Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

拉曼放大器中放大的自发拉曼散射与拉曼开-关增益关系的研究

研究了拉曼放大器中放大的自发拉曼散射对拉曼开－关增益的影响，并提出了一种利用自发拉曼散射谱来调整拉曼放大器位曼开－关增益平坦的方法，实验采用4个波长为14xx nm的激光二极管作为抽运源，75km的G．652光纤作为传输介质，获得了C波段附近的光放大，同时对此给出了合理的理论解释。     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

像管亮度增益与背景测试仪

论述像管亮度增益与背景测试仪的原理，介绍仪器的组成以及测试数据的处理方法。     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.     

On Rado's Boundedness Conjecture

We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a₁,a₂, and a₃ are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a₁x₁+a₂x₂+a₃x₃=0, then for every finite coloring of the positive integers there is a monochromatic solution to a₁x₁+a₂x₂+a₃x₃=0.     

类锂硅离子软X射线激光研究

在激光等离子体典型参数条件下，利用碰撞－辐模型计算了类锂硅离子５ｆ－３ｄ和４ｆ－３ｄ跃的粒子数反转比率和激光增益系数。讨论了不同热带条件和不同冷却速度下，激光增益系统数的变化。计算结果表明，高功率，短脉冲激光生产的高温等离子体在快速冷却条件下能产生软Ｘ射的线激光增益。     

Gain saturation in quantum-well heterostructures

The effect of radiation gain saturation in quantum-well heretostructures was investigated in the system GaAs—AlGaAs with regard to the spectral line broadening and the type of radiation polarization. Belarusian State University, 4, F. Skorina Ave., Minsk, 220050, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 797–800, November–December, 1997.