In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the r...In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.展开更多
Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic ...Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.展开更多
Group discussions are very important in oral English classes. It maximizes students＇ speaking time in a specified-time period. Group discussions have a strong positive effect on the atmosphere in the classroom and th...Group discussions are very important in oral English classes. It maximizes students＇ speaking time in a specified-time period. Group discussions have a strong positive effect on the atmosphere in the classroom and the behaviors of the students as they can get more ideas from their friends, and sometimes students don＇t even understand the topic for discussion but by interacting with others they can understand the topic. Particularly it is a good warm-up in conversational classes. The most important reason for using group discussions before speaking tasks is to reduce students＇ nervousness of making mistakes. And this encourages students to be more active in speaking class.展开更多
Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K) of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the seco...Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K) of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the second p-class group G=Gal(F<sub>p</sub><sup>2</sup>K∣K) of K, complementary techniques are deve- loped for finding the nilpotency class and coclass of . An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(τ (K),ù(K)) of all 34631 real quadratic fields K=Q(√d) with discriminants 0d<10<sup>8</sup> and 3-class group of type (3, 3). The results admit extensive statistics of the second 3-class groups G=Gal(F<sub>3</sub><sup>2</sup>K∣K) and the 3-class field tower groups G=Gal(F<sub>3</sub><sup>∞</sup>K∣K).展开更多
Objective:In this research,we tried to explore how short-term mindfulness(STM)intervention affects adoles-cents’anxiety,depression,and negative and positive emotion during the COVID-19 pandemic.Design:10 classes were...Objective:In this research,we tried to explore how short-term mindfulness(STM)intervention affects adoles-cents’anxiety,depression,and negative and positive emotion during the COVID-19 pandemic.Design:10 classes were divided into experiment groups(5 classes;n=238)and control(5 classes;n=244)randomly.Hospital Anxi-ety and Depression Scale(HADS)and Positive and Negative Affect Schedule(PANAS)were used to measure par-ticipants’dependent variables.In the experiment group,we conducted STM practice interventions every morning in theirfirst class from March to November 2020.No interventions were conducted in the control group.Methods:Paired-sample t-tests were used to identify if a significant difference exists between every time point of the experimental and control groups.Repeated ANOVA and Growth Mixture Model(GMM)were used to analyze the tendency of positive and negative emotions,anxiety,and depression in the experimental group.Results and Conclusions:(1)With the intervention of STM,there was a significant decrease in negative emotions and an increase in positive emotions in the experimental group,whereas there were non-significant differences in the control group.(2)To explore the heterogeneity trajectories of dependent variables,we built a GMM and found there were two latent growth classes in the trajectories.(3)The results of the models showed their trajec-tories were downward,which meant that the levels of anxiety,depression,and negative emotions of participants decreased during the STM training period.Nonetheless,the score of positive affect showed upward in three loops of intervention,which indicated that the level of the participants’positive affect increased through the STM inter-vention.(4)This research indicated that STM should be given increasing consideration to enhance mental health during the worldwide outbreak of COVID-19.展开更多
The article investigates on the educational value and upon the teacher of support, trying to clarify some aspects of inclusive education and school integration. Starting from the central role of the teacher of support...The article investigates on the educational value and upon the teacher of support, trying to clarify some aspects of inclusive education and school integration. Starting from the central role of the teacher of support is analysed by the task of its educational dimension, the different competences that are required to him, the aspects linked to the action of didactic that teachers can intervene to increase the level of integration and inclusion in the classroom, the best possible practices to be used in the classroom in order to better value the individual differences and to increase the highest possible educational success for students with special educational needs. Finally, it is hoped the use of cooperative learning, rather than learn by competitiveness and individualistic, since encourage more interaction between disabled and non-disabled students, a greater empathy between them, without forgetting that inclusive education is facilitated in school environments in which the teaching is active and where difficulties and problems that arise are analyzed to produce improvements.展开更多
For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been famil...For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been familiar for the ?elds Q(√2p) with a prime p ≡ 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x2 + 32y2 and illustrated in terms of graphs.展开更多
For F = Q（√εpq）, ε∈ {±1,±2}, primes -p ≡ q ≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups of F equal to 1 or 2 such that we can calculate their densitie...For F = Q（√εpq）, ε∈ {±1,±2}, primes -p ≡ q ≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups of F equal to 1 or 2 such that we can calculate their densities. All results are stated in terms of congruence relations of p, q modulo 2^n, the quartic residue symbol （1/q）4 and binary quadratic forms such as q^h（-2p）/^4 = x^2 ＋ 2py^2 where h（-2p） is the class number of Q（√-2p）. The results are very useful for numerical computations.展开更多
A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations.At the ...A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations.At the same time,a method is given which can be used to simplify the known results.Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.展开更多
A necessary condition is presented for the ideal class group of an imaginary quadratic function field K=k(D)(k=F-q(x),2q)to be of exponent≤2.The condition is proved to be sufficient in some cases.An analogue of Loubo...A necessary condition is presented for the ideal class group of an imaginary quadratic function field K=k(D)(k=F-q(x),2q)to be of exponent≤2.The condition is proved to be sufficient in some cases.An analogue of Louboutin’s result in function field case is particularly presented.展开更多
Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class grou...Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.展开更多
Let E / K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of E is described by the image of a map uK and hence an upper bound of its order is given in terms of the class numbers of the S-idea...Let E / K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of E is described by the image of a map uK and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.展开更多
Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessaryand sufficient condition is given for the class group H(K) to contain a cyclic subgroup of anyorder n, which holds true for both r...Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessaryand sufficient condition is given for the class group H(K) to contain a cyclic subgroup of anyorder n, which holds true for both real and imaginary fields K. Then several series of functionfields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, aregiven, for which the class groups H(K) are proved to contain cyclic subgroups of order n.展开更多
In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n,...In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n.[展开更多
Based on the action of the mapping class group on the space of measured foliations,we construct a new boundary of the mapping class group and study the structure of this boundary.As an application,for any point in Tei...Based on the action of the mapping class group on the space of measured foliations,we construct a new boundary of the mapping class group and study the structure of this boundary.As an application,for any point in Teichmüller space,we consider the orbit of this point under the action of the mapping class group and describe the closure of this orbit in the Thurston compactification and the Gardiner-Masur compactification of Teichmüller space.We also construct some new points in the Gardiner-Masur boundary of Teichmüller space.展开更多
It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results co...It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI（δE,T） under the action of the Galois group, where E = F（ζp^n ） and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F（ζ3）.展开更多
Imaginary cyclic fields of degree p-1 which have two distinct unramified cyclic extensions of degree p are produced using elementary properties of the Lucas sequences. An infinite family of imaginary cyclic fields of ...Imaginary cyclic fields of degree p-1 which have two distinct unramified cyclic extensions of degree p are produced using elementary properties of the Lucas sequences. An infinite family of imaginary cyclic fields of degree p-1 are then given with the p-rank of the ideal class groups of at least two.展开更多
Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the cl...Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface M with a free and proper group action in this paper.Their construction is based on the exact sequence given by the fibration F_(0)^(G) M→F(M/G,n).The conclusion is closely connected with the braid group of the quotient space.Comparing with the situation without the group action,there is a big difference when the quotient space is T^(2).展开更多
Let F = Q（√-p1p2） be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol （p1/p2） = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the followi...Let F = Q（√-p1p2） be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol （p1/p2） = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold： （1） The quartic residue symbols （p1/p2）4 = （p2/p1）4 = 1; （2） Either both p1 and p2 are represented by the form a^2 ＋ 32b^2 over Z and p^h2＋（2p1）/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 ＋ 32b^2 over Z and p^h2＋（2p1）/4=ε（2x^2-p1y^2）,x,y∈Z,ε∈{±1},where h＋（2p1） is the narrow class number of Q（√2p1）,Moreover, we also generalize these results.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1237101812201236)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.B240201093/2013)the Natural Science Foundation of the Anhui Higher Education Institutions(Grant No.2022AH051907)。
文摘In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.
文摘Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.
文摘Group discussions are very important in oral English classes. It maximizes students＇ speaking time in a specified-time period. Group discussions have a strong positive effect on the atmosphere in the classroom and the behaviors of the students as they can get more ideas from their friends, and sometimes students don＇t even understand the topic for discussion but by interacting with others they can understand the topic. Particularly it is a good warm-up in conversational classes. The most important reason for using group discussions before speaking tasks is to reduce students＇ nervousness of making mistakes. And this encourages students to be more active in speaking class.
文摘Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K) of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the second p-class group G=Gal(F<sub>p</sub><sup>2</sup>K∣K) of K, complementary techniques are deve- loped for finding the nilpotency class and coclass of . An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(τ (K),ù(K)) of all 34631 real quadratic fields K=Q(√d) with discriminants 0d<10<sup>8</sup> and 3-class group of type (3, 3). The results admit extensive statistics of the second 3-class groups G=Gal(F<sub>3</sub><sup>2</sup>K∣K) and the 3-class field tower groups G=Gal(F<sub>3</sub><sup>∞</sup>K∣K).
基金Regional Science Fund Project of Northwest Normal University,Grant No.31660281.
文摘Objective:In this research,we tried to explore how short-term mindfulness(STM)intervention affects adoles-cents’anxiety,depression,and negative and positive emotion during the COVID-19 pandemic.Design:10 classes were divided into experiment groups(5 classes;n=238)and control(5 classes;n=244)randomly.Hospital Anxi-ety and Depression Scale(HADS)and Positive and Negative Affect Schedule(PANAS)were used to measure par-ticipants’dependent variables.In the experiment group,we conducted STM practice interventions every morning in theirfirst class from March to November 2020.No interventions were conducted in the control group.Methods:Paired-sample t-tests were used to identify if a significant difference exists between every time point of the experimental and control groups.Repeated ANOVA and Growth Mixture Model(GMM)were used to analyze the tendency of positive and negative emotions,anxiety,and depression in the experimental group.Results and Conclusions:(1)With the intervention of STM,there was a significant decrease in negative emotions and an increase in positive emotions in the experimental group,whereas there were non-significant differences in the control group.(2)To explore the heterogeneity trajectories of dependent variables,we built a GMM and found there were two latent growth classes in the trajectories.(3)The results of the models showed their trajec-tories were downward,which meant that the levels of anxiety,depression,and negative emotions of participants decreased during the STM training period.Nonetheless,the score of positive affect showed upward in three loops of intervention,which indicated that the level of the participants’positive affect increased through the STM inter-vention.(4)This research indicated that STM should be given increasing consideration to enhance mental health during the worldwide outbreak of COVID-19.
文摘The article investigates on the educational value and upon the teacher of support, trying to clarify some aspects of inclusive education and school integration. Starting from the central role of the teacher of support is analysed by the task of its educational dimension, the different competences that are required to him, the aspects linked to the action of didactic that teachers can intervene to increase the level of integration and inclusion in the classroom, the best possible practices to be used in the classroom in order to better value the individual differences and to increase the highest possible educational success for students with special educational needs. Finally, it is hoped the use of cooperative learning, rather than learn by competitiveness and individualistic, since encourage more interaction between disabled and non-disabled students, a greater empathy between them, without forgetting that inclusive education is facilitated in school environments in which the teaching is active and where difficulties and problems that arise are analyzed to produce improvements.
基金Project supported by the National Natural Science Foundation of China (No.10371054) and 02KJB11006.
文摘For quadratic number ?elds F = Q(√2p1 ···pt?1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The resultsgeneralize nicely what has been familiar for the ?elds Q(√2p) with a prime p ≡ 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x2 + 32y2 and illustrated in terms of graphs.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10771100, 10971250）
文摘For F = Q（√εpq）, ε∈ {±1,±2}, primes -p ≡ q ≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups of F equal to 1 or 2 such that we can calculate their densities. All results are stated in terms of congruence relations of p, q modulo 2^n, the quartic residue symbol （1/q）4 and binary quadratic forms such as q^h（-2p）/^4 = x^2 ＋ 2py^2 where h（-2p） is the class number of Q（√-2p）. The results are very useful for numerical computations.
基金supported by National Natural Science Foundation of China(Grant Nos.10771100,10971250)
文摘A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations.At the same time,a method is given which can be used to simplify the known results.Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.
文摘A necessary condition is presented for the ideal class group of an imaginary quadratic function field K=k(D)(k=F-q(x),2q)to be of exponent≤2.The condition is proved to be sufficient in some cases.An analogue of Louboutin’s result in function field case is particularly presented.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M541064)National Natural Science Foundation of China(Grant No.11371043)National Basic Research Program of China(Grant No.2013CB834202)
文摘Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.
文摘Let E / K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of E is described by the image of a map uK and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.
文摘Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessaryand sufficient condition is given for the class group H(K) to contain a cyclic subgroup of anyorder n, which holds true for both real and imaginary fields K. Then several series of functionfields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, aregiven, for which the class groups H(K) are proved to contain cyclic subgroups of order n.
文摘In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n.[
文摘Based on the action of the mapping class group on the space of measured foliations,we construct a new boundary of the mapping class group and study the structure of this boundary.As an application,for any point in Teichmüller space,we consider the orbit of this point under the action of the mapping class group and describe the closure of this orbit in the Thurston compactification and the Gardiner-Masur compactification of Teichmüller space.We also construct some new points in the Gardiner-Masur boundary of Teichmüller space.
文摘It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI（δE,T） under the action of the Galois group, where E = F（ζp^n ） and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F（ζ3）.
基金Supported by the Japan Society for the Promotion of Science (JSPS) (No. 14540030) the JSPS Research Fellowships for Young Scientists
文摘Imaginary cyclic fields of degree p-1 which have two distinct unramified cyclic extensions of degree p are produced using elementary properties of the Lucas sequences. An infinite family of imaginary cyclic fields of degree p-1 are then given with the p-rank of the ideal class groups of at least two.
基金supported by the National Natural Science Foundation of China(No.11971112)。
文摘Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface M with a free and proper group action in this paper.Their construction is based on the exact sequence given by the fibration F_(0)^(G) M→F(M/G,n).The conclusion is closely connected with the braid group of the quotient space.Comparing with the situation without the group action,there is a big difference when the quotient space is T^(2).
基金Project supported by the National Natural Science Foundation of China(No.10371054)
文摘Let F = Q（√-p1p2） be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol （p1/p2） = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold： （1） The quartic residue symbols （p1/p2）4 = （p2/p1）4 = 1; （2） Either both p1 and p2 are represented by the form a^2 ＋ 32b^2 over Z and p^h2＋（2p1）/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 ＋ 32b^2 over Z and p^h2＋（2p1）/4=ε（2x^2-p1y^2）,x,y∈Z,ε∈{±1},where h＋（2p1） is the narrow class number of Q（√2p1）,Moreover, we also generalize these results.
