In many scientific fields and several problems, Block Circulant Matrices (BCM) have been used for a long period of time. Each row of the BCM is a cyclic shift of its upper row to the right. BCM has been studied widely and there are closed-form solutions for problems of BCM. In these problems, the properties of near-BCM and BCM lead to a significant decrease in computational cost and efforts. In other words, these matrices are useful to perform some computational operations at the low cost. This study introduces a method for transforming a structure into a new type of Block Circulant Structure (BCS) by applying minor modifications. Furthermore, transformation of structural matrices into Block Circulant Matrices is discussed, and the properties of these matrices are then described in details. The methods introduce calculating eigenvalues and eigenvectors of these matrices instead of calculating the inverse of their matrices. To achieve this goal, the properties of near-Block and Block Circulant Matrices are used to analyze the structural stiffness matrices. In addition, the inverse of stiffness matrices for structures are calculated and utilized in structural mechanics. For clarification of efficiency and accuracy of the method, some examples are presented.
Digital watermarking is one of the best solutions again the copyright infringement, duplicates, verifies data and illegal distribution of digital media. Recently, the protection of digital audio signals is one of the attracting and interesting topics for scientific and researchers. In this paper we propose a blind audio watermarking mechanism in which it has high capacity, transparency and resistance simultaneously based on digital wavelet transform (DWT) algorithm. The key principle of this work is that in the DWT procedure, using two filters; break down the original audio signal into several sub-bands and transform them on a specific frequency range. It should be noted that the 8 bits of watermarked signal is selected and transform to the original signal. In order to increase the watermarking resistance, framing the high frequency coefficients of the third level of the wavelet and calculate the frames average and place them in the frame memory prime. Moreover, TLBO algorithm used to determination of embedding and extraction coefficients in order to increase the SNR ratio in the embedding process and decrease the bit error rate (BER) in the extraction process. This method increases the embedding payload capacity while the audio SNR and extracted image BER have good qualify. Moreover, experimental results shown that this method has 13kbs hiding rate,ascendency imperceptibility, good payload capacity and intense robustness when resisting against various attacks such as MP3 compression, re-quantization, low-pass filtering, amplitude scaling, re-sampling, echo addition and noise corruption.
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