Residue-residue contacts are very important in forming protein structure. In this work, we calculated the average probability of residue-residue contacts in 470 globular proteins and analyzed the distribution of conta...Residue-residue contacts are very important in forming protein structure. In this work, we calculated the average probability of residue-residue contacts in 470 globular proteins and analyzed the distribution of contacts in the different interval of residues using Contacts of Structural Units (CSU) and Structural Classification (SCOP) software. It was found that the relationship between the average probability PL and the residue distance L for four structural classes of proteins could be expressed as lgPL=a+b×L, where a and b are coefficients. We also discussed the connection between two aspects of proteins which have equal array residue number and found that the distribution probability was stable (or un-stable) if the proteins had the same (or different) comnact (for examnle svnthase) in the same structural class.展开更多
This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smoo...This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].展开更多
In block ciphers,the nonlinear components,also known as sub-stitution boxes(S-boxes),are used with the purpose of inducing confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the ...In block ciphers,the nonlinear components,also known as sub-stitution boxes(S-boxes),are used with the purpose of inducing confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Gaussian integers(GI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.But the prime field dependent on the Elliptic curve(EC)provides one S-box at a time by fixing three parameters a,b,and p.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.展开更多
In block ciphers,the nonlinear components,also known as substitution boxes(S-boxes),are used with the purpose to induce confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the poi...In block ciphers,the nonlinear components,also known as substitution boxes(S-boxes),are used with the purpose to induce confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves,chaotic maps,and Gaussian integers has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers(EI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.However,in the same way,by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve(EC),chaotic maps,and Gaussian integers.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.展开更多
The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely ma...The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.展开更多
基金Project supported by the National Natural Science Foundation of
China (Nos. 29874012 20174036+2 种基金 20274040) and the Natural
Science Foundation of Zhejiang Province (No. 10102) and the
Science Technology Development Plan of Wenzhou City (No.
S2002A0
文摘Residue-residue contacts are very important in forming protein structure. In this work, we calculated the average probability of residue-residue contacts in 470 globular proteins and analyzed the distribution of contacts in the different interval of residues using Contacts of Structural Units (CSU) and Structural Classification (SCOP) software. It was found that the relationship between the average probability PL and the residue distance L for four structural classes of proteins could be expressed as lgPL=a+b×L, where a and b are coefficients. We also discussed the connection between two aspects of proteins which have equal array residue number and found that the distribution probability was stable (or un-stable) if the proteins had the same (or different) comnact (for examnle svnthase) in the same structural class.
基金Project supported by the DGICYT Grant (No. MTM2007-60016)the Junta de Andalucía Grant(No. P07-FQM-2863)
文摘This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].
文摘In block ciphers,the nonlinear components,also known as sub-stitution boxes(S-boxes),are used with the purpose of inducing confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Gaussian integers(GI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.But the prime field dependent on the Elliptic curve(EC)provides one S-box at a time by fixing three parameters a,b,and p.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.
基金extend their appreciation to the Deanship of Scientific Research at King Khalid University,for funding this work through the General Research Groups Program under Grant No.R.G.P.2/109/43.
文摘In block ciphers,the nonlinear components,also known as substitution boxes(S-boxes),are used with the purpose to induce confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves,chaotic maps,and Gaussian integers has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers(EI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.However,in the same way,by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve(EC),chaotic maps,and Gaussian integers.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.
文摘The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.
