exist between them. In this approach, geometric and radiometric features of roads are integrated by a cost function and a set of selected points of a crossing road. Its performances were tested on satellite images of Algeria country.

Keywords: Satellite image, road network, nodes.

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Authors: T. Y. Liu, C. H Lin., Y. M Ferng

Abstract:

Wind energy is one of the clean renewable energy. However, the low frequency (20-200HZ) noise generated from the wind turbine blades, which bothers the residents, becomes the major problem to be developed. It is useful for predicting the aerodynamic noise by flow field and pressure distribution analysis on the wind turbine blades. Therefore, the main objective of this study is to use different turbulence models to analyze the flow field and pressure distributions of the wing blades.

Three-dimensional Computation Fluid Dynamics (CFD) simulation of the flow field was used to calculate the flow phenomena for the National Renewable Energy Laboratory (NREL) Phase VI horizontal axis wind turbine rotor. Two different flow cases with different wind speeds were investigated: 7m/s with 72rpm and 15m/s with 72rpm.

Four kinds of RANS-based turbulence models, Standard k-ε, Realizable k-ε, SST k-ω, and v2f, were used to predict and analyze the results in the present work. The results show that the predictions on pressure distributions with SST k-ω and v2f turbulence models have good agreements with experimental data.

Keywords: Horizontal Axis Wind Turbine, turbulence model, noise.

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Authors: Khin S. Aye

Abstract:

The present work was conducted to find out the effect of biofertilizer formulated with four species of bacteria (two species of Azotobacter and two species of Lysobacter) and zinc sulphate. Field experiments with mustard plant were conducted to study the effectiveness of soil application of zinc sulphate and biofertilizer at 0, 10, 20, 30, 40, 50 days after sowing. Plant height and condition of plant was found to be increased significantly using a mixture of biofertilizer and zinc sulphate than other treatments after 40 days sowing. Three treatments were also used in this field experiment such as bacteria only, zinc sulphate only and mixture of biofertilizer and zinc sulphate. The treatment using a mixture of zinc sulphate and biofertilizer had the best yield (4688.008 kg/ha) within 50 days of sowing and performed better than other treatments. Field experiment using zinc sulphate only was second best yield (3380.75Kg/ha) and biofertilizer only treatment gave (2639.04kg/ha).

Keywords: biofertilizer, zinc sulphate, mustard plant, bacteria

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Authors: Marcello Bettoni

Abstract:

As a learning theory tries to borrow from science a framework to found its method, it shows paradoxes and paralysing contraddictions. This results, on one hand, from adopting a learning/teaching model as it were a mere “transfer of data" (mechanical learning approach), and on the other hand from borrowing the complexity theory (an indeterministic and non-linear model), that risks to vanish every educational effort. This work is aimed at describing existing criticism, unveiling the antinomic nature of such paradoxes, focussing on a view where neither the mechanical learning perspective nor the chaotic and nonlinear model can threaten and jeopardize the educational work. Author intends to go back over the steps that led to these paradoxes and to unveil their antinomic nature. Actually this could serve the purpose to explain some current misunderstandings about the real usefulness of Ict within the youth-s learning process and growth.

Keywords: Antinomy, complexity, Leibniz, paradox

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Authors: R. Ramli, S. Sameon

Abstract:

There has been a strong link between computermediated education and constructivism learning and teaching theory.. Acknowledging how well the constructivism doctrine would work online, it has been established that constructivist views of learning would agreeably correlate with the philosophy of open and distance learning. Asynchronous and synchronous communications have placed online learning on the right track of a constructive learning path. This paper is written based on the social constructivist framework, where knowledge is constructed from social communication and interaction. The study explores the possibility of practicing this theory through incorporating online discussion in the syllabus and the ways it can be implemented to contribute to young people-s personality and social development by addressing some aspects that may contribute to the social problem such as prejudice, ignorance and intolerance.

Keywords: Educational Technology, Internet, Personal Development, Student Exchange

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

Keywords: Electrically conducting elastico-viscous fluid, symmetry solution, Homotopy perturbation method, Padé approximation, 4th order Runge–Kutta, Maple

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Authors: Zaini Mohd-Zain, Mohd-Saufee A.F. Mohd-Ismail, Norlida Buniyamin

Abstract:

Staphylococcus aureus, one of the microflora in a human external auditory canal (EAC) is frequently exposed to highfrequency electromagnetic field (HF-EMF) generated by mobile phones. It is normally non-pathogenic but in certain circumstances, it can cause infections. This study investigates the changes in the physiology of S. aureus when exposed to HF-EMF of a mobile phone. Exponentially grown S. aureus were exposed to two conditions of EMF irradiation (standby-mode and on-call mode) at four durations; 15, 30, 45 and 60 min. Changes in the viability and biofilm production of the S. aureus were compared between the two conditions of exposure. EMF from the standby-mode has enhanced the growth of S. aureus but during on-call, the growth was suppressed. No significant difference in the amount of biofilm produced in both modes of exposure was observed. Thus, HF-EMF of mobile phone affects the viability of S. aureus but not its ability to produce biofilm.

Keywords: Electromagnetic field, mobile phone, biofilm, Staphylococcus aureus

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Authors: Jinsiang Shaw, Ray Pan, Yin-Chieh Chang

Abstract:

In this paper, an magnetorheological (MR) mount with fuzzy sliding mode controller (FSMC) is studied for vibration suppression when the system is subject to base excitations. In recent years, magnetorheological fluids are becoming a popular material in the field of the semi-active control. However, the dynamic equation of an MR mount is highly nonlinear and it is difficult to identify. FSMC provides a simple method to achieve vibration attenuation of the nonlinear system with uncertain disturbances. This method is capable of handling the chattering problem of sliding mode control effectively and the fuzzy control rules are obtained by using the Lyapunov stability theory. The numerical simulations using one-dimension and two-dimension FSMC show effectiveness of the proposed controller for vibration suppression. Further, the well-known skyhook control scheme and an adaptive sliding mode controller are also included in the simulation for comparison with the proposed FSMC.

Keywords: adaptive sliding mode controller, fuzzy sliding modecontroller, magnetorheological mount, skyhook control.

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

Abstract:

This paper aims to analysis the behavior of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Currentvoltage curves are particularly analyzed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: Electrostatic precipitator, current-voltage characteristics, Least Squares method, electric field, magnetic field.

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Authors: Anurag Gaur, Nidhi, Shashi Sharma

Abstract:

Targeted drug delivery is a method of delivering medication to a patient in a manner that increases the concentration of the medication in some parts of the body relative to others. Targeted drug delivery seeks to concentrate the medication in the tissues of interest while reducing the relative concentration of the medication in the remaining tissues. This improves efficacy of the while reducing side effects. In the present work, we investigate the effect of magnetic field, flow rate and particle concentration on the capturing of magnetic particles transported in a stent implanted fluidic channel. Iron oxide magnetic nanoparticles (Fe3O4) nanoparticles were synthesized via co-precipitation method. The synthesized Fe3O4 nanoparticles were added in the de-ionized (DI) water to prepare the Fe3O4 magnetic particle suspended fluid. This fluid is transported in a cylindrical tube of diameter 8 mm with help of a peristaltic pump at different flow rate (25-40 ml/min). A ferromagnetic coil of SS 430 has been implanted inside the cylindrical tube to enhance the capturing of magnetic nanoparticles under magnetic field. The capturing of magnetic nanoparticles was observed at different magnetic magnetic field, flow rate and particle concentration. It is observed that capture efficiency increases from 47-67% at magnetic field 2-5kG, respectively at particle concentration 0.6mg/ml and at flow rate 30 ml/min. However, the capture efficiency decreases from 65 to 44% by increasing the flow rate from 25 to 40 ml/min, respectively. Furthermore, it is observed that capture efficiency increases from 51 to 67% by increasing the particle concentration from 0.3 to 0.6 mg/ml, respectively.

Keywords: Capture efficiency, Implant assisted-Magnetic drug targeting (IA-MDT), Magnetic nanoparticles, in vitro study.

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Authors: Aouachria Mekki

Abstract:

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

Keywords: Path integral, formalism, Propagator.

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