On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

pH-responsive microgels containing hydrophilic crosslinking co-monomers: shell-exploding microgels through design

pH-responsive microgels are crosslinked polymer colloids that swell when the pH approaches the pK _a of the particles. They have potential application for injectable gels for tissue repair and drug delivery systems. This study focuses on the pH-triggered gelation behaviour of a series of poly (EA/MAA/X) microgels. EA and MAA are ethylacrylate and methacrylic acid. Here, we investigate the effect of crosslinking monomer type (X) on microgel properties. The crosslinking monomers used were poly (ethyleneglycol) dimethacrylate (PEGD), ethyleneglycol dimethacrylate (EGD) and butanediol diacrylate (BDD). The microgel containing PEGD (m-PEGD) is a new system. The microgel containing BDD (m-BDD) was used as a control system. The concentrated microgel dispersions formed physical gels when the pH was increased to 5.3?C6.7, and the polymer volume fractions (? _p ) were above about 0.05. Evidence from photon correlation spectroscopy (PCS) and dynamic rheology was presented for abrupt pH-triggered increases, and then decreases of the hydrodynamic diameters for m-PEGD and the microgel prepared using EGD (m-EGD). This appears to be tuneable through crosslinker structure. An unexpected gelation behaviour, which may involve a new gel state for microgels, was found for m-PEGD dispersions. Uniquely, those dispersions formed gels at pH values less than the microgel's pK _a . This behaviour was linked to an outer-shell electrostatic repulsive interaction. The data point to a phenomenon, whereby the m-PEGD shells appear to explode at pH values above 7.0. The control microgel prepared, using BDD (m-BDD), did not show any evidence of shell fragmentation at any pH. That microgel has potential as a model pH-responsive microgel system in that the properties measured by PCS and rheology agreed well. To probe that system in more detail, the rheological data for m-BDD was analysed using scaling theory. The variation of the storage modulus (G') with ? _p gave a scaling exponent of 2.0.     

Frequency and temperature dependence of a.c. conductivity of vitreous silver phosphate electrolytes

The a.c. conductivity behaviour in the 20–300 K temperature range has been investigated for (Ag₂S)_x(AgPO₃)_1−x and (Ag₂SO₄)_x(AgPO₃)_1−x glasses at various salt contents (x). The temperature dependence at selected frequencies in the radioand micro-wave region displays several relaxational contributions which are indistinct in the frequency domain. The low temperature experimental data are discussed and a proposed ‘new universality’ has been examined.     

Note on a proposed weighted residual method for solving nonlinear differential boundary problems

A proposed iterative method for solving nonlinear differential two-point boundary value problems is generalized and shown to be equivalent to using the standard method of adjoints on a linearized form of the nonlinear boundary-value problem.     

O.R. in the Company Car Fleet: When Simple is Efficient

The management of a large fleet of company vehicles represents a significant administrative activity, particularly when the company is a motor vehicle manufacturer and the fleet consists of its own products. The approach taken by the Operational Research Group was to cross departmental boundaries to smooth vehicle ordering, reduce inventories of vehicles awaiting delivery and optimize resale values. The method steers between two potential pitfalls: that of ‘optimizing’ one affected department to the detriment of others, and that of developing sophisticated scheduling and forecasting algorithms which the users would not understand and therefore not trust.     

Properties of a representation of a basis for the null space

Given a rectangular matrixA(x) that depends on the independent variablesx, many constrained optimization methods involve computations withZ(x), a matrix whose columns form a basis for the null space ofA ^T(x). WhenA is evaluated at a given point, it is well known that a suitableZ (satisfyingA ^T Z = 0) can be obtained from standard matrix factorizations. However, Coleman and Sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously withx; they also suggest several techniques for adapting these schemes so as to ensure continuity ofZ in the neighborhood of a given point.This paper is an extension of an earlier note that defines the procedure for computingZ. Here, we first describe howZ can be obtained byupdating an explicit QR factorization with Householder transformations. The properties of this representation ofZ with respect to perturbations inA are discussed, including explicit bounds on the change inZ. We then introduceregularized Householder transformations, and show that their use implies continuity of the full matrixQ. The convergence ofZ andQ under appropriate assumptions is then proved. Finally, we indicate why the chosen form ofZ is convenient in certain methods for nonlinearly constrained optimization.The research of the Stanford authors was supported by the U.S. Department of Energy Contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; the National Science Foundation Grants MCS-7926009 and ECS-8312142; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-84-K-0156.The research of G.W. Stewart was supported by the Air Force Office of Scientific Research Contract AFOSR-82-0078.     

The effect of stereochemistry on the mass spectra of the bis(trimethyl-silyl) esters of maleic and fumaric acids

The mass spectra of the bis(trimethylsilyl) esters of maleic and fumaric acids provide a simple and particularly striking example of the influence of stereochemistry on the electron-impact-induced fragmentation of organic molecules. The results provide evidence for the structural significance of the m/e 147 ion, which is considerably more intense in the maleate spectrum than in the fumurate spectrum.