Search results for: Square Enclosure
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 661

Search results for: Square Enclosure

451 Variable Regularization Parameter Normalized Least Mean Square Adaptive Filter

Authors: Young-Seok Choi

Abstract:

We present a normalized LMS (NLMS) algorithm with robust regularization. Unlike conventional NLMS with the fixed regularization parameter, the proposed approach dynamically updates the regularization parameter. By exploiting a gradient descent direction, we derive a computationally efficient and robust update scheme for the regularization parameter. In simulation, we demonstrate the proposed algorithm outperforms conventional NLMS algorithms in terms of convergence rate and misadjustment error.

Keywords: Regularization, normalized LMS, system identification, robustness.

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450 Levels of Students’ Understandings of Electric Field Due to a Continuous Charged Distribution: A Case Study of a Uniformly Charged Insulating Rod

Authors: Thanida Sujarittham, Narumon Emarat, Jintawat Tanamatayarat, Kwan Arayathanitkul, Suchai Nopparatjamjomras

Abstract:

Electric field is an important fundamental concept in electrostatics. In high-school, generally Thai students have already learned about definition of electric field, electric field due to a point charge, and superposition of electric fields due to multiple-point charges. Those are the prerequisite basic knowledge students holding before entrancing universities. In the first-year university level, students will be quickly revised those basic knowledge and will be then introduced to a more complicated topic—electric field due to continuous charged distributions. We initially found that our freshman students, who were from the Faculty of Science and enrolled in the introductory physic course (SCPY 158), often seriously struggled with the basic physics concepts—superposition of electric fields and inverse square law and mathematics being relevant to this topic. These also then resulted on students’ understanding of advanced topics within the course such as Gauss's law, electric potential difference, and capacitance. Therefore, it is very important to determine students' understanding of electric field due to continuous charged distributions. The open-ended question about sketching net electric field vectors from a uniformly charged insulating rod was administered to 260 freshman science students as pre- and post-tests. All of their responses were analyzed and classified into five levels of understandings. To get deep understanding of each level, 30 students were interviewed toward their individual responses. The pre-test result found was that about 90% of students had incorrect understanding. Even after completing the lectures, there were only 26.5% of them could provide correct responses. Up to 50% had confusions and irrelevant ideas. The result implies that teaching methods in Thai high schools may be problematic. In addition for our benefit, these students’ alternative conceptions identified could be used as a guideline for developing the instructional method currently used in the course especially for teaching electrostatics.

Keywords: Electrostatics Electric field due to continuous charged distributions, inverse square law, superposition principle, levels of student understandings.

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449 Analysis of Gamma-Ray Spectra Using Levenberg-Marquardt Method

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

Abstract:

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

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

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448 Trapping Efficiency of Diesel Particles Through a Square Duct

Authors: Francis William S, Imtiaz Ahmed Choudhury, Ananda Kumar Eriki, A. John Rajan

Abstract:

Diesel Engines emit complex mixtures of inorganic and organic compounds in the form of both solid and vapour phase particles. Most of the particulates released are ultrafine nanoparticles which are detrimental to human health and can easily enter the body by respiration. The emissions standards on particulate matter release from diesel engines are constantly upgraded within the European Union and with future regulations based on the particles numbers released instead of merely mass, the need for effective aftertreatment devices will increase. Standard particulate filters in the form of wall flow filters can have problems with high soot accumulation, producing a large exhaust backpressure. A potential solution would be to combine the standard filter with a flow through filter to reduce the load on the wall flow filter. In this paper soot particle trapping has been simulated in different continuous flow filters of monolithic structure including the use of promoters, at laminar flow conditions. An Euler Lagrange model, the discrete phase model in Ansys used with user defined functions for forces acting on particles. A method to quickly screen trapping of 5 nm and 10 nm particles in different catalysts designs with tracers was also developed. Simulations of square duct monoliths with promoters show that the strength of the vortices produced are not enough to give a high amount of particle deposition on the catalyst walls. The smallest particles in the simulations, 5 and 10 nm particles were trapped to a higher extent, than larger particles up to 1000 nm, in all studied geometries with the predominant deposition mechanism being Brownian diffusion. The comparison of the different filters designed with a wall flow filter does show that the options for altering a design of a flow through filter, without imposing a too large pressure drop penalty are good.

Keywords: Diesel Engine trap, thermophoresis, Exhaust pipe, PM-Simulation modeling.

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447 A New True RMS-to-DC Converter in CMOS Technology

Authors: H. Asiaban, E. Farshidi

Abstract:

This paper presents a new true RMS-to-DC converter circuit based on a square-root-domain squarer/divider. The circuit is designed by employing up-down translinear loop and using of MOSFET transistors that operate in strong inversion saturation region. The converter offer advantages of two-quadrant input current, low circuit complexity, low supply voltage (1.2V) and immunity from the body effect. The circuit has been simulated by HSPICE. The simulation results are seen to conform to the theoretical analysis and shows benefits of the proposed circuit.

Keywords: Current-mode, squarer/divider, low-pass filter, converter, translinear loop, RMS-to-DC.

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446 A Low Power High Frequency CMOS RF Four Quadrant Analog Mixer

Authors: M. Aleshams, A. Shahsavandi

Abstract:

This paper describes a CMOS four-quadrant multiplier intended for use in the front-end receiver by utilizing the square-law characteristic of the MOS transistor in the saturation region. The circuit is based on 0.35 um CMOS technology simulated using HSPICE software. The mixer has a third-order inter the power consumption is 271uW from a single 1.2V power supply. One of the features of the proposed design is using two MOS transistors limitation to reduce the supply voltage, which leads to reduce the power consumption. This technique provides a GHz bandwidth response and low power consumption.

Keywords: RF-Mixer, Multiplier, cut-off frequency, power consumption

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445 Analysis of Plates with Varying Rigidities Using Finite Element Method

Authors: Karan Modi, Rajesh Kumar, Jyoti Katiyar, Shreya Thusoo

Abstract:

This paper presents Finite Element Method (FEM) for analyzing the internal responses generated in thin rectangular plates with various edge conditions and rigidity conditions. Comparison has been made between the FEM (ANSYS software) results for displacement, stresses and moments generated with and without the consideration of hole in plate and different aspect ratios. In the end comparison for responses in plain and composite square plates has been studied.

Keywords: ANSYS, Finite Element Method, Plates, Static Analysis.

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444 Evolutionary Dynamics on Small-World Networks

Authors: Jan Rychtar, Brian Stadler

Abstract:

We study how the outcome of evolutionary dynamics on graphs depends on a randomness on the graph structure. We gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increases; nevertheless, the increase is not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs.

Keywords: evolutionary dynamics, small-world networks

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443 Factors Militating the Organization of Intramural Sport Programs in Secondary Schools: A Case Study of the Ekiti West Local Government Area of Ekiti State, Nigeria

Authors: Adewole Taiwo Adelabu

Abstract:

The study investigated the factors militating the organization of intramural sports programs in secondary schools in Ekiti State, Nigeria. The purpose of the study was to identify the factors affecting the organization of sports in secondary schools and also to proffer possible solutions to these factors. The study employed the inferential statistics of chi-square (x2). Five research hypotheses were formulated. The population for the study was all the students in the government-owned secondary schools in Ekiti West Local Government of Ekiti State Nigeria. The sample for the study was 60 students in three schools within the local government selected through simple random sampling techniques. The instrument used for the study was a self-developed questionnaire by the researcher for data collection. The instrument was presented to experts and academicians in the field of Human Kinetics and Health Education for construct and content validation. A reliability test was conducted which involves 10 students who are not part of the study. The test-retest coefficient of 0.74 was obtained which attested to the fact that the instrument was reliable enough for the study. The validated questionnaire was administered to the students in their various schools by the researcher with the help of two research assistants; the questionnaires were filled and returned to the researcher immediately. The data collected were analyzed using the descriptive statistics of frequency count, percentage and mean to analyze demographic data in section A of the questionnaire, while inferential statistics of chi-square was used to test the hypotheses at 0.05 alpha level. The results of the study revealed that personnel, fund, schedule (time) were significant factors that affect the organization of intramural sport programs among students in secondary schools in Ekiti West Local Government Area of the State. The study also revealed that organization of intramural sports programs among students of secondary schools will improve and motivate students’ participation in sports beyond the local level. However, facilities and equipment is not a significant factor affecting the organization of intramural sports among secondary school students in Ekiti West Local Government Area.

Keywords: Challenge, militating, intramural sport, programs.

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442 Simulation of Tracking Time Delay Algorithm using Mathcad Package

Authors: Mahmud Hesain ALdwaik, Omar Hsiain Eldwaik

Abstract:

This paper deals with tracking and estimating time delay between two signals. The simulation of this algorithm accomplished by using Mathcad package is carried out. The algorithm we will present adaptively controls and tracking the delay, so as to minimize the mean square of this error. Thus the algorithm in this case has task not only of seeking the minimum point of error but also of tracking the change of position, leading to a significant improving of performance. The flowchart of the algorithm is presented as well as several tests of different cases are carried out.

Keywords: Tracking time delay, Algorithm simulation, Mathcad, MSE

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441 Compact Planar Antenna for UWB Applications

Authors: Rezaul Azim, Mohammad Tariqul Islam, Norbahiah Misran

Abstract:

In this paper, a planar antenna for UWB applications has been proposed. The antenna consists of a square patch, a partial ground plane and a slot on the ground plane. The proposed antenna is easy to be integrated with microwave circuitry for low manufacturing cost. The flat type antenna has a compact structure and the total size is 14.5×14.5mm2. The result shows that the impedance bandwidth (VSWR≤ 2) of the proposed antenna is 12.49 GHz (2.95 to 15.44 GHz), which is equivalent to 135.8%. Details of the proposed compact planar UWB antenna design is presented and discussed.

Keywords: Planar antenna, partial ground plane, ultrawideband(UWB) antenna.

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440 End Point Detection for Wavelet Based Speech Compression

Authors: Jalal Karam

Abstract:

In real-field applications, the correct determination of voice segments highly improves the overall system accuracy and minimises the total computation time. This paper presents reliable measures of speech compression by detcting the end points of the speech signals prior to compressing them. The two different compession schemes used are the Global threshold and the Level- Dependent threshold techniques. The performance of the proposed method is tested wirh the Signal to Noise Ratios, Peak Signal to Noise Ratios and Normalized Root Mean Square Error parameter measures.

Keywords: Wavelets, End-points Detection, Compression.

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439 Quasi-Permutation Representations for the Group SL(2, q) when Extended by a Certain Group of Order Two

Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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438 Design of Digital Differentiator to Optimize Relative Error

Authors: Vinita V. Sondur, Vilas B. Sondur, Narasimha H. Ayachit

Abstract:

It is observed that the Weighted least-square (WLS) technique, including the modifications, results in equiripple error curve. The resultant error as a percent of the ideal value is highly non-uniformly distributed over the range of frequencies for which the differentiator is designed. The present paper proposes a modification to the technique so that the optimization procedure results in lower maximum relative error compared to the ideal values. Simulation results for first order as well as higher order differentiators are given to illustrate the excellent performance of the proposed method.

Keywords: Differentiator, equiripple, error distribution, relative error.

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437 Some Characterizations of Isotropic Curves In the Euclidean Space

Authors: Süha Yılmaz, Melih Turgut

Abstract:

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.

Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.

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436 0.13-µm Complementary Metal-Oxide Semiconductor Vector Modulator for Beamforming System

Authors: J. S. Kim

Abstract:

This paper presents a 0.13-µm Complementary Metal-Oxide Semiconductor (CMOS) vector modulator for beamforming system. The vector modulator features a 360° phase and gain range of -10 dB to 10 dB with a root mean square phase and amplitude error of only 2.2° and 0.45 dB, respectively. These features make it a suitable for wireless backhaul system in the 5 GHz industrial, scientific, and medical (ISM) bands. It draws a current of 20.4 mA from a 1.2 V supply. The total chip size is 1.87x1.34 mm².

Keywords: CMOS, vector modulator, beamforming, wireless backhaul, ISM.

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435 Some Results on New Preconditioned Generalized Mixed-Type Splitting Iterative Methods

Authors: Guangbin Wang, Fuping Tan, Deyu Sun

Abstract:

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.

Keywords: Preconditioned, GMTS method, linear system, convergence, comparison.

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434 Exponential Stability of Numerical Solutions to Stochastic Age-Dependent Population Equations with Poisson Jumps

Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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433 On Maneuvering Target Tracking with Online Observed Colored Glint Noise Parameter Estimation

Authors: M. A. Masnadi-Shirazi, S. A. Banani

Abstract:

In this paper a comprehensive algorithm is presented to alleviate the undesired simultaneous effects of target maneuvering, observed glint noise distribution, and colored noise spectrum using online colored glint noise parameter estimation. The simulation results illustrate a significant reduction in the root mean square error (RMSE) produced by the proposed algorithm compared to the algorithms that do not compensate all the above effects simultaneously.

Keywords: Glint noise, IMM, Kalman Filter, Kinematics, Target Tracking.

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432 Modified Hankel Matrix Approach for Model Order Reduction in Time Domain

Authors: C. B. Vishwakarma

Abstract:

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

Keywords: Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error.

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431 Deployment of Service Quality Characteristics

Authors: Shuki Dror

Abstract:

This work discusses an innovative methodology for deployment of service quality characteristics. Four groups of organizational features that may influence the quality of services are identified: human resource, technology, planning, and organizational relationships. A House of Service Quality (HOSQ) matrix is built to extract the desired improvement in the service quality characteristics and to translate them into a hierarchy of important organizational features. The Mean Square Error (MSE) criterion enables the pinpointing of the few essential service quality characteristics to be improved as well as selection of the vital organizational features. The method was implemented in an engineering supply enterprise and provides useful information on its vital service dimensions.

Keywords: HOQ, organizational features, service quality.

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430 Machine Learning Techniques for Short-Term Rain Forecasting System in the Northeastern Part of Thailand

Authors: Lily Ingsrisawang, Supawadee Ingsriswang, Saisuda Somchit, Prasert Aungsuratana, Warawut Khantiyanan

Abstract:

This paper presents the methodology from machine learning approaches for short-term rain forecasting system. Decision Tree, Artificial Neural Network (ANN), and Support Vector Machine (SVM) were applied to develop classification and prediction models for rainfall forecasts. The goals of this presentation are to demonstrate (1) how feature selection can be used to identify the relationships between rainfall occurrences and other weather conditions and (2) what models can be developed and deployed for predicting the accurate rainfall estimates to support the decisions to launch the cloud seeding operations in the northeastern part of Thailand. Datasets collected during 2004-2006 from the Chalermprakiat Royal Rain Making Research Center at Hua Hin, Prachuap Khiri khan, the Chalermprakiat Royal Rain Making Research Center at Pimai, Nakhon Ratchasima and Thai Meteorological Department (TMD). A total of 179 records with 57 features was merged and matched by unique date. There are three main parts in this work. Firstly, a decision tree induction algorithm (C4.5) was used to classify the rain status into either rain or no-rain. The overall accuracy of classification tree achieves 94.41% with the five-fold cross validation. The C4.5 algorithm was also used to classify the rain amount into three classes as no-rain (0-0.1 mm.), few-rain (0.1- 10 mm.), and moderate-rain (>10 mm.) and the overall accuracy of classification tree achieves 62.57%. Secondly, an ANN was applied to predict the rainfall amount and the root mean square error (RMSE) were used to measure the training and testing errors of the ANN. It is found that the ANN yields a lower RMSE at 0.171 for daily rainfall estimates, when compared to next-day and next-2-day estimation. Thirdly, the ANN and SVM techniques were also used to classify the rain amount into three classes as no-rain, few-rain, and moderate-rain as above. The results achieved in 68.15% and 69.10% of overall accuracy of same-day prediction for the ANN and SVM models, respectively. The obtained results illustrated the comparison of the predictive power of different methods for rainfall estimation.

Keywords: Machine learning, decision tree, artificial neural network, support vector machine, root mean square error.

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429 New Product-Type Estimators for the Population Mean Using Quartiles of the Auxiliary Variable

Authors: Amer Ibrahim Falah Al-Omari

Abstract:

In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.

Keywords: Product estimator, auxiliary variable, simple random sampling, extreme ranked set sampling

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428 A Novel Antenna Design for Telemedicine Applications

Authors: Amar Partap Singh Pharwaha, Shweta Rani

Abstract:

To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.

Keywords: BFO, electrical permittivity, fractals, Koch curve.

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427 New Data Reuse Adaptive Filters with Noise Constraint

Authors: Young-Seok Choi

Abstract:

We present a new framework of the data-reusing (DR) adaptive algorithms by incorporating a constraint on noise, referred to as a noise constraint. The motivation behind this work is that the use of the statistical knowledge of the channel noise can contribute toward improving the convergence performance of an adaptive filter in identifying a noisy linear finite impulse response (FIR) channel. By incorporating the noise constraint into the cost function of the DR adaptive algorithms, the noise constrained DR (NC-DR) adaptive algorithms are derived. Experimental results clearly indicate their superior performance over the conventional DR ones.

Keywords: Adaptive filter, data-reusing, least-mean square (LMS), affine projection (AP), noise constraint.

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426 The Relative Efficiency Based on the MSE in Generalized Ridge Estimate

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A relative efficiency is defined as Ridge Estimate in the general linear model. The relative efficiency is based on the Mean square error. In this paper, we put forward a parameter of Ridge Estimate and discussions are made on the relative efficiency between the ridge estimation and the General Ridge Estimate. Eventually, this paper proves that the estimation is better than the general ridge estimate, which is based on the MSE.

Keywords: Ridge estimate, generalized ridge estimate, MSE, relative efficiency.

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425 Automation of Packing Cell in Fresh Fish Facilities

Authors: Omid Mirmotahari, Yngvar Berg, Mats Hovin

Abstract:

The problem discussed in this paper involves packing fresh fish fileet of the northern Cod into a standard square container. The fish is first cleaned and split and then collected on a belt ready to be stacked in a container. The aim of our work is to pack the fish into the container with constraints on the amount of overlap allowed for the fileets. The current focus is to design a packing cell that can be real-time and of practical use, while finding the optimal solution to the degree of overlap and minimise the unused space of the container.

Keywords: Facilities Planning and Management, Intelligent Systems, Manufacturing Systems, Operations Research, Production Planning and Control.

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424 Switching Behaviors of HfO2/NiSix Based RRAM

Authors: Z. X. Chen, Z. Fang, X. P. Wang, G. -Q. Lo, D. -L. Kwong, Y. H. Wu

Abstract:

This paper presents a study of Ni-silicides as the bottom electrode of HfO2-based RRAM. Various silicidation conditions were used to obtain different Ni concentrations within the Ni-silicide bottom electrode, namely Ni2Si, NiSi, and NiSi2. A 10nm HfO2 switching material and 50nm TiN top electrode was then deposited and etched into 500nm by 500nm square RRAM cells. Cell performance of the Ni2Si and NiSi cells were good, while the NiSi2 cell could not switch reliably, indicating that the presence of Ni in the bottom electrode is important for good switching.

Keywords: HfO2-based, Ni-silicide, NiSi, resistive RAM (RRAM).

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423 A Hygrothermal Analysis and Structural Performance of Wood-Frame Wall Systems with Low-Permeance Exterior Insulation

Authors: Marko Spasojevic, Ying Hei Chui, Yuxiang Chen

Abstract:

Increasing the level of exterior insulation in residential buildings is a popular way for improving the thermal characteristic of building enclosure and reducing heat loss. However, the layout and properties of materials composing the wall have a great effect on moisture accumulation within the wall cavity, long-term durability of a wall as well as the structural performance. A one-dimensional hygrothermal modeling has been performed to investigate moisture condensation risks and the drying capacity of standard 2×4 and 2×6 light wood-frame wall assemblies including exterior low-permeance extruded polystyrene (XPS) insulation. The analysis considered two different wall configurations whereby the rigid insulation board was placed either between Oriented Strand Board (OSB) sheathing and the stud or outboard to the structural sheathing. The thickness of the insulation varied between 0 mm and 50 mm and the analysis has been conducted for eight different locations in Canada, covering climate zone 4 through zone 8. Results show that the wall configuration with low-permeance insulation inserted between the stud and OSB sheathing accumulates more moisture within the stud cavity, compared to the assembly with the same insulation placed exterior to the sheathing. On the other hand, OSB moisture contents of the latter configuration were markedly higher. Consequently, the analysis of hygrothermal performance investigated and compared moisture accumulation in both the OSB and stud cavity. To investigate the structural performance of the wall and the effect of soft insulation layer inserted between the sheathing and framing, forty nail connection specimens were tested. Results have shown that both the connection strength and stiffness experience a significant reduction as the insulation thickness increases. These results will be compared with results from a full-scale shear wall tests in order to investigate if the capacity of shear walls with insulated sheathing would experience a similar reduction in structural capacities.

Keywords: Hygrothermal analysis, insulated sheathing, moisture performance, nail joints, wood shear wall.

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422 Optimal Solution of Constraint Satisfaction Problems

Authors: Jeffrey L. Duffany

Abstract:

An optimal solution for a large number of constraint satisfaction problems can be found using the technique of substitution and elimination of variables analogous to the technique that is used to solve systems of equations. A decision function f(A)=max(A2) is used to determine which variables to eliminate. The algorithm can be expressed in six lines and is remarkable in both its simplicity and its ability to find an optimal solution. However it is inefficient in that it needs to square the updated A matrix after each variable elimination. To overcome this inefficiency the algorithm is analyzed and it is shown that the A matrix only needs to be squared once at the first step of the algorithm and then incrementally updated for subsequent steps, resulting in significant improvement and an algorithm complexity of O(n3).

Keywords: Algorithm, complexity, constraint, np-complete.

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