This paper reports a systematic experimental investigation on the dynamics in the low-frequency region in an erbium-doped fibre-ring laser with loss modulation. A rich variety of bifurcation is analyzed through the bi...This paper reports a systematic experimental investigation on the dynamics in the low-frequency region in an erbium-doped fibre-ring laser with loss modulation. A rich variety of bifurcation is analyzed through the bifurcation diagram and structured with the concept of the winding numbers. The coexistence of multiple attractors and the crisis that appear in the saddle-node bifurcations, and an interesting structure of bifurcation which is similar to the bifurcations in high-frequency range, have been observed.展开更多
In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if <em>n</em> is not a square, square root of <em&g...In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if <em>n</em> is not a square, square root of <em>n</em> is not a rational number”. And then some conceptions of ring, integral domain, ideal, quotient ring in Advanced algebra, have been introduced. Integers can be regarded as an integral domain, the rational numbers can be regard as a fractional domain. Evens and odds are principal ideals in integral domain. The operations on evens and odds are operations on quotient ring. After introducing “the minimalist form” in fraction ring. The paper proves the main conclusion: in a integral domain, multiplicative subset <em>S</em> produces a fraction ring <em>S</em><sup><span style="white-space:nowrap;">−</span>1</sup><em>R</em>, and <em>n</em> is not a square element in <em>R</em>, then to every element <em>a</em><span style="white-space:nowrap;">∈</span><em>R</em>, <span style="white-space:nowrap;"><em>a</em><sup>2</sup>≠<em>n</em></span>.展开更多
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a an...Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.展开更多
针对格基环签名方案的陷门基尺寸过大以及环成员的公钥需要数字证书认证的问题,提出一种NTRU(Number Theory Research Unit)格上的身份基环签名方案(NTRU-IBRS)。首先,使用NTRU格上的陷门生成算法生成系统的主公私钥对;然后,将主私钥作...针对格基环签名方案的陷门基尺寸过大以及环成员的公钥需要数字证书认证的问题,提出一种NTRU(Number Theory Research Unit)格上的身份基环签名方案(NTRU-IBRS)。首先,使用NTRU格上的陷门生成算法生成系统的主公私钥对;然后,将主私钥作为陷门信息并对单向函数进行求逆运算以得到环成员的私钥;最后,基于小整数解(SIS)问题使用拒绝抽样技术生成环签名。安全性分析表明,NTRU-IBRS在随机预言机模型下具有匿名性以及适应性选择消息和身份攻击下的存在不可伪造性。性能分析与实验仿真表明,与理想格上的环签名方案和NTRU格上的身份基可链接环签名方案相比,在存储开销方面,NTRU-IBRS的系统私钥长度下降了0~99.6%,签名私钥长度的下降了50.0%~98.4%;在时间开销方面,NTRU-IBRS的总时间开销减少了15.3%~21.8%。将NTRU-IBRS应用于动态车联网(IoV)场景中,模拟结果表明NTRU-IBRS在车辆交互期间能够同时保证隐私安全和提高通信效率。展开更多
文摘This paper reports a systematic experimental investigation on the dynamics in the low-frequency region in an erbium-doped fibre-ring laser with loss modulation. A rich variety of bifurcation is analyzed through the bifurcation diagram and structured with the concept of the winding numbers. The coexistence of multiple attractors and the crisis that appear in the saddle-node bifurcations, and an interesting structure of bifurcation which is similar to the bifurcations in high-frequency range, have been observed.
文摘In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if <em>n</em> is not a square, square root of <em>n</em> is not a rational number”. And then some conceptions of ring, integral domain, ideal, quotient ring in Advanced algebra, have been introduced. Integers can be regarded as an integral domain, the rational numbers can be regard as a fractional domain. Evens and odds are principal ideals in integral domain. The operations on evens and odds are operations on quotient ring. After introducing “the minimalist form” in fraction ring. The paper proves the main conclusion: in a integral domain, multiplicative subset <em>S</em> produces a fraction ring <em>S</em><sup><span style="white-space:nowrap;">−</span>1</sup><em>R</em>, and <em>n</em> is not a square element in <em>R</em>, then to every element <em>a</em><span style="white-space:nowrap;">∈</span><em>R</em>, <span style="white-space:nowrap;"><em>a</em><sup>2</sup>≠<em>n</em></span>.
文摘Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.
文摘针对格基环签名方案的陷门基尺寸过大以及环成员的公钥需要数字证书认证的问题,提出一种NTRU(Number Theory Research Unit)格上的身份基环签名方案(NTRU-IBRS)。首先,使用NTRU格上的陷门生成算法生成系统的主公私钥对;然后,将主私钥作为陷门信息并对单向函数进行求逆运算以得到环成员的私钥;最后,基于小整数解(SIS)问题使用拒绝抽样技术生成环签名。安全性分析表明,NTRU-IBRS在随机预言机模型下具有匿名性以及适应性选择消息和身份攻击下的存在不可伪造性。性能分析与实验仿真表明,与理想格上的环签名方案和NTRU格上的身份基可链接环签名方案相比,在存储开销方面,NTRU-IBRS的系统私钥长度下降了0~99.6%,签名私钥长度的下降了50.0%~98.4%;在时间开销方面,NTRU-IBRS的总时间开销减少了15.3%~21.8%。将NTRU-IBRS应用于动态车联网(IoV)场景中,模拟结果表明NTRU-IBRS在车辆交互期间能够同时保证隐私安全和提高通信效率。
