Liquid chromatography of the s-triazines

Summary A series of thirty s-triazine compounds have been separated using reversed-phase high-pressure liquid chromatography. A relationship between substituent activity and retention time was developed to predict molecular structure.Work partially completed at the CIBA-GEIGY Corp., McIntosh, Ala., USA.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Large cycles in random generalized Johnson graphs

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.     

Two Hamiltonian cycles

If the line graph of a graph G decomposes into Hamiltonian cycles, what is G? We answer this question for decomposition into two cycles.     

Oriented hypergraphs: Balanceability

An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.     

Hamilton cycles in line graphs of 3-hypergraphs

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.     

On bandwidth sums of graphs

ＯＮＢＡＮＤＷＩＤＴＨＳＵＭＳＯＦＧＲＡＰＨＳＹＡＯＢＩＮＧ（姚兵）;ＷＡＮＧＪＩＡＮＦＡＮＧ（王建方）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＮｏｒｉｈｗｅｓｔｅｔｅｒｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｌａｎｚｈｏｕ７３００７０,Ｃｈｉ...     

Lasers without photons — or should it be lasers with too many photons?

Expanding the fields of a laser cavity in a set of orthonormal modes is a standard technique in laser theory. Expansion in a normal mode set is also the basis of the concept of photons. A substantial number of practical lasers do not, however, support any kind of normal or orthogonal cavity modes, and thus, their fields cannot be represented (at least not easily) in terms of normal modes, or photons. This leads to a number of unusual results, including situations in which the lowest-order mode of a cavity can contain substantially more energy than the total energy in the cavity, as well as enhanced quantum spontaneous emission far stronger than the single extra photon level characteristic of an ordinary laser oscillator. We review the theoretical origins of these unusual effects and present experimental confirmation of greatly enhanced Schawlow-Townes fluctuations in an unstable-resonator laser with a Petermann-noise enhancement factor of several hundred times.Dedicated to H. Walther on the occasion on his 60th birthday     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.