A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bije...A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.展开更多
Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the...Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find the wth root in the finite ground field GF(p)to build representative collective signature schemes,but the chosen modulo p has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where N is an even number and t_(0),t_(1),t_(2) are prime numbers of equal magnitude,about 80 bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K_(w)^(1)_(1) K^(w)_(2)^(2);w_(1)=t_(0)t_(1) and w_(2)=t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group nanager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.展开更多
The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamilt...The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.展开更多
Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete ...Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete logarithm problem of the elliptic curve,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find W^(th)the root in the finite ground field to build representative collective signature schemes,but the chosen modulo has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where is an even number and t_(0),t_(1),t_(2)are prime numbers of equal magnitude,about 80bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K^(W_(1))_(1)K^(W_(2))_(2);and t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group manager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.展开更多
In this paper,we determine the Sombor index and some other vertex-degree-based topological indices for the nil-clean graphs of Z_(n),the ring of integers modulo n.
In two previous papers,the first named author jointly with Florian Luca and Henryk Iwaniec,have studied the distribution modulo 1 of sequences which have linear growth and are mean values of multiplicative functions o...In two previous papers,the first named author jointly with Florian Luca and Henryk Iwaniec,have studied the distribution modulo 1 of sequences which have linear growth and are mean values of multiplicative functions on the set of all the integers.In this note,we give a first result concerning sequences with linear growth associated to the mean values of multiplicative functions on a set of polynomial values,proving the density modulo 1 of the sequencem[∑((m2+1))(m2+1)(m≤n)]n.This result is but an illustration of the theme which is currently being developed in the PhD thesis of the second named author.展开更多
Resolution modulo is an extension of first-order resolution in which rewrite rules are used to rewrite clauses during the search. In the first version of this method, clauses are rewritten to arbitrary propositions. T...Resolution modulo is an extension of first-order resolution in which rewrite rules are used to rewrite clauses during the search. In the first version of this method, clauses are rewritten to arbitrary propositions. These propositions are needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e., when it rewrites clauses to clauses. We show in this paper how to transform any rewrite system into a clausal one, preserving the existence of cut free proofs of any sequent.展开更多
As semi-conductor technologies move down to the nanometer scale, leakage power has become a significant component of the total power consumption. In this paper, we present a leakage-aware modulo scheduling algorithm t...As semi-conductor technologies move down to the nanometer scale, leakage power has become a significant component of the total power consumption. In this paper, we present a leakage-aware modulo scheduling algorithm to achieve leakage energy saving for applications with loops on Very Long Instruction Word （VLIW） architectures. The proposed algorithm is designed to maximize the idleness of function units integrated with the dual-threshold domino logic, and reduce the number of transitions between the active and sleep modes. We have implemented our technique in the Trimaran compiler and conducted experiments using a set of embedded benchmarks from DSPstone and Mibench on the cycle-accurate VLIW simulator of Trimaran. The results show that our technique achieves significant leakage energy saving compared with a previously published DAG-based （Directed Acyclic Graph） leakage-aware scheduling algorithm.展开更多
Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mo...Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mod n in(Z/nZ)^(2) such that xi∈(Z/nZ)^(×)for i∈J⊆{1,2}.展开更多
This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
文摘A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.
文摘Digital signature schemes are often built based on the difficulty of the discrete logarithm problems,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find the wth root in the finite ground field GF(p)to build representative collective signature schemes,but the chosen modulo p has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where N is an even number and t_(0),t_(1),t_(2) are prime numbers of equal magnitude,about 80 bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K_(w)^(1)_(1) K^(w)_(2)^(2);w_(1)=t_(0)t_(1) and w_(2)=t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group nanager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.
文摘The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.
基金funding for this research from Duy Tan University,Danang,Vietnam.
文摘Digital signature schemes in general and representative collective digital signature schemes,in particular,are often built based on the difficulty of the discrete logarithm problem on the finite field,of the discrete logarithm problem of the elliptic curve,of the problem of factor analysis,of the problem of finding the roots modulo of large primes or a combination of the difficult problems mentioned above.In this paper,we use the new difficult problem,which is to find W^(th)the root in the finite ground field to build representative collective signature schemes,but the chosen modulo has a special structure distinct p=Nt_(0)t_(1)t_(2)+1,where is an even number and t_(0),t_(1),t_(2)are prime numbers of equal magnitude,about 80bits.The characteristics of the proposed scheme are:i)The private key of each signer consists of 2 components(K_(1),K_(2)),randomly selected,but the public key has only one component(Y)calculated by the formula Y=K^(W_(1))_(1)K^(W_(2))_(2);and t_(0)t_(2);and ii)The generated signature consists of a set of 3 components(e,S_(1),S_(2)).We use the technique of hiding the signer’s public key Y,which is the coefficientλgenerated by the group manager,in the process of forming the group signature and representative collective signature to enhance the privacy of all members of the signing collective.
基金supported by the National Natural Science Foundation of China(Nos.12261001,12461001)the Research Foundation Ability Enhancement Project for Young and Middle aged Teachers in Guangxi Universities(No.025KY0477)。
文摘In this paper,we determine the Sombor index and some other vertex-degree-based topological indices for the nil-clean graphs of Z_(n),the ring of integers modulo n.
文摘In two previous papers,the first named author jointly with Florian Luca and Henryk Iwaniec,have studied the distribution modulo 1 of sequences which have linear growth and are mean values of multiplicative functions on the set of all the integers.In this note,we give a first result concerning sequences with linear growth associated to the mean values of multiplicative functions on a set of polynomial values,proving the density modulo 1 of the sequencem[∑((m2+1))(m2+1)(m≤n)]n.This result is but an illustration of the theme which is currently being developed in the PhD thesis of the second named author.
基金Supported by the French National Research Agency–National Natural Science Foundation of China under Grant No.61161130530National Natural Science Foundation of China under Grant No.60833001
文摘Resolution modulo is an extension of first-order resolution in which rewrite rules are used to rewrite clauses during the search. In the first version of this method, clauses are rewritten to arbitrary propositions. These propositions are needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e., when it rewrites clauses to clauses. We show in this paper how to transform any rewrite system into a clausal one, preserving the existence of cut free proofs of any sequent.
基金supported by the National Natural Science Foundation of China under Grant Nos. 60873006 and 61070049the International Collaborative Research Program under Grant No. 2010DFB10930+1 种基金the Beijing Science Foundation under Grant No.KZ200910028007the Australian Research Council (ARC) under Grant No. DP0881330
文摘As semi-conductor technologies move down to the nanometer scale, leakage power has become a significant component of the total power consumption. In this paper, we present a leakage-aware modulo scheduling algorithm to achieve leakage energy saving for applications with loops on Very Long Instruction Word （VLIW） architectures. The proposed algorithm is designed to maximize the idleness of function units integrated with the dual-threshold domino logic, and reduce the number of transitions between the active and sleep modes. We have implemented our technique in the Trimaran compiler and conducted experiments using a set of embedded benchmarks from DSPstone and Mibench on the cycle-accurate VLIW simulator of Trimaran. The results show that our technique achieves significant leakage energy saving compared with a previously published DAG-based （Directed Acyclic Graph） leakage-aware scheduling algorithm.
基金supported by National Natural Science Foundation of China(Grant No.11571328).
文摘Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mod n in(Z/nZ)^(2) such that xi∈(Z/nZ)^(×)for i∈J⊆{1,2}.
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
