polynomial bound on the number of scattering poles on montre que dans la diffusion par un potentiel infiniment differentiable a support compact les poles de l operateur de diffusion sont a distribution polynomiale

finite hexavalent edge primitive graphs abstract weiss 1973 determined all cubic edge primitive graphs and guo feng and li recently determined all tetravalent and pentavalent edge primitive graphs notice that their method is difficult to treat the bigger valency case because the edge stabilizers may be insoluble in this paper we study hexavalent edge primitive graphs by using line graphs the s arc transitivity of such graphs are determined and the automorphism groups of such graphs besides k 6 6 are proved to be almost simple two families of hexavalent edge primitive graphs are also completely determined

scattering resonances of convex obstacles for general boundary conditions we study the distribution of resonances for smooth strictly convex obstacles under general boundary conditions we show that under a pinched curvature condition for the boundary of the obstacle the resonances are separated into cubic bands and the distribution in each band satisfies weyl s law

geometric bounds on the density of resonances for semiclassical problems in this paper we shall give upper bounds on the number of resonances in certain regions in the complex plane close to the real axis for semiclassical operators like h 2 v x when h is small

lower bounds for resonance widths in potential and obstacle scattering explicit lower bounds are given for the size of the imaginary parts of resonances for schrodinger operators with non trapping or trapping potentials and for the dirichlet laplacian in the exterior of a star shaped obstacle both acting in three dimensions

the maximal subgroups of the baby monster i abstract in this paper we describe the completion of the determination of the maximal subgroups of the baby monster simple group our results are proved using computer calculations with matrix generators for the group the full details of the calculations will appear elsewhere

self similar viscous incompressible flow along an unbounded corner the self similar viscous flow of incompressible fluid along the right angle unbounded corner with nonzero streamwise pressure gradient is considered the corner layer equations for this case are derived and their asymptotic series are analyzed it is shown that self similar corner layer equations have two solutions even at a zero streamwise pressure gradient the numerical procedure for the integration of corner layer equations is developed and numerical calculations are performed at several values of power exponent for a streamwise pressure gradient distribution

on primitive permutation groups with small suborbits and their orbital graphs abstract in this paper we study finite primitive permutation groups with a small suborbit based on the classification result of quirin math z 122 1971 267 and wang comm algebra 20 1992 889 we first produce a precise list of primitive permutation groups with a suborbit of length 4 in particular we show that there exist no examples of such groups with the point stabiliser of order 2 4 3 6 clarifying an uncertain question since 1970s then we analyse the orbital graphs of primitive permutation groups with a suborbit of length 3 or of length 4 we obtain a complete classification of vertex primitive arc transitive graphs of valency 3 and valency 4 and we prove that there exist no vertex primitive half arc transitive graphs of valency less than 10 finally we construct vertex primitive half arc transitive graphs of valency 2 k for infinitely many integers k with 14 as the smallest valency

stability of the laminar boundary layer in a streamwise corner this work examines the stability of viscous incompressible flow along a streamwise corner often called the corner boundary layer problem the semi infinite boundary value problem satisfied by small amplitude disturbances in the blending boundary layer region is obtained the mean secondary flow induced by the corner exhibits a flow reversal in this region uniformly valid first approximations to solutions of the governing differential equations are derived uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate langer variable approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two dimensional boundary layer profiles viscous incompressible laminar flow along a streamwise corner formed by the intersection of two solid surfaces is often referred to as the corner boundary layer problem in the theoretical model of this problem two flat plates which are infinite in the streamwise and spanwise directions intersect such that the line of intersection the corner line is normal to the plane containing their leading edges the basic flow is along the line of intersection most theoretical work assumes a rectangular corner this situation is shown in figure 1

a characterization and another construction of janko s group graphs r with the following properties are classified i f is g s transitive for some s 4 and some group g g 1 2 where g is the girth of f and ii f is connected a new construction of j3 is given

the infinitude of 7 arc transitive graphs abstract by theorems of tutte weiss and others it is known that there are no finite symmetric graphs of degree greater than 2 with automorphism group transitive on 8 arcs and that 7 arc transitivity can occur only in the case of graphs of degree 3 m 1 in this article it is shown that there are infinitely many 7 arc transitive finite quartic graphs indeed for all but finitely many positive integers n there is a finite connected 7 arc transitive quartic graph with the alternating group a n acting transitively on its 7 arcs and another with the symmetric group s n acting transitively on its 7 arcs the proof uses a construction involving permutation representations of a generic infinite group to produce an infinite family of finite graphs with the required properties

s arc transitive graphs and normal subgroups abstract we study s arc transitive graphs with s 2 and give a characterisation of the actions of vertex transitive normal subgroups an interesting consequence of this characterisation states that each non bipartite 3 arc transitive graph is a normal cover of a 2 arc transitive graph admitting a simple group or a locally primitive graph admitting a simple group with a soluble vertex stabiliser

the maximal subgroups of the chevalley groups g2 q with q odd the ree groups 2g2 q and their automorphism groups

morrey campanato estimates for helmholtz equations abstract we derive uniform weighted l 2 and morrey campanato type estimates for helmholtz equations in a medium with a variable index which is not necessarily constant at infinity our technique is based on a multiplier method with appropriate weights which generalize those of morawetz for the wave equation we also extend our method to the wave equation

particle image velocimetry measurement of laminar boundary layer in a streamwise corner measurement of velocity profiles along a laminar boundary layer in a streamwise corner was carried out by using particle image velocimetry in contrast to conventional hot wire anemometry to make the measurement successful the laser light source for particle image velocimetry was placed at a far downstream station and a light sheet was emitted in parallel to the corner intersection line the platewas tilted at very small angles relative to the freestream to realize the laminar flow starting from the corner leading edge discussions on the characteristic features of the velocity profile in the bisector plane are given based on the measurement data it was found that the measured velocity profiles correspond to the blasius branch solution of the theoretical corner layer equations

similarity and stability of the laminar boundary layer in a streamwise corner the study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state and outstanding differences between various experimental and theoretical results are analysed new experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the reynolds number much above about 10 4 the new results also help to explain the differences between various experimental results and between theory and experiment which have characterized the corner boundary layer problem for several years by extrapolation an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient if the layer were stable in that state the predicted profile is compared with the results of current theories

scattering frequencies and gevrey 3 singularities on etudie les frequences de diffusion k pour le laplacien dans la region r n o exterieur a un obstacle analytique compact on suppose que n est impair et qu on impose des conditions de dirichlet sur

a classification of the maximal subgroups of the finite alternating and symmetric groups following the classification of finite simple groups one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups that is of groups x such that x0 u x aut x for some finite non abelian simple group x0 the problem has been solved for most sporadic groups and groups of lie type of low rank see 19 sects 3 43 for discussion and references this paper is a contribution to the case where x0 is an alternating group a so that for n 6 x is a or s the maximal subgroups of a and s are known for several classes of degrees n

finite edge transitive cayley graphs and rotary cayley maps this paper aims to develop a theory for studying cayley graphs especially for those with a high degree of symmetry the theory consists of analysing several types of basic cayley graphs normal bi normal and core free and analysing several operations of cayley graphs core quotient normal quotient and imprimitive quotient it provides methods for constructing and characterising various combinatorial objects such as half transitive graphs orientable and non orientable regular cayley maps vertex transitive non cayley graphs and permutation groups containing certain regular subgroups in particular a characterisation is given of locally primitive holomorph cayley graphs and a classification is given of rotary cayley maps of simple groups also a complete classification is given of primitive permutation groups that contain a regular dihedral subgroup