Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design st...Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.展开更多
This paper studies the problem of primality testing for numbers of the form h · 2~n± 1,where h < 2~n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers i...This paper studies the problem of primality testing for numbers of the form h · 2~n± 1,where h < 2~n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers in certain cases, which runs in deterministic quasi-quadratic time. In particular, the authors construct a Lucasian primality test for numbers of the form 3 · 5 · 17 · 2~n± 1, where n is a positive integer, in half of the cases among the congruences of n modulo 12, by means of a Lucasian sequence with a suitable seed not depending on n. The methods of Bosma(1993), Berrizbeitia and Berry(2004), Deng and Huang(2016) can not test the primality of these numbers.展开更多
This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the incl...This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.展开更多
在这篇文章中,我们讨论了数学模型1:maxf(x),x∈{x|x=(x_1,x_2,…,x_n),sum from j=1 to n a_(ij)x_j≤b_i,i=1,2,…,m,x_i≥1且为整数},其中f(x)={c_jx_j}且sum from j=1 to n aI(ij)≤b_i,并给出了模型1最大最优解的定义以及最大最优...在这篇文章中,我们讨论了数学模型1:maxf(x),x∈{x|x=(x_1,x_2,…,x_n),sum from j=1 to n a_(ij)x_j≤b_i,i=1,2,…,m,x_i≥1且为整数},其中f(x)={c_jx_j}且sum from j=1 to n aI(ij)≤b_i,并给出了模型1最大最优解的定义以及最大最优解的充分必要条件,根据该条件,我们介绍了求模型1的最大最优解的两个算法:Primal算法和Threshold算法。展开更多
Discusses the use of the notion of fuzzy point to study some basic algebraic structures, such as group, semi group and ideal and then clarifies the links between the fuzzy point approach and the classical fuzzy approach.
This letter presents a k-party RSA key sharing scheme and the related algorithms are presented. It is shown that the shared key can be generated in such a collaborative way that the RSA modulus is publicly known but n...This letter presents a k-party RSA key sharing scheme and the related algorithms are presented. It is shown that the shared key can be generated in such a collaborative way that the RSA modulus is publicly known but none of the parties is able to decrypt the enciphered message individually.展开更多
In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain...In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.展开更多
The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution;...The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution; primal CO is generated through coalification, which can lead to forecasting mistakes. Through theoretical analysis, primal CO generation and emission from coal seams was determined.In this study, six coal samples were analyzed under six different experimental conditions. The results demonstrated the change in coal seam primal gas and concentration as functions of time, different coal samples, occurrence, various gas types and composition concentration, which are in agreement with the previous study on primal CO generation. Air charging impacts on primal gas emission. Analysis of the experimental data with SPSS demonstrates that the relationship between primal CO concentration and time shows a power exponent distribution.展开更多
Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple struct...Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].展开更多
In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharm...In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharma and Saxena [1]. We further develop a method to extract a very good primal solution from a given dual solution. We later demonstrate the efficacies and the significance of these methods on 150 random problems.展开更多
A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not con...A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.展开更多
This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable t...This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.展开更多
In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
In Ovid’s story Cephisus,the river-god,forces the beautiful nymph,Liriope into love-making under the waves.She gets pregnant and gives birth to Narcissus.The mother asks seer Tiresias if her son will live to a full a...In Ovid’s story Cephisus,the river-god,forces the beautiful nymph,Liriope into love-making under the waves.She gets pregnant and gives birth to Narcissus.The mother asks seer Tiresias if her son will live to a full age;his answer is“If he doesn’t discover himself”.Narcissus reaching a fountain to drink,the mirror of the water enchants him.From this dramatic moment he cannot leave the spring.Narcissus is notable to grasp why he cannot reach the desperately desired image.In the mirror of the water he does not only see his own figure but in the waves he is confronted with the primal scene repeatedly.We argue that the image in the water reflects the coitus of his parents.It terrifies him while simultaneously he becomes envious.His discovery leads him to death.The paper is based on dreams and clinical material of a psychoanalytical case.Our concept is in accord with some of the insights about narcissism of Lacan,Kohut,and Kernberg.展开更多
文摘Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.
基金supported by the National Natural Science Foundation of China under Grant Nos.11601202,11401312,11701284the High-Level Talent Scientific Research Foundation of Jinling Institute of Technology under Grant Nos.jit-b-201526,RCYJ201408+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions under Grant No.17KJB110004National Key R.and D.Program “Cyberspace Security” Key Special Project under Grant No.2017YFB0802800
文摘This paper studies the problem of primality testing for numbers of the form h · 2~n± 1,where h < 2~n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers in certain cases, which runs in deterministic quasi-quadratic time. In particular, the authors construct a Lucasian primality test for numbers of the form 3 · 5 · 17 · 2~n± 1, where n is a positive integer, in half of the cases among the congruences of n modulo 12, by means of a Lucasian sequence with a suitable seed not depending on n. The methods of Bosma(1993), Berrizbeitia and Berry(2004), Deng and Huang(2016) can not test the primality of these numbers.
文摘This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.
文摘在这篇文章中,我们讨论了数学模型1:maxf(x),x∈{x|x=(x_1,x_2,…,x_n),sum from j=1 to n a_(ij)x_j≤b_i,i=1,2,…,m,x_i≥1且为整数},其中f(x)={c_jx_j}且sum from j=1 to n aI(ij)≤b_i,并给出了模型1最大最优解的定义以及最大最优解的充分必要条件,根据该条件,我们介绍了求模型1的最大最优解的两个算法:Primal算法和Threshold算法。
文摘Discusses the use of the notion of fuzzy point to study some basic algebraic structures, such as group, semi group and ideal and then clarifies the links between the fuzzy point approach and the classical fuzzy approach.
基金Supported by the National Natural Science Foundation of China (No.69825102)
文摘This letter presents a k-party RSA key sharing scheme and the related algorithms are presented. It is shown that the shared key can be generated in such a collaborative way that the RSA modulus is publicly known but none of the parties is able to decrypt the enciphered message individually.
文摘In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.
基金provided by the National Natural Science Foundation of China(No.U1261214)
文摘The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution; primal CO is generated through coalification, which can lead to forecasting mistakes. Through theoretical analysis, primal CO generation and emission from coal seams was determined.In this study, six coal samples were analyzed under six different experimental conditions. The results demonstrated the change in coal seam primal gas and concentration as functions of time, different coal samples, occurrence, various gas types and composition concentration, which are in agreement with the previous study on primal CO generation. Air charging impacts on primal gas emission. Analysis of the experimental data with SPSS demonstrates that the relationship between primal CO concentration and time shows a power exponent distribution.
文摘Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].
文摘In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharma and Saxena [1]. We further develop a method to extract a very good primal solution from a given dual solution. We later demonstrate the efficacies and the significance of these methods on 150 random problems.
基金Supported by the Doctoral Educational Foundation of China of the Ministry of Education(20020486035)
文摘A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.
基金Supported by the National Natural Science Foun-dation of China (70371032) the Doctor Educational Foundation ofthe Ministry of Education (20020486035)
文摘This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.
基金This project is supported by the National Science Foundation of China
文摘In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
文摘In Ovid’s story Cephisus,the river-god,forces the beautiful nymph,Liriope into love-making under the waves.She gets pregnant and gives birth to Narcissus.The mother asks seer Tiresias if her son will live to a full age;his answer is“If he doesn’t discover himself”.Narcissus reaching a fountain to drink,the mirror of the water enchants him.From this dramatic moment he cannot leave the spring.Narcissus is notable to grasp why he cannot reach the desperately desired image.In the mirror of the water he does not only see his own figure but in the waves he is confronted with the primal scene repeatedly.We argue that the image in the water reflects the coitus of his parents.It terrifies him while simultaneously he becomes envious.His discovery leads him to death.The paper is based on dreams and clinical material of a psychoanalytical case.Our concept is in accord with some of the insights about narcissism of Lacan,Kohut,and Kernberg.
