regular orbits of nilpotent subgroups of solvable linear groups abstract we settle a conjecture of walter carlip 1994 2 conjecture 1 3 suppose that g is a finite solvable group v is a finite faithful f g module over a field of characteristic p and assume o p g 1 let h be a nilpotent subgroup of g assume that h involves no wreath product z r z r for r 2 or r a mersenne prime then h has at least one regular orbit on v

about a numerical method of successive interpolations for functional hammerstein integral equations a new and robust numerical method for hammerstein functional integral equations is proposed the convergence and the numerical stability of the method are mathematically proved and tested on some examples

fast multilevel augmentation methods for nonlinear boundary integral equations we propose a fast algorithm for the solution of the nonlinear boundary integral equation resulting from a reformulation of a boundary value problem of the laplace equation with nonlinear boundary conditions the fast algorithm is developed by using the multilevel augmentation method introduced recently by chen wu and xu for general nonlinear integral equations in conjunction with a matrix truncation strategy and an error control technique of numerical integrations for integrals appeared in the process of solving the equation we prove that the proposed algorithm has an optimal convergence order up to a logarithmic factor and a nearly linear computational complexity order measured in the number of multiplications and functional evaluations numerical experiments are presented to demonstrate its approximation accuracy and computational efficiency verifying the theoretical estimates and to compare performance of the proposed algorithm with that of the atkinson and chandler algorithm

perfect isometries for blocks with abelian defect groups and dihedral inertial quotients of order 6 abstract let b be a p block of a finite group g with an abelian defect group p and let e be a root of b in c g p if the inertial quotient e n g p e p c g p is a dihedral group of order 6 then there is a perfect isometry from the group of generalized characters of the group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

extrapolation of nystrom solution for two dimensional nonlinear fredholm integral equations abstract in this paper we analyze the existence of asymptotic error expansion of the nystrom solution for two dimensional nonlinear fredholm integral equations of the second kind we show that the nystrom solution admits an error expansion in powers of the step size h and the step size k for a special choice of the numerical quadrature the leading terms in the error expansion for the nystrom solution contain only even powers of h and k beginning with terms h2p and k2q these expansions are useful for the application of richardson extrapolation and for obtaining sharper error bounds numerical examples show that how richardson extrapolation gives a remarkable increase of precision in addition to faster convergence

on p blocks with abelian defect groups and inertial index 2 or 3 ii abstract let g be a finite group and b be a p block of g with an abelian defect group and inertial index 2 or 3 in this paper we determine some generalized decomposition numbers of the block b

second order structural identification procedure via state space based system identification a theory is presented for transforming the system theory based realization models into the corresponding physical coordinate based structural models the theory has been implemented into a computational procedure and applied to several example problems the results show that the present transformation theory yields an objective model basis possessing a unique set of structural parameters from an infinite set of equivalent system realization models for proportionally damped systems the transformation directly and systematically yields the normal modes and modal damping when nonproportional damping is present the relative magnitude and phase of the damped mode shapes are separately characterized and a corrective transformation is then employed to capture the undamped normal modes and nondiagonal modal damping matrix namics equations has hampered the application and acceptance of the system theory based structural identification techniques and can eventually curtail the progress of hybrid experimental analyti cal modeling and design efforts the present paper offers a theory for transforming the system theory based realization models into the corresponding physical coordinate based structural models since a key idea employed in the development of the present theory is an objective common basis normalization it is designated as a common basis normal ized structural identification cbsi procedure the resultant model is unique for a given sequence of markov parameters which in turn are uniquely determined for a linear structure with given inputs and outputs therefore the realized model after transformation has a one to one correspondence with the physical parameters of the system and can either yield data for finite ele ment model correlation or alternatively for direct calculation of mass stiffness and damping matrices of the original structure specifically we begin with the so called mcmillan transformation employed by longman and juang9 and show that the mcmillan transformation does not in general yield the desired structural nor mal modes to arrive at an objective transformation basis of gener alized coordinates we invoke two invariance properties the first is the output invariance property viz the outputs are invariant with respect to any choice of generalized coordinates the second is the normal mode identity viz for proportionally damped cases the mode shapes for the displacement velocity and acceleration vectors are the same there are several byproducts that the present theory provides primarily due to the common basis normalization employed in the theory first the present transformation theory allows the integra tion of different realized models with varying actuator and sensor locations if they arise from the same structure second each sensor and actuator or groups of sensors and actuators can be processed in parallel and combined concurrently or sequentially for the con struction of a global model third it can facilitate a decentralized real time control implementation from a structural dynamics point of view the transformation to an objective basis provides a state space model coinciding with the canonical form of the second order equations of motion thus extracting the classical real valued parameters of interest to modal testing mass normalized normal modes and the general modal damping matrix while maintaining the system equivalence properties of the state space form

extrapolation of the iterated collocation method for integral equations of the second kind for integral equations of the second kind with appropriate smoothness of both kernel and exact solution it is known that the iterated collocation method based on discontinuous piecewise polynomials of order r and on collocation at the gauss points can exhibit a uniform superconvergent error of order 2r this paper shows that the order of the iterated collocation approximation on an arbitrary mesh can be further improved by one step of richardson extrapolation assuming the calculation to be repeated with each subinterval halved

quasi isolated blocks and brauer s height zero conjecture this paper has two main results firstly we complete the parametrisation of all p blocks of nite quasi simple groups by nding the so called quasi isolated blocks of exceptional groups of lie type for bad primes this relies on the explicit decomposition of lusztig induction from suitable levi subgroups our second major result is the proof of one direction of brauer s long standing height zero conjecture on blocks of nite groups using the

superconvergent nystrom and degenerate kernel methods for hammerstein integral equations in a recent paper we introduced new methods called superconvergent nystrom and degenerate kernel methods for approximating the solution of fredholm integral equations of the second kind with a smooth kernel in this paper these methods are applied to numerically solve the hammerstein equations by using an interpolatory projection at gauss points onto the space of discontinuous piecewise polynomials of degree r 1 we prove that as for fredholm integral equations the proposed methods exhibit convergence orders 3r and 4r for the iterated version several numerical examples are given to demonstrate the effectiveness of the current methods

extrapolation of a discrete collocation type method of hammerstein equations abstract in recent papers kumar and sloan introduced a new collocation type method for numerical solution of hammerstein integral equations kumar studied a discretized version of this method and obtained superconvergence rate for the discrete approximation to the exact solution in this paper the asymptotic error expansion of a discrete collocation type method for hammerstein integral equations is obtained we show that when piecewise polynomials of degree p 1 are used and numerical quadrature is used to approximate the definite integrals occurring in this method the approximation solution admits an error expansion in powers of the step size h for a special choice of collocation points and numerical quadrature rule the leading terms in the error expansion for the collocation solution contain only even powers of the step size h beginning with a term h2p thus richardson s extrapolation can be performed on the solution and this will increase the accuracy of numerical solution greatly some numerical results are given to illustrate this theory

perfect isometries for blocks with abelian defect groups and cyclic inertial quotients of order 4 abstract let b be a p block of a finite group g with an abelian defect group p and e a root of b in c g p if the inertial quotient e n g p e p c g p is a cyclic group of order 4 there is a perfect isometry from the group of generalized characters of the group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

a note on olssonʼs conjecture abstract for a p block b of a finite group g with defect group d olsson conjectured that k 0 b d d where k 0 b is the number of characters in b of height 0 and d denotes the commutator subgroup of d brauer deduced olsson s conjecture in the case where d is a dihedral 2 group using the fact that certain algebraically conjugate subsections are also conjugate in g we generalize brauer s argument for arbitrary primes p and arbitrary defect groups this extends two results by robinson for p 3 we show that olsson s conjecture is satisfied for defect groups of p rank 2 and for minimal non abelian defect groups

notes on p blocks of characters of finite groups let g be a finite group and let p be a fixed prime number in this paper we shall study the numbers of irreducible characters in a p block of g with an abelian defect group and the contributions of subsections to the inner product of irreducible characters of g as is seen in 10 111 broue and puig s generalized characters which are defined in 3 are relevant for the study of p blocks with abelian defect groups they will play an important role in this paper too let k be the algebraic number field containing the gi th roots of 1 let p be a prime ideal divisor of p in k and let o be the ring of p integers in k let b be a p block and let n b be a subsection associated with b n b is a pair such that ii is a p element of g and b is a p block of c n associated with b in 3 n b is called a b g brauer element let x be an ordinary irreducible character in b the function x is the central function on g which vanishes outside the p section of rc and which is such that x x np x npe where p is a p regular element of c n and e is the block idempotent of oc n corresponding to b following i for x xi e b we denote by m xs x3 the inner product of 9 and x rnpx is equal to the inner product of 3 b and 2 by brauer and ma s orthogonality relation rnpxf is called the contribution of n b to the inner product x x by l 5b

on the brauer feit bound for abelian defect groups we improve the brauer feit bound on the number of irreducible characters in a p block for abelian defect groups by making use of halasi and podoski every coprime linear group admits a base of size two http arxiv org abs 1212 0199v1 7 and kessar and malle ann math 178 2 321 384 11 we also prove brauer s k b conjecture for 2 blocks with abelian defect groups of rank at most 5 and 3 blocks and 5 blocks with abelian defect groups of rank at most 3

on the ostrogradski instability for higher order derivative theories and a pseudo mechanical energy a two degree of freedom spring mass system described by two coupled second order odes is considered from a higher order one particle hoop viewpoint a lagrangian leading to the single fourth order differential equation now contains time derivatives greater than the first order the hamiltonian constructed according to ostrogradski s method traditionally regarded as the conserved energy of the system is negative for one of the modes of vibration an attribute that would lead to a conclusion in some branches of physics that the mode is unphysical reversing this process a given fourth order equation with no apparent underlying second order structure is cast into a coupled second order form allowing one to construct a pseudo mechanical energy which unlike the ostrogradski hamiltonian is always positive the introduction of a viscous damping element leads to velocity and jerk third derivative dependent terms within the hoop description in contrast a physical realisation leading to an isolated velocity dependent term in the hoop description shows the instability to be flutter caused by external excitation at the higher natural frequency rather than an exchange of energy between positive and negative energy modes

a new collocation type method for hammerstein integral equations on presente une methode du type de collocation pour la resolution numerique des equations integrales d hammerstein on etablit la convergence de l approximation desiree vers la solution exacte

a discrete collocation type method for hammerstein equations in recent papers we have considered the numerical solution of the hammerstein equation y t f t int a b k t s g s y s ds quad t in a b by a method that first applies the standard collocation procedure to an equivalent equation for z t g t y t and then obtains an approximation to y by use of the equation y t f t int a b k t s z s ds quad t in a b we study here a discretized version of the above method this arises when numerical quadrature is used to approximate the definite integrals occurring in the said method we consider the use of interpolatory quadrature rules and we seek the discrete collocation approximation to z in certain piecewise polynomial function spaces our principal result gives the precision required of a quadrature rule to guarantee the best possible super convergence rate for the discrete approximation to y in the case where the kernel k is sufficiently smooth this rate is of the same order as the rate for an approximation to y obtain

perfect isometries for blocks with abelian defect groups and klein four inertial quotients abstract let b be a p block of a finite group g with an abelian defect group p and e a root of b in cg p if the inertial quotient e ng p e cg p is a klein four group there is a so called perfect isometry from the group of generalized characters of a suitable twisted group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

cartan matrices and brauerʼs k b conjecture ii abstract this paper continues sambale 2011 28 we show that the methods developed there also work for odd primes in particular we prove brauer s k b conjecture for defect groups which contain a central cyclic subgroup of index at most 9 as a consequence the k b conjecture holds for 3 blocks of defect at most 3 in the second part of the paper we illustrate the limits of our methods by considering an example then we use the work of kessar koshitani and linckelmann 13 and thus the classification to show that the k b conjecture is satisfied for 2 blocks of defect 5 except for the extraspecial defect group d 8 d 8 as a byproduct we also obtain the block invariants of 2 blocks with minimal nonmetacyclic defect groups some proofs rely on computer computations with gap the gap group 2008 10

a fast multiscale solver for modified hammerstein equations abstract this paper presents a fast solver called the multilevel augmentation method for modified nonlinear hammerstein equations when we utilize the method to solve a large scale problem most of components of the solution can be computed directly and lower frequency components can be obtained by solving a fixed low order algebraic nonlinear system the advantage of using the algorithm to modified equations is that it leads to reduce the cost of numerical integrations greatly the optimal error estimate of the method is established and the nearly linear computational complexity is proved finally numerical examples are presented to confirm the theoretical results and illustrate the efficiency of the method

extraction of normal modes and full modal damping from complex modal parameters a procedure for extracting the structural normal modes and nondiagonal damping matrix from damped system realization parameters is presented the procedure utilizes the state space realization of experimental data obtained using identification algorithms such as the eigensystem realization algorithm and polyreference this realization is first decomposed into the complex damped modes of the system and each mode is then transformed into an equivalent real valued approximation of a second order system the transformation yields an approximation of the normal mode frequencies mode shapes and damping ratios the procedure then develops a corrective transformation that accounts for the modal coupling implicit in nonproportional damping thus yielding the correct structural normal modes and a nondiagonal modal damping matrix for the realization solutions for the corrective transformation are shown to be subject to a displacement consistency criterion the damping identification procedure is demonstrated for both overdetermined more sensors than modes and underdetermined more modes than sensors problems using simulated data