Decimal Sequence Research Articles

Compound faults identification of rolling bearing based on one-dimensional mixed binary pattern

To address the difficulty in extracting the characteristics of combined failure of rolling bearings, a novel fault identification method, one-dimensional mixed binary pattern (1D-MBP), is proposed. Firstly, regarding that variance can better highlight the partial weak failure information of sequence than median, the binarization of vibration signals based on one-dimensional local binary pattern (1D-LBP) is carried out with variance as criterion. Meanwhile, binarization sequence is converted to decimal sequence as the local conversion signal (LCS). Secondly, considering that failure information of rolling bearings is reflected in partial and global texture, the paper proposed the method of gaining global weighted mean value by weighting partial mean value with partial energy. Binarize vibration signals based on one-dimensional global binary pattern (1D-GBP) with obtained global weighted mean value as criterion and convert the obtained binarized sequence into decimal as the global conversion signal (GCS). Thirdly, signals are reconstructed by obtained LCS and GCS to get 1D-MBP signal. Finally, combined failure types of bearing can be identified from 1D-MBP signals based on TEAGER energy spectrum (TES). The result indicates that the 1D-MBP not only can effectively control noise components in vibration signal but also can precisely identify the combined failure types of rolling bearings.

Enhancing the kinetic complexity of 2-D digital coupled chaotic lattice

A 2-dimensional coupled logistic map lattice model and a 2-dimensional Logistic-nested-Sine map are proposed in this paper. In order to strengthen complexity of 2-dimensional coupled logistic map lattice, chaotic sequences are transformed to binary sequences, and new decimal sequences are constructed by perturbed binary sequences. Numerical experimental results demonstrate that this method can increase the complexity and ergodicity of 2-dimensional coupled logistic map lattice effectively. The initial values of the 2-dimensional coupled logistic map lattice are determined by utilization of the SHA 512 hash function. The row and column positions of pixels are shuffled completely in permutation process. Unlike 1-dimensional linear diffusion operation, we have adopted two-dimensional space diffusion began from random semi-surround. Keys security, correlation coefficient, information entropy, and ability of defending differential attack are analyzed to confirm the security of our encryption scheme. Experimental results confirm that the proposed algorithm can encrypt image effectively.

스프레드시트 환경에서 근사 분수와 직선의 기울기를 이용한 무리수의 대안적 지도법

The purpose of this study was to explore the possibility of interconnection between non-fractional representation and non-circular decimal representation in irrational teaching and learning of school mathematics and to examine the possibility of field application. First, through the analysis of previous studies, it was found that the core of understanding irrational concepts is the intuitive perception of convergence and the inference of acyclicity. And through mathematical analysis, we confirmed that finite decimal sequences and approximate fractional sequences should be learning contents. In this regard, we applied engineering tools in teaching and learning activity of irrational numbers and analyzed the process by which engineering tools become learners’ mathematical tools and then learning occurs, that is, instrument genesis. As a result, in the activity of finding finite fractions of square roots, students gained a meaningful understanding by focusing on the meaning of square root symbols and square roots as objects from inputting functions and operations and using drag. And in the activity to solve the task ‘Can a graph cross a grid point?’, Students could infer the acyclicity of the decimal representation of irrational numbers by observing the approximate fraction as the slope. Thus, this study is expected to be a basic reference of teaching and learning of irrational numbers to construct a mental image of real numbers completeness axiom.

On k-Error Linear Complexity of Binary Sequences Derived From Euler Quotients Modulo 2p

We consider the $k$-error linear complexity of binary sequences derived from Eluer quotients modulo $2p$ ($p>3$ is an odd prime), recently introduced by J. Zhang and C. Zhao. We adopt certain decimal sequences to determine the values of $k$-error linear complexity for all $k>0$. Our results indicate that such sequences have good stability from the viewpoint of cryptography.

A robust blind watermarking framework based on Dn structure

In this paper, a new robust watermarking framework is designed using the discrete cosine transform (DCT), binary decimal sequence (d-sequence) and Dn-structure. The core idea is to generate a binary d-sequence based on random number generator (RNG) and some secret keys. This binary sequence is then utilized to generate reference sets based on Dn-structure. For embedding purpose, the host image is transformed using DCT and selected coefficients are employed to construct a macro block. Each binary watermark bit is securely embedded into macro block by utilizing the reference set. The reverse process is finally formulated to extract the watermark at the receiver end. The proposed technique is experimentally analyzed using various quality metrics and attacks. The comprehensive experimental results illustrate that the proposed watermarking scheme is robust to both geometric distortions (resizing, cropping, wrapping and random row deletion) and general signal processing attacks (various noise addition, blurring, high pass filtering, image sharpening, contrast adjustment, Histogram equalization and gamma correction and JPEG compression) and outperforms state-of-the-art watermarking methods.

A simplified watermarking algorithm based on lifting wavelet transform

This paper presents a new blind image watermarking scheme using binary decimal sequence (d-sequence) and lifting wavelet transform (LWT) for copyright protection. The core idea is to produce a d- sequence based on random number generator (RNG) algorithm and secret keys. A reference set is then generated using the d-sequence for embedding purpose. For embedding, the host image is decomposed into different frequency bands using the LWT and watermark bits are then embedded in selected band, considering the reference set. The extensive experimental results, comparative and security analysis demonstrate the better robustness of the proposed scheme against different kind of attacks.

A Module Layout Method of Emergency Rescue Equipment Box Based on Layer Space

Module layout of emergency rescue equipment box is a special three-dimensional (3D) bin-packing problem, whose mathematical description is that under the condition of fixed capacity, the corresponding value of equipment in the box is maximized. Through the analysis of the characteristics of the emergency rescue equipment box, three evaluation indexes, including the average height of centroid, the average distance of access and the functional distance of equipment, were proposed first. In order to obtain a more ideal 3D packing scheme, a module layout method based on layer space using genetic algorithm was also proposed. These equipments to be arranged were encoded in decimal. According to the fitness function and the objective function, the selection, crossover and mutation operations of decimal sequence were conducted. After the iteration, the value of objective function gradually approached to the optimal solution. To evaluate the performance of the proposed method, some simulations under the MATLAB were performed. Finally, the experimental results show that the proposed method can achieve a better optimization effect, proving its effectiveness and feasibility.

Quantum Image Encryption Based on Henon Mapping

Quantum image processing has great significance as a branch of quantum computing. This paper gives a quantum image encryption based on Henon mapping, which breaks away from the restriction of classical computers and does the work in quantum computers end to end, including the generation of the chaos sequence, the encryption and the decryption. The algorithm is based on the GQIR quantum image representation model and the two-dimensional Henon chaotic mapping. However, the decimal sequence generated by Henon mapping can not be directly applied to quantum computers. Hence, we reform the Henon mapping by binary shift. The quantum image is encrypted by being XORed with the quantum Henon mapping. Simulation experiments indicate that the encrypted image has good radomness and the pixel values are evenly distributed. Since the chaotic sequence itself is suitable for image encryption, coupled with its own quantum confidentiality, the encryption method of this paper is safe, convenient and reliable.

A survey on the applications of Niho exponents

The Niho exponent was introduced by Yoji Niho, who investigated the cross-correlation function between an m-sequence and its decimation sequence in 1972. Since then, Niho exponents have been used in other research areas such as in cryptography and coding theory. In this paper, we introduce some research problems related to Niho exponents and survey some recent progress in the application of Niho exponents. Some open problems in the areas of sequence design, cryptography and coding theory regarding Niho exponents are also presented.

On the Correlation Distribution for a Niho Decimation

Let $p$ be a prime, $n=2m$ and $d=3p^{m}-2$ with $m\geq 2$ , and $\gcd (d,p^{n}-1)=1$ . In this paper, the correlation distribution between a $p$ -ary $m$ -sequence of period $p^{n}-1$ and its $d$ -decimation sequence is investigated in a unified approach. Some results for the binary case are extended to the general case. It is shown that the problem of determining the correlation distribution for $d$ can be reduced to that of solving two combinatorial problems related to the unit circle of the finite field $\mathbb {F}_{p^{n}}$ . For an arbitrary odd prime $p$ , it seems difficult to solve these two problems. However, for $p=3$ , by studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over $\mathbb {F}_{3^{n}}$ , the two problems are solved, and thus, the corresponding correlation distribution for $d$ is completely determined. It is noteworthy that this is the first time that the correlation distribution for a non-binary Niho decimation has been determined since 1976.

Two families of Niho sequences having four-valued cross correlation with m-sequences

For two odd integers $m$ and $s$ with $1\leq~s<m$ and ${\rm~gcd}(m,s)=1$, let $h$ satisfy $h(2^{s}-1)\equiv1~({\rm~mod}\,2^{m}+1)$ and $d=(h+1)(2^{m}-1)+1$.The cross correlation function between a binary $m$-sequence of period $2^{2m}-1$ and its $d$-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let $n$ be an even integer and $k$ be an integer with $1\leq~k\leq~\frac{n}{2}$. For an odd prime $p$ and a $p$-ary $m$-sequence $\{s(t)\}$ of period $p^{n}-1$, define $u(t)=\sum_{i=0}^{\frac{p^{k}-1}{2}}s(d_{i}t)$, where $d_{i}=ip^{\frac{n}{2}}+p^{k}-i$ and $i=0,1,\ldots,~\frac{p^{k}-1}{2}$. It is proved that the cross correlation function between $\{u(t)\}$ and $\{s(t)\}$ is three-valued or four-valued depending on whether $k$ is equal to$\frac{n}{2}$ or not, and the distribution is also determined.

A new kind of steganography schemes for image

Message security is more and more important in our modern life. As encryption arousing suspicion easily, steganography which aims at hiding secret message in a cover and has little influence on the cover becomes popular. There are many steganography algorithms having been proposed. Most of them are based on binary, but binary sequence is longer than ternary sequence of a same decimal sequence. In this paper, to have a shorter sequence to represent secret message and protect it, we propose a new method to deal with secret message and get a binary sequence, a ternary sequence and a quaternary sequence. For the ternary sequence and quaternary sequence, we propose a ternary JSteg method and a quaternary JSteg method; this method can keep the histogram characters. So for same secret message, our method will have less influence on the cover.

A new kind of steganography schemes for image

Message security is more and more important in our modern life. As encryption arousing suspicion easily, steganography which aims at hiding secret message in a cover and has little influence on the cover becomes popular. There are many steganography algorithms having been proposed. Most of them are based on binary, but binary sequence is longer than ternary sequence of a same decimal sequence. In this paper, to have a shorter sequence to represent secret message and protect it, we propose a new method to deal with secret message and get a binary sequence, a ternary sequence and a quaternary sequence. For the ternary sequence and quaternary sequence, we propose a ternary JSteg method and a quaternary JSteg method; this method can keep the histogram characters. So for same secret message, our method will have less influence on the cover.

An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

In this paper, let $n=2k$ and $d=3\cdot 2^{k}-2$ with $k\geq 3$ and $\gcd (d,2^{n}-1)=1$ . Based on some analysis of certain equations over finite fields and the number of codewords with Hamming weight five in Zetterberg code, the correlation distribution between a binary $m$ -sequence of period $2^{n}-1$ and its $d$ -decimation sequence is completely determined. This solves a ten-year-old open problem proposed by Dobbertin et al.

Decimal Sequence based Imperceptible Audio Watermarking

Digital watermarking has been proposed as a new, alternative method to enforce intellectual property rights and protect digital media from tempering. Digital watermarking is defined as imperceptible, robust and secure communication of data related to the host signal, which includes embedding into and extracted from the host signal. The main challenge in digital audio watermarking is that if the perceptual transmitter is fixed, the design of watermark system cannot obtain high watermark data rate and high robustness at the same time. The main objective of this paper is to development of an audio watermarking algorithm which obtain high watermark data rate and high quality of audio at the same time General Terms Decimal Sequence, Audio Watermarking.

On the Cross-Correlation of a $p$-Ary ${m}$-Sequence of Period $p^{2m}-1$ and Its Decimated Sequences by $ {{ (p^{m}+1)^{2}}/ { 2(p+1)}}$

In this paper, for an odd prime , we investigate into the cross-correlation of a p-ary m-sequence m(t) of period p ;n ;-1 and its d-decimated sequences m(dt+l), 0≤l ;m ;+1)/2, where d=(pm+1)2/2(p+l), n=2m, and m is an odd integer. There are (pm+1)/2 distinct decimated sequences m(dt+l) since gcd(d,pn-1)=(pm+1)/2. It is shown that the magnitude of the cross-correlation values is upper bounded by (p+1)/2 pn/2+1 . We also construct the sequence family F from these sequences, where the family size is pm and the correlation magnitude is upper bounded by (pm+1)/2 pn/2+1.

Analysis of the Number of Terms in the Generation Polynomial of the Decimation Sequence

In this paper, we discuss the relationship between the generation polynomial of a linear sequence and its decimation sequence over the finite field 𝔽2. Then we propose an upper bound of the number of terms in the generation polynomial of a decimation sequence of a linear sequence whose generation polynomial is trinomial. Finally, we suggest a method to calculate the terms of a decimation polynomial and their number directly, which can be used in the construction of irreducible polynomials with a controlled number of terms, when the source trinomial and the decimation distance satisfy a certain condition.

Cross-Correlation Distribution of $p$-ary $m$-Sequence of Period $p^{4k}-1$ and Its Decimated Sequences by $\left({{ p^{2k}+1}\over { 2}}\right)^{2}$

For an odd prime p, n=4k, and d=((p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> +1)/2) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , there are (p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> +1)/2 distinct decimated sequences s(dt+l), 0lesl<(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> +)/2,of a p-ary m-sequence s(t) of period p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1 because gcd(d,p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1)=(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> +1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l),0lesl<(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> +1)/2, takes the values in {-1, -1 -radic(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ),-1+radic(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ),-1+2radic(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> )} and their cross-correlation distribution is also derived.

Cross-Correlation Distribution of p-Ary m-Sequence and Its p+1 Decimated Sequences with Shorter Period

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = pk + 1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l p + 1, for a p-ary m-sequence s(t) of period pn-1 because gcd(d, pn-1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p√pn if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + √pn. Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pn-1 is constructed, whose family size is pn and Cmax is 1 + p√pn.

An Improved Method of Content Based Image Watermarking

We consider texture, luminance, corner and the edge information in the image to generate a mask that makes the addition of the watermark less perceptible to the human eye. The operation of embedding and extraction of the watermark is done in the frequency domain thereby providing robustness against common frequency-based attacks including image compression and filtering. We use decimal sequences for watermarking instead of pseudo random sequences, providing us with a greater flexibility in the choice of sequence. Weighted Peak Signal to Noise Ratio is used to evaluate the perceptual change between the original and the watermarked image