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
For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function field...For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.展开更多
In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more expl...In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more explicitly for six types of real quadratic function fields. As a consequence, six classes of real quadratic function fields with ideal class number greater than one are given.[展开更多
The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the...The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.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
A parametrization of quadratic function fields whose divisor class numbers are divisible by 3 is obtained by using free parameters when the characteristics of the fields are not 3.
Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other p...Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.展开更多
Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields...Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields K are obtained whose ideal class groups contain cyclic subgroups of order n. In particular, the ideal classnumbers of these function fields are divisible by n.展开更多
Suppose that K is a cyclic number field with odd prime degree. The unit group U_K of the integer ring O_K is U_K={+1}×V_K (direct product), where V_K is the group of units with norm 1. By Dirichet Unit Theorem, V...Suppose that K is a cyclic number field with odd prime degree. The unit group U_K of the integer ring O_K is U_K={+1}×V_K (direct product), where V_K is the group of units with norm 1. By Dirichet Unit Theorem, V_K is free Abelian展开更多
We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.展开更多
The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR s...The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD （T） method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.展开更多
Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. ...Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. Let M be a monic polynomialin R=F<sub>q</sub>[T]. The Carlitz action of M on a∈k<sup>ac</sup> is defined展开更多
The paper summarizes and discusses the recent advances of proteins as functional interlayers in organic field-effect transistors（OFETs）.Specific focus is given on the proteins integrated into the device structure,ei...The paper summarizes and discusses the recent advances of proteins as functional interlayers in organic field-effect transistors（OFETs）.Specific focus is given on the proteins integrated into the device structure,either to act as dielectric materials or to perform as the functional interlayer between the dielectric and the organic semiconductor（OSC）.The main emphasis is give to the location and the specific effect of protein layers in the structure of OFETs.Besides,the possibility of amyloid serving as useful building blocks for OFET is discussed.展开更多
For the hyperelliptic curve y^2=f(x) over F_q with deg(f)≥5, there is a singular point (0, 1, 0), such that a curve is not smooth. But the codes which are constructed by using hyperelliptic curves can be discussed ba...For the hyperelliptic curve y^2=f(x) over F_q with deg(f)≥5, there is a singular point (0, 1, 0), such that a curve is not smooth. But the codes which are constructed by using hyperelliptic curves can be discussed basing on the theory of arithmetic of quadratic function fields.展开更多
A series of maximal independent systems of cyclotomic units for cyclotomic functionfields and their subfields are constructed as an analogue of Ramachandra’s and Levesque’scyclotomic unit systems in cyclotomic numbe...A series of maximal independent systems of cyclotomic units for cyclotomic functionfields and their subfields are constructed as an analogue of Ramachandra’s and Levesque’scyclotomic unit systems in cyclotomic number fields. The indexes of subgroups generated bythese unit systems in the whole unit groups are calculated and compared.展开更多
This note is concerned in constructing a series of maximal independent systems of cyclotomic units in cyclotomic function fields and their subfields. Let us introduce basic facts on cyclotomic function fields briefly ...This note is concerned in constructing a series of maximal independent systems of cyclotomic units in cyclotomic function fields and their subfields. Let us introduce basic facts on cyclotomic function fields briefly (see Refs. [1—3] for detail).展开更多
Let L/Fq(T) be a tame abelian extension of type (l, l,...l). The ratio of the degree zero divisor dass number (as well as the ideal class number) of L to the product of corresponding class numbers of all cydic subfiel...Let L/Fq(T) be a tame abelian extension of type (l, l,...l). The ratio of the degree zero divisor dass number (as well as the ideal class number) of L to the product of corresponding class numbers of all cydic subfields of L is clearly determined.展开更多
In this note we show that the Mason’s upper bound of deg(u) for S-units u andv satisfying u + v = 1 over function field K = k(C) can be attained for any algebraicallyclosed coefficient field k and for some hyperellip...In this note we show that the Mason’s upper bound of deg(u) for S-units u andv satisfying u + v = 1 over function field K = k(C) can be attained for any algebraicallyclosed coefficient field k and for some hyperelliptic or Artin-Schreier curve C over k withany given genus g≥0.展开更多
In this paper, the nonlinear transient dynamic response of functionally graded material （FGM） sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using...In this paper, the nonlinear transient dynamic response of functionally graded material （FGM） sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy＇s third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction. Based on Reddy＇s theory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton＇s principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading, triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variable- coefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.展开更多
Let k = Fq(T),q=pn, and let K=k((?)p)be the cyclotomic function field with conduc-tor P = P(T), and suppose K+ is the maximal real subfield of K, hp(h+p) is the class number of divisor group (of degree zero) of K(K+),...Let k = Fq(T),q=pn, and let K=k((?)p)be the cyclotomic function field with conduc-tor P = P(T), and suppose K+ is the maximal real subfield of K, hp(h+p) is the class number of divisor group (of degree zero) of K(K+), and h-p=hp/h+p(∈ Ⅱ). This paper proves that for any fixed q≥3, there exist infinite many irreducible manic polynomial P∈Fq[T] such that p\h+p and pq-2\h-p. In addition, all regular quadratic irreducible polynomials in Fq[T] for 2≤p≤269 are determined.展开更多
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For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.
文摘In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more explicitly for six types of real quadratic function fields. As a consequence, six classes of real quadratic function fields with ideal class number greater than one are given.[
文摘The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.
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.
基金Supported by National Natural Science Foundation of China （Grant No. 10131010）
文摘A parametrization of quadratic function fields whose divisor class numbers are divisible by 3 is obtained by using free parameters when the characteristics of the fields are not 3.
基金Project supported by the National Natural Science Foundation of China(Grand Nos.11147158 and 11264020)the Natural Science Foundation of Jiangxi Province,China(Grand No.2010GQW0031)the Scientific Research Program of the Education Bureau of Jiangxi Province,China(Grand No.GJJ12483)
文摘Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071041).
文摘Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields K are obtained whose ideal class groups contain cyclic subgroups of order n. In particular, the ideal classnumbers of these function fields are divisible by n.
文摘Suppose that K is a cyclic number field with odd prime degree. The unit group U_K of the integer ring O_K is U_K={+1}×V_K (direct product), where V_K is the group of units with norm 1. By Dirichet Unit Theorem, V_K is free Abelian
文摘We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11147158 and 11264020the Jiangxi Province Natural Science Foundation under Grant No 2010GQW0031the Jiangxi Province Scientific Research Program of the Education Bureau under Grant No GJJ12483
文摘The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD （T） method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.
文摘Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. Let M be a monic polynomialin R=F<sub>q</sub>[T]. The Carlitz action of M on a∈k<sup>ac</sup> is defined
基金funding from the National Natural Science Foundation of China(NSFC,Nos.21374057,51303100)the Fundamental Research Funds for the Central Universities(No.GK201502001,GK201301006)+6 种基金the 111 Project(No.B14041)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT_14R33)Natural Science Basic Research Plan in Shaanxi Province of China(No.2015JM2048)Open Project of State Key Laboratory of Supramolecular Structure and Materials(No.sklssm201626)the support of the Project funded by China Postdoctoral Science Foundation(No.2014M560747)Natural Science Basic Research Plan in Shaanxi Province of China(No.2016JM5024)the Scientific Research Program funded by Shaanxi Provincial Education Department(No.14JK1801)
文摘The paper summarizes and discusses the recent advances of proteins as functional interlayers in organic field-effect transistors（OFETs）.Specific focus is given on the proteins integrated into the device structure,either to act as dielectric materials or to perform as the functional interlayer between the dielectric and the organic semiconductor（OSC）.The main emphasis is give to the location and the specific effect of protein layers in the structure of OFETs.Besides,the possibility of amyloid serving as useful building blocks for OFET is discussed.
文摘For the hyperelliptic curve y^2=f(x) over F_q with deg(f)≥5, there is a singular point (0, 1, 0), such that a curve is not smooth. But the codes which are constructed by using hyperelliptic curves can be discussed basing on the theory of arithmetic of quadratic function fields.
文摘A series of maximal independent systems of cyclotomic units for cyclotomic functionfields and their subfields are constructed as an analogue of Ramachandra’s and Levesque’scyclotomic unit systems in cyclotomic number fields. The indexes of subgroups generated bythese unit systems in the whole unit groups are calculated and compared.
文摘This note is concerned in constructing a series of maximal independent systems of cyclotomic units in cyclotomic function fields and their subfields. Let us introduce basic facts on cyclotomic function fields briefly (see Refs. [1—3] for detail).
基金This work was done at USTC when the author was a graduate student in a special program of Nankai University.
文摘Let L/Fq(T) be a tame abelian extension of type (l, l,...l). The ratio of the degree zero divisor dass number (as well as the ideal class number) of L to the product of corresponding class numbers of all cydic subfields of L is clearly determined.
文摘In this note we show that the Mason’s upper bound of deg(u) for S-units u andv satisfying u + v = 1 over function field K = k(C) can be attained for any algebraicallyclosed coefficient field k and for some hyperelliptic or Artin-Schreier curve C over k withany given genus g≥0.
基金the support from the National Natural Science Foundation of China(NNSFC) through Grant No.11472056Beijing Key Laboratory Open Research Project KF20171123202
文摘In this paper, the nonlinear transient dynamic response of functionally graded material （FGM） sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy＇s third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction. Based on Reddy＇s theory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton＇s principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading, triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variable- coefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.
文摘Let k = Fq(T),q=pn, and let K=k((?)p)be the cyclotomic function field with conduc-tor P = P(T), and suppose K+ is the maximal real subfield of K, hp(h+p) is the class number of divisor group (of degree zero) of K(K+), and h-p=hp/h+p(∈ Ⅱ). This paper proves that for any fixed q≥3, there exist infinite many irreducible manic polynomial P∈Fq[T] such that p\h+p and pq-2\h-p. In addition, all regular quadratic irreducible polynomials in Fq[T] for 2≤p≤269 are determined.
