Further explorations into ternary complementary pairs

In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358-375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduced more new primitive pairs than could be inferred previously, concluding with some conjectures reflecting the patterns that were beginning to arise in light of the new approach.In this paper we take what appears to be the natural next step, by investigating these patterns among those lengths and weights that are within easy computational distance from the last length considered therein, length 14. We give complete results up to length 21, and partial results up to length 28. (Ironically, although we proceed analytically by weight first then length, for computational reasons we are bound, in this empirical investigation, to proceed according to length first.)Thus we provide support for the previous conjectures, and shed enough new light to speculate further as to the likely ultimate shape of the theory. Since short term work on TCPs will require massive acquisition of data about small pairs, we also discuss affixes—a computational strategy that arose out of the investigations culminating in this article.     

双环、三纤互耦全光纤熔锥滤波器用正常色散的双折射光纤所作的暗孤子开关的开关条件

通过将熔锥结构中强、弱耦合段的总幅度耦合系数与滤波网络方程中的幅度耦合系数等效的方法,定量分析了双环、三纤互耦滤波器的频谱特性。实验滤波器通带特性的测试结果与理论分析基本吻合。所测滤波器的中心波长、抑制度、半功率带宽及插入损耗分别为1.27 μm,>13 dB、72 μm及3.9 dB。在正常色散的双折射光纤中传输的暗孤子对之间由于耦合周期性交换能量,一个暗孤子可把能量完全转给另一暗孤子,因此双折射光纤可作光开关。本文讨论了椭圆角为35°的双折射光纤的开关条件,发现脉冲只有以特定的极化角入射才有开关现象产生,而且建立了光纤长度与孤子对相差、初始能量差的解释关系。     

Chaos in PDEs and Lax Pairs of Euler Equations

Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1) transversal homoclinic orbits, (2) Silnikov homoclinic orbits. Around the transversal homoclinic orbits in infinite-dimensional autonomous systems, the author was able to prove the existence of chaos through a shadowing lemma. Around the Silnikov homoclinic orbits, the author was able to prove the existence of chaos through a horseshoe construction.Very recently, there has been a breakthrough by the author in finding Lax pairs for Euler equations of incompressible inviscid fluids. Further results have been obtained by the author and collaborators.     

Induced characters, Mackey analysis and primitive ideal spaces of nilpotent discrete groups

Let G be a nilpotent discrete group and Prim(C^*(G)) the primitive ideal space of the group C^*-algebra C^*(G). If G is either finitely generated or has absolutely idempotent characters, we are able to describe the hull-kernel topology on Prim(C^*(G)) in terms of a topology on a parametrizing space of subgroup-character pairs. For that purpose, we introduce and study induced traces and develop a Mackey machine for characters. We heavily exploit the fact that the groups under consideration have the property that every faithful character vanishes outside the finite conjugacy class subgroup.     

A Generalization about Congruent Pairs on a Set

ＡＧｅｎｅｒａｌｉｚａｔｉｏｎａｂｏｕｔＣｏｎｇｒｕｅｎｔＰａｉｒｓｏｎａＳｅｔＨｕａｎｇＪｕｎｍｉｎ（黄骏敏）（ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃａｎｃｅｌｔｈｅｃｏｎｄｉｔｉｏｎ...     

205Tl NMR studies: Ion pairing of Tl+ and (CH3)2Tl+ with NO 3 − and ClO 4 − in various solvents

The concentration dependence of the²⁰⁵Tl chemical shifts of Tl⁺ and of (CH₃)₂Tl⁺ ions was determined in several solvents with NO ₃ ^– and ClO ₄ ^– counterions. In general, increased ion pairing caused a low-frequency shift of the²⁰⁵Tl resonance, with the exceptions of (CH₃)₂TlNO₃ inn-butylamine and TlNO₃ in N,N-dimethylformamide (DMF) and in hexamethylphosphorotriamide (HMPA). In HMPA,²⁰⁵Tl linewidths of both Tl⁺ and (CH₃)₂Tl⁺ increased dramatically with dilution below 0.1M. Analysis of the data allowed ion-pair formation constants and²⁰⁵Tl chemical shifts for the ion-paired cation and for the free (solvated) cation to be estimated for some of the solvents.     

On Extended Polar Decomposition

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.     

Congruent Pairs On a Set

ＣｏｎｇｒｕｅｎｔＰａｉｒｓＯｎａＳｅｔＺｈｕＺｕｏｔｏｎｇ；（朱作桐）ＨｕａｎｇＪｕｎｍｉｎ（黄军民）（ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉｎｔｒｏｄ...     

Lie-Cartan pairs

The algorithms common to exterior derivation, exterior covariant derivation and vector valued cohomology of Lie-Algebras are presented within a unified frame.