Quadratic extensions of totally real quintic fields

In this work, we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than in absolute value. For each field in the list we give its discriminant, the discriminant of its subfield, a relative polynomial generating the field over one of its subfields, the corresponding polynomial over , and the Galois group of its Galois closure.

We have examined the existence of several non-isomorphic fields with the same discriminants, and also the existence of unramified extensions and cyclic extensions.

     

A Difference Set in \left( {\mathbb{Z}/4\mathbb{Z}} \right)^3 \times \mathbb{Z}/5\mathbb{Z}

We present a (320, 88, 24)-difference set in , the existence of which was previously open. This new difference set improves a theorem of Davis-Jedwab with the removal of the exceptional case. It also enables us to state a theorem of Schmidt on Davis-Jedwab difference sets more neatly.     

Dedekind Complete Commutative BCK-algebras

We study Dedekind complete commutative BCK-algebras with the relative cancellation property and their connection with corresponding universal groups. We shall characterize Dedekind orthogonally complete atomic and Archimedean BCK-algebras, generalizing results of Jakubík known for MV-algebras. Finally, we characterize those Dedekind complete and atomic commutative BCK-algebras that are isomorphic to direct products of basic BCK-chains, generalizing a result of Cignoli for MV-algebras.     

A Singular Equation of Length Four Over Groups

Let G be a group and t an unknown. In this paper we prove that the equation atbtct^–1dt^–1 = 1 (a,b,c,d G, a² 1, c² 1, bd 1) has a solution over G. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over G.2000 Mathematics Subject Classification: 20E06     

Computation of relative class numbers of CM-fields by using Hecke -functions

We develop an efficient technique for computing values at of Hecke -functions. We apply this technique to the computation of relative class numbers of non-abelian CM-fields which are abelian extensions of some totally real subfield . We note that the smaller the degree of the more efficient our technique is. In particular, our technique is very efficient whenever instead of simply choosing (the maximal totally real subfield of ) we can choose real quadratic. We finally give examples of computations of relative class numbers of several dihedral CM-fields of large degrees and of several quaternion octic CM-fields with large discriminants.

     

在玻璃转变温度及其以上温区聚苯乙烯/聚氧化乙烯共混物的动力学弛豫行为

用熔融共混法制备了不同组分的聚苯乙烯(PS)与聚氧化乙烯(PEO)共混物(PS/PEO).在玻璃转变温度T_g及其以上温区,利用相对能量耗散技术研究了该共混物的动力学行为.结果发现,在能量耗散-温度曲线上出现了两个弛豫型的耗散峰(α峰和α′峰).分析表明,α峰是与PS玻璃转变有关的特征耗散峰; α′峰则对应于一种“液-液转变”.两者的弛豫时间τ都不满足Arrhenius关系.此外,还研究了组分对这两个弛豫型耗散峰的影响,并给予了定性的解释. 关键词： 相对能量耗散 玻璃转变 力学弛豫     

红外中带滤光片的结构、带宽估算及调整

中波红外波段在航天、气象、遥感等领域有着重要的应用，为了提高信噪比，系统中经常使用高质量的红外中带滤光片。相对带宽是红外中带滤光片重要的指标，主要取决于光学薄膜的膜系结构和具体设计。首先给出双截止组合型、F-P型、多半波型等几种膜系结构，归纳了相对带宽估算公式。同时从实用性出发，对一些具体膜系结构进行了相对带宽估算和综合分析，结果表明多半波结构最为可行。针对多半波结构，提出了间隔层膜料和光学厚度的选择、采用等效膜、调整膜层折射率等相对带宽调整的方法。最后，利用上述相对带宽调整方法对红外中带滤光片进行了设计，给出了实际镀制结果，滤光片相对带宽指标满足设计要求。     

中等尺寸SiN团簇结构和相对稳定性的研究(21≤N≤50,N=60)

在过去二十年里,对中等尺寸硅团簇的研究一直十分活跃.为阐明低能团簇从中等到大尺寸的生长行为,我们对SiN团簇在21≤N≤50,和N=60的结构和相对稳定性进行论述.对Si21-Si29,除Si27外最低能量结构是扁长形.对N≥30,SiN团簇倾向于形成填充富勒烯结构.随着团簇尺寸的增大(N≥41),内部开始出现四面体结构,可视为金刚石晶格结构形成的初始阶段.当团簇尺寸达到N=60时,其已偏离小团簇的类分子行为,但向块体结构的转变还没完成.中等尺寸硅团簇的填充富勒烯结构可以被看作是从类分子向块体过渡的中间阶段.     

Relative position determination of a lunar rover using high-accuracy multi-frequency same-beam VLBI

Multi-frequency same-beam VLBI means that two explorers with a small separation angle are simultaneously observed with the main beam of receiving antennas. In the same-beam VLBI, the differential phase delay between two explorers and two receiving telescopes can be obtained with a small error of several picoseconds. The differential phase delay, as the observable of the same-beam VLBI, gives the separation angular information of the two explorers in the celestial sphere. The two-dimensional relative position on the plane-of-sky can thus be precisely determined with an error of less than 1 m for a distance of 3.8×105 km far away from the earth, by using the differential phase delay obtained with the four Chinese VLBI stations. The relative position of a lunar rover on the lunar surface can be determined with an error of 10 m by using the differential phase delay data and the range data for the lander when the lunar topography near the rover and the lander can be determined with an error of 10 m.     

二次曲面和平面位置关系的判式

在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离.