a brick tetrahedron finite element interface with stable hybrid explicit implicit time stepping for maxwell s equations a new brick tetrahedron finite element interface with stable hybrid explicit implicit time stepping for maxwell s equations is described and tested the tetrahedrons are connected directly to the bricks as opposed to previous curl conforming formulations that use an intermediate layer of pyramids the electric field is expanded in linear edge elements which yields a discontinuous tangential electric field at the brick tetrahedron interface and this discontinuity is treated by nitsche s method in addition tangential continuity for an arbitrary constant electric field is imposed in the strong sense at the interface which makes it possible to avoid penalization that perturbs the frequency spectrum this hybridization preserves the null space of the curl curl operator and is free from non physical spurious modes which is confirmed by numerical tests the implicit newmark time stepping scheme is employed for the tetrahedrons which allows for local mesh refinement without reduced time step for the brick elements spatial lumping and explicit time stepping is employed which yields the standard finite difference time domain scheme furthermore we prove that the explicit implicit time stepping employed at the hybrid interface is stable for time steps up to the courant limit of the explicitly time stepped bricks second order of convergence is achieved for field solutions without singular behavior the reflection from the brick tetrahedron interface is small and scattering from a thin layer of tetrahedrons indicates levels at approximately 49db for a resolution of 14 cells per wavelength

generation and random generation from simple groups to maximal subgroups abstract let g be a finite group and let d g be the minimal number of generators for g it is well known that d g 2 for all non abelian finite simple groups we prove that d h 4 for any maximal subgroup h of a finite simple group and that this bound is best possible we also investigate the random generation of maximal subgroups of simple and almost simple groups by applying a recent theorem of jaikin zapirain and pyber we show that the expected number of random elements generating such a subgroup is bounded by an absolute constant we then apply our results to the study of permutation groups in particular we show that if g is a finite primitive permutation group with point stabilizer h then d g 1 d h d g 4

the q deformation of symmetry transformations preserving the radial form of the schrodinger equation proofs are given that the symmetry transformations preserving the radial form of the schrodinger equation lead to matching conditions which are essentially the same as the classical ones power law potentials are treated as illustrative examples in particular the dimensional q deformed coulomb system is converted into a q deformed harmonic oscillator acting again in space dimensions we also found that q deformed 1 n energy formulae are covariant under such transformations to first 1 n order

on classifying all full factorisations and multiple factorisations of the finite almost simple groups abstract we present some general results on factorisations of almost simple groups these results are consequences of the classification of all maximal factorisations of almost simple groups due to liebeck saxl and the second author and are needed for applications to the theory of quasiprimitive permutation groups

conformal finite different time domain fdtd with overlapping grids it is shown how to use many overlapping conformal grids in the neighborhood of the scatterer while using a rectangular grid away from the scatterer for solving maxwell s equations the locally conformal grids allow better approximation of the boundary condition on the scattering object while the rectangular grid preserves the simplicity and accuracy of the regular finite difference time domain fdtd algorithm these grids overlap typically about three zones it is shown how to connect together the calculations done in different overlapping grids

the quantum schrodinger equation and the q deformation of the hydrogen atom by employing the non commutative differential calculus on the quantum orthogonal planes the authors investigate the deformed version of the schrodinger equation for the attractive coulomb potential v r e2 r the solutions show the quantum group symmetry and the calculated energy eigenvalues seem to be proportional to n 2 which is in agreement with the energy levels of the hydrogen atom in the limit of q to 1

application of stable fem fdtd hybrid to scattering problems a recently developed stable finite element method fem finite difference time domain fdtd hybrid that eliminates the staircase approximation of complex geometries is tested by convergence studies for radar cross sections for a conducting sphere 1 db accuracy in all directions is obtained with nine cells per wavelength whereas the nasa almond requires a higher resolution of about 15 cells per wavelength for scatterers with a smooth boundary the results converge quadratically with the mesh size but for a horizontally polarized wave incident on the nasa almond the order of convergence is lower because of singular fields at the tip

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

quasiprimitive groups containing a transitive alternating group abstract this paper classifies quasiprimitive permutation groups with a transitive subgroup which is isomorphic to a n for some n 5

completeness of coherent states associated with self similar potentials and ramanujan s integral extension of the beta function a decomposition of identity is given as a complex integral over the coherent states associated with a class of shape invariant self similar potentials there is a remarkable connection between these coherent states and ramanujan s integral extension of the beta function

analysis of photonic crystals using the hybrid finite element finite difference time domain technique based on the discontinuous galerkin method summary two dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite element time domain fetd method and the finite difference time domain fdtd method this hybrid fetd fdtd method uses the discontinuous galerkin method as framework for domain decomposition to the best of our knowledge this is the first hybrid fetd fdtd method that allows non conformal meshes between different fetd and fdtd subdomains it is also highly parallelizable these properties are very suitable for the computation of periodic structures with curved surfaces numerical examples for the computation of the scattering parameters of two dimensional photonic bandgap structures are presented as applications of the hybrid fetd fdtd method numerical results demonstrate the efficiency and accuracy of the proposed hybrid method copyright 2012 john wiley sons ltd

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

quantum and classical mechanics of q deformed systems quantum and classical mechanics of a system of q deformed bosonic oscillators are considered the q deformed heisenberg weyl algebra of creation and destruction operators is realized by differential operators in a space of functions of real commutative variables the corresponding hilbert space is constructed in this approach the deformation parameter turns out to be a function of the planck constant an oscillator frequency and a parameter with dimension of length the hamiltonian path integral is derived and its semiclassical approximation is investigated to obtain the corresponding q deformed classical theory the phase space spanned by the usual commutative coordinates is shown to be a cylinder in classical theory the dimensional parameter introduced determines its radius it is argued that the q deformation can be associated with a special non canonical transformation the principle of least action for the classical q deformed system is formulated a representation of uq m in a space of functions on a phase space spanned by commutative coordinates is constructed

quasiprimitive groups and blow up decompositions abstract the blow up construction by l g kovacs has been a very useful tool for studying embeddings of finite primitive permutation groups into wreath products in product action in the present paper we extend the concept of a blow up to finite quasiprimitive permutation groups and use it to study embeddings of finite quasiprimitive groups into wreath products

a note on the solvability of groups abstract let m be a maximal subgroup of a finite group g and k l be a chief factor such that l m while k m we call the group m k l a c section of m and we define sec m to be the abstract group that is isomorphic to a c section of m for every maximal subgroup m of g assume that sec m is supersolvable then any composition factor of g is isomorphic to l 2 p or z q where p and q are primes and p 1 mod 8 this result answer a question posed by y wang s li c sections of maximal subgroups of finite groups j algebra 229 2000 86 94

maximum principles and bounds in a class of fourth order uniformly elliptic equations this paper is devoted to a class of fourth order uniformly elliptic equations posed by schaefer in 1987 we obtain maximum principles for certain functions which are defined on solutions of the elliptic equations the principles are then used to deduce some bounds on important quantities in the physical problems of interest

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

a stable fdtd subgridding method based on finite element formulation with hanging variables the finite element time domain fetd method based on the use of hanging variables to generate nested grids is used as an interface between the coarse and fine grids in the fdtd subgridding method since the formulation for treating hanging variables is based on a galerkin type intergrid boundary operator the resulting fdtd subgridding algorithm is guaranteed to be stable numerical examples such as the computation of resonant modes of a 3 d rectangular resonant cavity and 2 d tez scattering by a pec cylinder and a naca airfoil are presented to verify the stability and accuracy of the proposed subgridding algorithm

domain decomposition fdtd algorithm for the analysis of a new type of e plane sectorial horn with aperture field distribution optimization in this paper a universal and efficient approach of domain decomposition finite difference time domain fdtd dd fdtd is presented for the analysis of a new type of horn antenna e plane sectorial horn with field amplitude taper and phase correction in the aperture the power fed into the horn is redistributed to achieve the optimal field amplitude distribution in the aperture and meanwhile the field phase is corrected by metal lens compared with conventional e plane sectorial horns the new horn antenna takes the advantages of low sidelobe level short physical length and wide flare angle etc moreover the most important property of this horn is the weak coupling with each other when it is used as the element of a phased array antenna the field analysis of such a horn antenna is an extremely complicated three dimensional em boundary value problem the domain decomposition fdtd method is presented in this paper to break through the drawback the whole horn is decomposed into several subdomains and the meshes are created in local coordinates in the iteration procedure of fdtd the data are exchanged between adjacent subdomains with overlapped meshes the aperture field distribution voltage standing wave ratio and pattern calculated by the dd fdtd method are in good agreement with the experimental data

stability of explicit implicit hybrid time stepping schemes for maxwell s equations an improved version of the stable fem fdtd hybrid method t rylander and a bondeson comput phys commun 125 75 2000 for maxwell s equations is presented the new formulation has a modified time stepping scheme and is rigorously proven to be stable for time steps up to the stability limit for the fdtd the new scheme gives less reflection at the boundary between the structured and unstructured grids than the original formulation the hybrid method is compared to the fdtd with staircasing for scattering from a conducting sphere the discretization errors of the hybrid show quadratic dependence on mesh size while the scaling is less clear for the fdtd the fdtd gives errors that are 5 60 times higher than that of the hybrid depending on resolution and staircasing strategy

the maximality of monomial subgroups of linear groups over division rings abstract the monomial subgroups are proved to be maximal in gl n k or sl n k for arbitrary division rings k with some exceptions

the primitive permutation groups of degree less than 2500 abstract in this paper we use the o nan scott theorem and aschbacher s theorem to classify the primitive permutation groups of degree less than 2500

green function on the q symmetric space invariant distance on the non commutative algebra is constructed and the generalized functions on the q symmetric space are introduced the green function and the kernel on m are derived a path integration is formulated the green function for the free massive scalar field on the non commutative einstein space is presented

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

electric and magnetic losses modeled by a stable hybrid with explicit implicit time stepping for maxwell s equations a stable hybridization of the finite element method fem and the finite difference time domain fdtd scheme for maxwell s equations with electric and magnetic losses is presented for two dimensional problems the hybrid method combines the flexibility of the fem with the efficiency of the fdtd scheme and it is based directly on ampere s and faraday s law the electric and magnetic losses can be treated implicitly by the fem on an unstructured mesh which allows for local mesh refinement in order to resolve rapid variations in the material parameters and or the electromagnetic field it is also feasible to handle larger homogeneous regions with losses by the explicit fdtd scheme connected to an implicitly time stepped and lossy fem region the hybrid method shows second order convergence for smooth scatterers the bistatic radar cross section rcs for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2 is achieved for about 20 points per wavelength the monostatic rcs for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners a careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non trivial test case which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses

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

transitive subgroups of primitive permutation groups abstract we investigate the finite primitive permutation groups g which have a transitive subgroup containing no nontrivial subnormal subgroup of g the conclusion is that such primitive groups are rather rare and that their existence is intimately connected with factorisations of almost simple groups a corollary is obtained on primitive groups which contain a regular subgroup heavily involved in our proofs are some new results on subgroups of simple groups which have orders divisible by various primes for example another corollary implies that for every simple group t apart from l 3 3 u 3 3 and l 2 p with p a mersenne prime there is a collection consisting of two or three odd prime divisors of t such that if m is a subgroup of t of order divisible by every prime in then m is divisible by all the prime divisors of t and we obtain a classification of such subgroups m

new oblique thin wire formalism in the fdtd method with multiwire junctions a new oblique thin wire formalism based on holland s approach is proposed in the fdtd method the principal achievement of this new formalism is to enable us to model a junction correctly between several oblique wires to this end an important criterion is proposed the continuity of the current traces in the grid must be maintained at each node of the yee cell that contains a part of one or several wires this condition prevents undamped parasite oscillations on the wire current responses in addition our approach offers versatility in its usage first the extremities of the wire can be placed freely in a yee cell second it operates in lossy medium and finally the sensitivity of the wire is minimized when inclined or shifted with regards to this last point the in cell inductance of a wire segment is formulated to take account of the segment position and its obliquity in the yee cell

topological generation of exceptional algebraic groups abstract let g be a simple algebraic group over an algebraically closed field k and let c 1 c t be non central conjugacy classes in g in this paper we consider the problem of determining whether there exist g i c i such that g 1 g t is zariski dense in g first we establish a general result which shows that if is an irreducible subvariety of g t then the set of tuples in generating a dense subgroup of g is either empty or dense in in the special case c 1 c t by considering the dimensions of fixed point spaces we prove that this set is dense when g is an exceptional algebraic group and t 5 assuming k is not algebraic over a finite field in fact for g g 2 we only need t 4 and both of these bounds are best possible as an application we show that many faithful representations of exceptional algebraic groups are generically free we also establish new results on the topological generation of exceptional groups in the special case t 2 which have applications to random generation of finite exceptional groups of lie type in particular we prove a conjecture of liebeck and shalev on the random r s generation of exceptional groups

wkb equivalent potentials for the q deformed harmonic oscillator wkb equivalent potentials wkb ep giving the same spectrum as the q deformed harmonic oscillator with the symmetry suq 2 are determined while in the case of q being real the wkb ep goes to infinity as one moves away from the origin in the case of q being a phase the wkb ep goes to a finite limiting value thus resembling for example the modified poschl teller potential

innately transitive subgroups of wreath products in product action a permutation group is innately transitive if it has a transitive minimal normal subgroup which is referred to as a plinth we study the class of finite innately transitive permutation groups that can be embedded into wreath products in product action this investigation is carried out by observing that such a wreath product preserves a natural cartesian decomposition of the underlying set previously we classified the possible embeddings in the case where the plinth is simple here we extend that classification and identify several different types of cartesian decompositions that can be preserved by an innately transitive group with a non abelian plinth these different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action we also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products

a parallel implicit explicit hybrid time domain method for computational electromagnetics the numerical solution of maxwell s curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method the practical problem area selected to illustrate the application of the approach is the simulation of three dimensional electromagnetic wave scattering the scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements the remainder of the computational domain is filled with a regular cartesian mesh these two meshes are overlapped to create a hybrid mesh for the numerical solution on the cartesian mesh an explicit finite difference method is adopted and an implicit explicit finite element formulation is employed on the unstructured mesh this approach ensures that computational efficiency is maintained if for any reason the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation a perfectly matched layer is added at the artificial far field boundary created by the truncation of the physical domain prior to the numerical solution the complete solution approach is parallelized to enable large scale simulations to be effectively performed examples are included to demonstrate the numerical performance that can be achieved

harmonic oscillator realization of the canonical q transformation exact realization of the canonical q transformation for q oscillators is obtained in the context of the harmonic oscillator realization of q oscillators

slq 2 realizations for kepler and oscillator potentials and q canonical transformations the realizations of the lie algebra corresponding to the dynamical symmetry group so 2 1 of the kepler and oscillator potentials are q deformed the q canonical transformation connecting two realizations is given and a general definition for the q canonical transformation is deduced a q schrodinger equation for a kepler like potential is obtained from the q oscillator schrodinger equation the energy spectrum and the ground state wavefunction are calculated

two point stabilisers of partition actions of linear groups a partition of a kl dimensional vector space v is a set of l subspaces each of dimension k such that their direct sum is the original space v in this paper we show that unless l 2 the action of a group l such that psl v l pgl v on the set of partitions of v into l subspaces of dimension k is base two there exist two partitions v and w such that l v w 1 we will also show that given any finite group g there exist k l and partitions v w such that l v w g these results complement work the author has done with partition actions of the symmetric groups

bfv brst analysis of the classical and quantum q deformations of the sl 2 algebra bfv brst charge for quantum algebras is not unique different constructions of it in classical and quantum phase space for the universal enveloping algebra of the q deformed sl 2 are discussed in the quantum framework a positive definite scalar product is used to introduce a co bfv brst charge to study the cohomology problem by means of the techniques of the non deformed case moreover deformation of the phase space without deforming the generators of sl 2 is considered h cross q deformation of the phase space is shown to yield the witten s second deformation for sl 2 to study the bfv brst cohomology problem when both the quantum phase space and the group are deformed a two parameter deformation of sl 2 is proposed and its bfv brst charge is given

q deformed star products and moyal brackets the standard and antistandard ordered operators acting on two dimensional q deformed phase space are shown to satisfy algebras which can be called q w q star products and q moyal brackets corresponding to these algebras are constructed some applications like defining q classical mechanics and q path integrals are discussed

fixed point ratios in actions of finite classical groups iii abstract this is the first in a series of four papers on fixed point ratios in actions of finite classical groups our main result states that if g is a finite almost simple classical group and is a faithful transitive non subspace g set then either fpr x x g 1 2 for all elements x g of prime order or g is one of a small number of known exceptions here fpr x denotes the proportion of points in which are fixed by x in this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups a further application concerning monodromy groups of covers of riemann surfaces is also outlined

constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules we present a las vegas algorithm which for a given matrix group known to be isomorphic modulo scalars to a finite alternating or symmetric group acting on the fully deleted permutation module produces an explicit isomorphism with the standard permutation representation of the group this algorithm exploits information available from the matrix representation and thereby is faster than existing black box recognition algorithms applied to these groups in particular it uses the fact that certain types of elements in these groups can be identified and constructed from the structure of their characteristic polynomials the algorithm forms part of a large scale program for computing with groups of matrices over finite fields when combined with existing black box recognition algorithms the results of this paper prove that any d dimensional absolutely irreducible matrix representation of a finite alternating or symmetric group over a finite field can be recognised with o d1 2 random group elements and o d1 2 matrix multiplications up to some logarithmic factors

a computer assisted analysis of some matrix groups abstract we use algorithms developed recently for the study of linear groups to investigate a sequence of matrix groups defined over gf 2 these are images of representations of certain finitely presented groups considered by soicher in a study of simplicial complexes related to the suzuki sequence graphs

hybrid finite difference time domain modeling of curved surfaces using tetrahedral edge elements a hybrid finite difference time domain fdtd method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces the method employs the conventional fdtd method for most of the regular region but introduces the tetrahedral edge based finite element scheme to model the region near the curved surfaces without any interpolation for the fields on the curved surface nor any additional stability constraint due to the finer division near the curved surfaces the novel finite element scheme is found to have second order accuracy unconditional stability programming ease and computational efficiency the hybrid method is applied to solve the electromagnetic scattering of three dimensional 3 d arbitrarily shaped dielectric objects to demonstrate its superior performance