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
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
The Venice Lagoon is exposed to atmospheric pollutants from industrial activities, thermoelectric power plants, petrochemical plants, incinerator, domestic heating, ship traffic, glass factories and vehicular emission...The Venice Lagoon is exposed to atmospheric pollutants from industrial activities, thermoelectric power plants, petrochemical plants, incinerator, domestic heating, ship traffic, glass factories and vehicular emissions on the mainland. In 2005, construction began on the mobile dams （MOSE）, one dam for each channel connecting the lagoon to the Adriatic Sea as a barrier against high tide. These construction works could represent an additional source of pollutants. PM10 samples were taken on random days between 2007 and 2010 at three different sites： Punta Sabbioni, Chioggia and Malamocco, located near the respective dam construction worksites. Chemical analyses of V, Cr, Fe, Co, Ni, Cu, Zn, As, Mo, Cd, Sb, T1 and Pb in PM10 samples were performed by Inductively coupled plasma- quadrupole mass spectrometry （ICP-QMS） and results were used to identify the main aerosol sources. The correlation of measured data with meteorology, and source apportionment, failed to highlight a contribution specifically associated to the emissions of the MOSE construction works. The comparison of the measurements at the three sites showed a substantial homogeneity of metal concentrations in the area. Source apportionment with principal component analysis （PCA） and positive matrix factorization （PMF） showed that a four principal factors model could describe the sources of metals in PM10. Three of them were assigned to specific sources in the area and one was characterised as a source of mixed origin （anthropogenic and crustal）. A specific anthropogenic source of PM10 rich in Ni and Cr, active at the Chioggia site, was also identified.展开更多
Data race is one of the most important concurrent anomalies in multi-threaded programs.Emerging con-straint-based techniques are leveraged into race detection,which is able to find all the races that can be found by a...Data race is one of the most important concurrent anomalies in multi-threaded programs.Emerging con-straint-based techniques are leveraged into race detection,which is able to find all the races that can be found by any oth-er sound race detector.However,this constraint-based approach has serious limitations on helping programmers analyze and understand data races.First,it may report a large number of false positives due to the unrecognized dataflow propa-gation of the program.Second,it recommends a wide range of thread context switches to schedule the reported race(in-cluding the false one)whenever this race is exposed during the constraint-solving process.This ad hoc recommendation imposes too many context switches,which complicates the data race analysis.To address these two limitations in the state-of-the-art constraint-based race detection,this paper proposes DFTracker,an improved constraint-based race detec-tor to recommend each data race with minimal thread context switches.Specifically,we reduce the false positives by ana-lyzing and tracking the dataflow in the program.By this means,DFTracker thus reduces the unnecessary analysis of false race schedules.We further propose a novel algorithm to recommend an effective race schedule with minimal thread con-text switches for each data race.Our experimental results on the real applications demonstrate that 1)without removing any true data race,DFTracker effectively prunes false positives by 68%in comparison with the state-of-the-art constraint-based race detector;2)DFTracker recommends as low as 2.6-8.3(4.7 on average)thread context switches per data race in the real world,which is 81.6%fewer context switches per data race than the state-of-the-art constraint based race detec-tor.Therefore,DFTracker can be used as an effective tool to understand the data race for programmers.展开更多
In tLis paper, we obtain a criterion (basically an algebraic discriminant) for f(x) to havethe maximal modulo p^d period. The principal part θ of the discriminant is based on thecoefficients of f(x) mod p and can be ...In tLis paper, we obtain a criterion (basically an algebraic discriminant) for f(x) to havethe maximal modulo p^d period. The principal part θ of the discriminant is based on thecoefficients of f(x) mod p and can be computed by a recursive method. In particular, thevalues of θ for p=2, 3, 5 and 7 are derived.展开更多
In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformat...In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.展开更多
This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of el...This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.展开更多
The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k sym...The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.展开更多
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.
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.
基金support of theItalian Ministry of Infrastructure and Transport-Venice Water Authority-through its dealer Consorzio Venezia Nuova
文摘The Venice Lagoon is exposed to atmospheric pollutants from industrial activities, thermoelectric power plants, petrochemical plants, incinerator, domestic heating, ship traffic, glass factories and vehicular emissions on the mainland. In 2005, construction began on the mobile dams （MOSE）, one dam for each channel connecting the lagoon to the Adriatic Sea as a barrier against high tide. These construction works could represent an additional source of pollutants. PM10 samples were taken on random days between 2007 and 2010 at three different sites： Punta Sabbioni, Chioggia and Malamocco, located near the respective dam construction worksites. Chemical analyses of V, Cr, Fe, Co, Ni, Cu, Zn, As, Mo, Cd, Sb, T1 and Pb in PM10 samples were performed by Inductively coupled plasma- quadrupole mass spectrometry （ICP-QMS） and results were used to identify the main aerosol sources. The correlation of measured data with meteorology, and source apportionment, failed to highlight a contribution specifically associated to the emissions of the MOSE construction works. The comparison of the measurements at the three sites showed a substantial homogeneity of metal concentrations in the area. Source apportionment with principal component analysis （PCA） and positive matrix factorization （PMF） showed that a four principal factors model could describe the sources of metals in PM10. Three of them were assigned to specific sources in the area and one was characterised as a source of mixed origin （anthropogenic and crustal）. A specific anthropogenic source of PM10 rich in Ni and Cr, active at the Chioggia site, was also identified.
基金This work is supported by the National Key Research and Development Program of China under Grant No.2023YFB4503400the National Natural Science Foundation of China under Grant Nos.62322205,62072195,and 61825202.
文摘Data race is one of the most important concurrent anomalies in multi-threaded programs.Emerging con-straint-based techniques are leveraged into race detection,which is able to find all the races that can be found by any oth-er sound race detector.However,this constraint-based approach has serious limitations on helping programmers analyze and understand data races.First,it may report a large number of false positives due to the unrecognized dataflow propa-gation of the program.Second,it recommends a wide range of thread context switches to schedule the reported race(in-cluding the false one)whenever this race is exposed during the constraint-solving process.This ad hoc recommendation imposes too many context switches,which complicates the data race analysis.To address these two limitations in the state-of-the-art constraint-based race detection,this paper proposes DFTracker,an improved constraint-based race detec-tor to recommend each data race with minimal thread context switches.Specifically,we reduce the false positives by ana-lyzing and tracking the dataflow in the program.By this means,DFTracker thus reduces the unnecessary analysis of false race schedules.We further propose a novel algorithm to recommend an effective race schedule with minimal thread con-text switches for each data race.Our experimental results on the real applications demonstrate that 1)without removing any true data race,DFTracker effectively prunes false positives by 68%in comparison with the state-of-the-art constraint-based race detector;2)DFTracker recommends as low as 2.6-8.3(4.7 on average)thread context switches per data race in the real world,which is 81.6%fewer context switches per data race than the state-of-the-art constraint based race detec-tor.Therefore,DFTracker can be used as an effective tool to understand the data race for programmers.
基金Project supported by the Postdoctoral Foundation of China.
文摘In tLis paper, we obtain a criterion (basically an algebraic discriminant) for f(x) to havethe maximal modulo p^d period. The principal part θ of the discriminant is based on thecoefficients of f(x) mod p and can be computed by a recursive method. In particular, thevalues of θ for p=2, 3, 5 and 7 are derived.
文摘In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.
文摘This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.
基金supported by the National Natural Science Foundation of China under Grant No. 61063041the Program for New Century Excellent Talents of Universities in Fujian Province under Grant No. JK2010047the Funds of the Education Department of Gansu Province under Grant No. 1001-09
文摘The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.
