The main purpose of this study is to investigate eighth-grade students¡¦ understanding of the equal sign and analyzed error types of quadratic equation in one variable. To achieve this purpose, the investigator did a survey and development instruments. Participants were 215 eighth-grade students who formed a convenient sample. There are three results. First, participants with a relational definition of the equal sign added to about 80% of the sample. Second, the performance of students with relational definitions is higher than the performance of students with operational definitions. Third, students¡¦ understanding of the equal sign was related to their respective problem-solving performance on quadratic equation in one variable. In this study, participants with an operational definition of the equal sign tended to guess randomly or leave a blank. Problem-solving performance of participants with a relational definition of the equal sign involved multiple strategies. The researcher suggested that teachers should strengthen students¡¦ understanding of equal sign and related students¡¦ prior algebraic knowledge.

In wireless communication systems, we may encounter many problems. One of the main issues is noise interference. To overcome the problem, the sender can use the Convolutional coding method to encode the data, and the receiver can utilize the Viterbi algorithm for decoding and correction purposes. Due to the high complexity of the Viterbi algorithm, the VLSI structure of Viterbi decoder will consume large amounts of power, leading the portable devices to short standby time and high operating temperature. In order to solve these problems we have to design a low power decoder. As a matter of fact, the Viterbi decoder can be actually shutdown when no noise interference exists. As a consequence, we use a detection circuit to determine whether the signal is influenced by noise. If the signal is interfered, we choose the Viterbi decoder to perform the decoding process. Otherwise, we utilize a low cost decoder to lessen the power consumed at the receiver end. In addition, dynamic adjustment of SMU module is also developed and implemented in the proposed decoder. SMU module consumes the most power in Viterbi decoder. So, our developed and goal is to reduce the usage of SMU module. If noise distribution is not so dense, we don¡¦t have to use high decoding ability to decode section data. Therefore, the registers in SMU can be decreased. Clock gating technique is adopted in this thesis to shutdown these idle registers to reduce the power consumption of SMU. The proposed decoder has been implemented and synthesized using the Artisan TSMC 0.13£gm standard cell library. Compared with the traditional Viterbi decoder, the proposed decoder can achieve 25% and nearly 60% power saving when the SNR is 1dB and 8dB respectively, with 6% area reduction. According to the above experimental results, we can say that the proposed decoder is able to reduce power consumption.

In wireless communication system, convolutional coding method is often used to encode the data. In decoding convolutional code (CC), Viterbi algorithm is considered to be the best mechanism. Viterbi decoder (VD) was developed to execute the algorithm on mobile devices more effectively. This decoder is often used on 2G and 3G mobile phones. However, on 2G phones, VD consumes about one third of total power consumption of the signal receiver. Therefore it is very necessary to reduce the power consumption of VD on 2G and 3G phones. VD uses large amount of register in survivor metric unit (SMU), so that the decoder can receive enough CC and converge automatically. The goal of this thesis is to decrease power consumption of SMU by using path metric compare unit (PMCU) to find the best state of path metric unit (PMU). This way decreases half of registers and multiplexers required in SMU, leading to significant area reduction in decoder. During the process of signal transmission in wireless communication, different causes like the atmosphere, outer space radiation and man-made will interfere the signal by different degree. The stronger the noise is, the more interference CC will get. The error detection circuit used will mark the sections with noise interference before the CC enters the VD. If CC is interfered, it will be decoded by the whole VD. Otherwise, it will be decoded by low power decoder, where the controller will start clock gating mechanism on SMU to close up unnecessary power consumption block. The power consumption of is varying proposed Adaptive Viterbi decoder according to the interference degree. When interference degree is high, the power consumption is 21% less than conventional VD; when interference is low, it is 44% less. The results show that the proposed method can effectively reduce the power consumption of VD.

In this thesis, we investigate the problem of channel estimation in the amplify-and-forward cooperative communication systems when the networks could be in the presence of selfish relays. The information received at the destination will be detected and then used to estimate the channel. In previous studies, the relays will deliver the information under the prerequisite for cooperation and the destination can receive the information sent from the source without any possible selfish relay. Therefore, the channel will be estimated under this over idealistic assumption. Unfortunately, the assumption does not make sense in real applications. Currently, we don¡¦t have a mechanism to guarantee the relays will always be cooperative. The performance of channel estimation will be significantly degraded when the selfish relays present in the network. Therefore, this thesis considers an amplify-and-forward cooperative communication system with direct transmission and proposes a detection mechanism to overcome the misbehaving relay problem. The detection mechanism employed estimation is based on likelihood ratio test using both direct transmission and relayed information. The detection result will then be used to reconstruct the codeword used for estimating product channel gain of the source-to-relay and relay- to-destination links. The mathematical derivation for the considered problem is developed and numerical simulations for illustration is also carried out in the thesis. The numerical simulation results verify that the proposed method is indeed able to achieve robust channel estimation.

Reversible watermarking techniques extract the watermark and recover the original image losslessly from the watermarked image. They have been applied to those sensitive fields, such as the medicine and the military. Since an embedding pixel value may exceed the limitation of pixel value during the embedding process, most of the reversible watermarking methods require a location-map to record those pixels for recovering cover images. Although the location-map can be compressed by a lossless compression algorithm, and then embed into the watermarked image, this lowers embedding capacity and increases the complexity of watermarking during the procedures of embedding and extraction. In this thesis, we propose a reversible location-map free of watermarking algorithm. This algorithm first exploits the sorting and the correlation of neighboring pixels to increase the embedding capacity. Next we find thresholds from the predicted values. If the predicted value of an embedding pixel is within the thresholds, we can ensure that the pixel has no underflow or overflow problem during embedding process. Therefore, we can recover the cover image without any distortion. The experimental results reveal that the performance of our proposed method outperforms that proposed by FUJIYOSHI et al. For example, the embedding capacity obtained by the proposed method is higher than that obtained by FUJIYOSHI et al. about 60%, and the PSNR of our scheme is higher than FUJIYOSHI et al. about 5 dB.

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This dissertation is mainly focused on the analysis, design and optimization of Low-density parity-check (LDPC) codes over channels with large alphabet sets and the applications on compressed sensing (CS) and flash memories. Compared to belief-propagation (BP) decoding, verification-based (VB) decoding has significantly lower complexity and near optimal performance when the channel alphabet set is large. We analyze the verification-based decoding of LDPC codes over the q-ary symmetric channel (q-SC) and propose the list-message-passing (LMP) decoding which off ers a good tradeoff between complexity and decoding threshold. We prove that LDPC codes with LMP decoding achieve the capacity of the q-SC when q and the block length go to infinity. CS is a newly emerging area which is closely related to coding theory and information theory. CS deals with the sparse signal recovery problem with small number of linear measurements. One big challenge in CS literature is to reduce the number of measurements required to reconstruct the sparse signal. In this dissertation, we show that LDPC codes with verification-based decoding can be applied to CS system with surprisingly good performance and low complexity. We also discuss modulation codes and error correcting codes (ECC’s) design for flash memories. We design asymptotically optimal modulation codes and discuss their improvement by using the idea from load-balancing theory. We also design LDPC codes over integer rings and fields with large alphabet sets for flash memories.

Double-Enveloping Reducers are used widely in various industries. In this study, a procedure is developed to analyze the geometric and kinematic properties of such a rotational reducer. In the mechanism, the globoidal worm profile is derived by using the sweeping method and the profile of the globoidal worm wheel is obtained by employing the screw theory. Based on Standards of the American Gear Manufacturers Association (AGMA 6030-C87), the involved parameters in designing and analyzing the reducer are revealed. Finally, the transmission errors based on tooth the contact analysis (TCA) are also reported.

International academia expressed doubt that china¡¦s statistical surveys reflect actual economic performance in 2001, in regard to the China¡¦s statistical accuracy, many scholars put forward different opinions. And compared the Chinese government's official figures with the countries of the world, lie in the question of investigating information on¡§ the degree of public¡¨ and the statistical surveys of¡§ report to a higher level officials¡¨. The main purpose of this research is probing into the problem of the Chinese government's official figures via the surveys of Chinese household income to prove that the distribution income of China to the initial data inaccuracy making China¡¦s household income unable to reflect the true. Therefore, we should doubt that China's statistics for lacking credibility on household income. Through the analysis structure of this text, we find out the following¡Gfirst of all, under the centralization type statistical system, the local statistical organization undertake the job of¡§survey¡¨ and¡§analysis¡¨ as the role of ¡§the sportsman and concurrently referee¡¨ make the question of statistical standard unable to improve. Secondly, with the Chinese non-sampling error proportion is far too larger. China statistical year book reported Chinese household income date merely conform to the ¡§salaried family¡¨¡F those who worked in the state-owned enterprise, but surveys date are not suitable for rural family and non state-owned enterprises worker¡¦s family. Moreover, through analyzing China¡¦s statistical education; the protection of the relent law and the impetus of the civil statistical work, my research discovered that the Chinese government's official figures are less accurate than those of industrialized countries and the supervision function are very weak. Finally, China has transformed its planned economy system into an initial socialist market economy system that interwove by the various forms and multiple interests relation, therefore strengthened the difficulty of statistical surveys of the professional. Especially under the turn rail environment deepening the degree of high-level and low-level officials¡§ the individual information asymmetric¡¨, and after the dismantling of the old supervise management system, the new statistical supervisal system is unable to confine yet. Contemporary the implemented statistical surveys of socialist market economy are more error then those of planned economy. On the above analyzes, I suggested that the Chinese government¡¦s official statistics should strengthened the sophisticated data compiling systems such as American statistics system that adopted the statistics system of social feedback and the statistics of decentralize, unable china to increase its social statistics and reduce the question of statistical surveys of¡§ report to a higher level officials¡¨, and heightening the Chinese statistical data a little more accurately.

Eddy current testing is a non-destructive testing method that has usually used for examination of carbon steel tubes. By using a high frequency electromagnetic field on the exciting probe, it is easy to figure out the impedance variation of the coil on impedance plane, and estimate the crack depth by measuring the angle of curve. However, different kind of tubes and electromagnetic properties resulted in different testing. The purpose of this study is to create the two dimensional axial symmetry model of eddy current testing by finite element software package FEMLAB. And it is easy to estimate the crack depth by figuring the impedance plane and evaluation curves by MATLAB. Furthermore, the research analyzed the variation of curves and angles on an impedance plane and tried to reduce testing errors. Over all, the analysis of some influence factors of eddy current testing in the present study not only provides a standard of estimating crack depth more accurately, but also reduces the evaluation errors.