• Korean Journal of Mathematics
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• v.18 no.2
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• pp.119-132
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for $a,b{\in}R$. In this paper, we study an extension of a reversible ring with its endomorphism. An endomorphism ${\alpha}$ of a ring R is called strong right (resp., left) reversible if whenever $a{\alpha}(b)=0$ (resp., ${\alpha}(a)b=0$) for $a,b{\in}R$, ba = 0. A ring R is called strong right (resp., left) ${\alpha}$-reversible if there exists a strong right (resp., left) reversible endomorphism ${\alpha}$ of R, and the ring R is called strong ${\alpha}$-reversible if R is both strong left and right ${\alpha}$-reversible. We investigate characterizations of strong ${\alpha}$-reversible rings and their related properties including extensions. In particular, we show that every semiprime and strong ${\alpha}$-reversible ring is ${\alpha}$-rigid and that for an ${\alpha}$-skew Armendariz ring R, the ring R is reversible and strong ${\alpha}$-reversible if and only if the skew polynomial ring $R[x;{\alpha}]$ of R is reversible.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1257-1272
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• 2019

This article concerns the structure of idempotents in reversible and pseudo-reversible rings in relation with various sorts of ring extensions. It is known that a ring R is reversible if and only if $ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba; and a ring R shall be said to be pseudoreversible if $0{\neq}ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba, where I(R) is the set of all idempotents in R. Pseudo-reversible is seated between reversible and quasi-reversible. It is proved that the reversibility, pseudoreversibility, and quasi-reversibility are equivalent in Dorroh extensions and direct products. Dorroh extensions are also used to construct several sorts of rings which are necessary in the process.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.11
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• pp.1233-1240
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• 2014

For the last three decades after the advent of the Toffoli gate in 1980, while many reversible circuit syntheses have been presented reversible embedding methods onto suitable reversible functions, only a few proposed direct irreversible-to-reversible mapping methods without reversible embedding. In this paper we present two effective policies to reduce the gate cost and complexity for the existing direct reversible mapping methods without reversible embedding. In order to develop new cost reduction policies we consider the cost influence of Toffoli module according to NOT gate arrangement in classical circuits. From this we deduced an inverse proportional property between inverting input numbers of classical AND/OR gates and reversible Toffoli module cost based on a fact - the inverting inputs of classical AND(OR) gates increase(decrease) the Toffoli module cost. We confirm the applications of the inverting input rearrangement and maximum fan-out policies preceding direct reversible mapping will be effective method to improve the reversible Toffoli module cost and complexity with the parallel using of the fan-out and supercell ones.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.532-543
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• 2003

In this paper, we proposed structure of a reversible discrete-time cellular neural network (DTCNN) for labeling digital images to protect copylight. First, we present the concept and the structure of reversible DTCNN, which can be used to generate 2D binary pseudo-random images sequences. We presented some, output examples of different kinds of reversible DTCNNs to show their complex behaviors. Then both the original image and the copyright label, which is often another binary image, are used to generate a binary random key image. The key image is then used to scramble the original image. Since the reversibility of a reversible DTCNN, the same reversible DTCNN can recover the copyright label from a labeled image. Due to the high speed of a DTCNN chip, our method can be used to label image sequences, e.g., video sequences, in real time. Computer simulation results are presented.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.209-227
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• 2021

In this paper, we deal with the question that what kind of properties does a ring gain when it satisfies symmetricity or reversibility by the way of nilpotent elements? By the motivation of this question, we approach to symmetric and reversible property of rings via nilpotents. For symmetricity, we call a ring R middle right-(resp. left-)nil symmetric (mr-nil (resp. ml-nil) symmetric, for short) if abc = 0 implies acb = 0 (resp. bac = 0) for a, c ∈ R and b ∈ nil(R) where nil(R) is the set of all nilpotent elements of R. It is proved that mr-nil symmetric rings are abelian and so directly finite. We show that the class of mr-nil symmetric rings strictly lies between the classes of symmetric rings and weak right nil-symmetric rings. For reversibility, we introduce left (resp. right) N-reversible ideal I of a ring R if for any a ∈ nil(R), b ∈ R, being ab ∈ I implies ba ∈ I (resp. b ∈ nil(R), a ∈ R, being ab ∈ I implies ba ∈ I). A ring R is called left (resp. right) N-reversible if the zero ideal is left (resp. right) N-reversible. Left N-reversibility is a generalization of mr-nil symmetricity. We exactly determine the place of the class of left N-reversible rings which is placed between the classes of reversible rings and CNZ rings. We also obtain that every left N-reversible ring is nil-Armendariz. It is observed that the polynomial ring over a left N-reversible Armendariz ring is also left N-reversible.

• Journal of Magnetics
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• v.17 no.3
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• pp.206-209
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• 2012

Peak interval for reversible permeability is presented for nondestructively evaluating the remanent life of 1Cr-0.5Mo steel. The method to measure the peak interval of reversible permeability is based on the value of reversible permeability is the same as the differential value of the hysteresis loop. The measurement principle is based on the first harmonics voltage induced in a sensing coil using a lock-in amplifier tuned to a frequency of the exciting voltage. Results obtained for the peak interval of reversible permeability and Rockwell hardness on the aged samples decrease as aging time and the Larson-Miller parameter increase. We could estimate the remanent life of 1Cr-0.5Mo steel by using the relationship between the peak interval of reversible permeability and the Larson-Miller parameter, nondestructively.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.531-542
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• 2014

In this paper, we apply some properties of reversible rings, Baerness of fixed rings, skew group rings and Morita Context rings to get conditions that shows fixed rings, skew group rings and Morita Context rings are reversible. Moreover, we investigate conditions in which Baer rings are reversible and reversible rings are Baer.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.639-644
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• 2009

In this paper, we begin with to introduce the concepts of IFP and strong IFP in near-rings and then give some characterizations of IFP in near-rings. Next we derive reversible IFP, and then equivalences of the concepts of strong IFP and strong reversibility. Finally, we obtain some conditions to become strong IFP in right permutable near-rings and strongly reversible near-rings.

• Journal of Korea Multimedia Society
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• v.25 no.9
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• pp.1291-1306
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• 2022

The dual image-based reversible data hiding scheme embeds secret data into two images to increase the embedding capacity of secret data. The dual image-based reversible data hiding scheme can transmit a lot of secret data. Therefore, various schemes have been proposed until recently. In 2021, Chen and Hong proposed a dual image-based reversible data hiding scheme that embeds a large amount of secret data using a reference matrix, secret data, and bit values. However, in this paper, more secret data can be embedded than Chen and Hong's scheme. To achieve this goal, the proposed scheme generates polynomials and shared values using secret sharing scheme, and embeds secret data using reference matrix and septenary number, and random value. Experimental results show that the proposed scheme can transmit more secret data to the receiver while maintaining the image quality similar to other dual image-based reversible data hiding schemes.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.443-460
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• 2023

A binary linear code is said to be a ℤ₂-double cyclic code if its coordinates can be partitioned into two subsets such that any simultaneous cyclic shift of the coordinates of the subsets leaves the code invariant. These codes were introduced in [6]. A ℤ₂-double cyclic code is called reversible if reversing the order of the coordinates of the two subsets leaves the code invariant. In this note, we give necessary and sufficient conditions for a ℤ₂-double cyclic code to be reversible. We also give a relation between reversible ℤ₂-double cyclic code and LCD ℤ₂-double cyclic code for the separable case and we present a few examples to show that such a relation doesn't hold in the non-separable case. Furthermore, we list examples of reversible ℤ₂-double cyclic codes of length ≤ 10.