on the limiting zeros of sampled multivariable systems for time invariant linear systems with single input single output it has been shown 3 that as the sampling period goes to 0 the zeros of the corresponding discrete time system obtained by sampling converge to some specific constant values determined only be the degrees of the finite and the infinite zeros of the original continuous time system it is natural to inquire the extent to which this result may be carried over to the case of multivariable systems in this note it is shown that the result is true also for multivariable systems if the difference among the degrees of infinite elementary divisors of the pencil corresponding to the original continuous system is less than two when the last condition is not satisfied the limiting values of the zeros of the discrete system depend in general not only on the integers cited above but also on system parameters

irreducible restrictions of representations of symmetric and alternating groups in small characteristics abstract building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups such a classification is known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas our results fit into the aschbacher scott program on maximal subgroups of finite classical groups

representations of the alternating group which are irreducible over subgroups let f be an algebraically closed field of characteristic p geq 0 and a n be the alternating group on n letters the main goal of this paper is to describe the pairs g e where e is an irreducible fa n module and g 3 the case p 0 has been treated by j saxl the problem is important for the classification of maximal subgroups in finite classical groups 2000 mathematical subject classification 20c20 20c30 20b35 20b20

stable zeros of sampled low pass systems abstract this paper studies analytical forms of criteria for ensuring that all zeros of a discrete system are stable when a continuous time strictly proper and low pass plant is sampled by use of a zero order hold necessary and sufficient conditions for stable zeros of a sampled system are developed they are related to coefficients of a continuous time transfer function and to a sampling period this paper also presents sufficient conditions which are expressed in terms of coefficients of a continuous time transfer function

an implicit explicit solution method for electro osmotic flow through three dimensional micro channels this paper presents a comprehensive finite element modelling approach to electro osmotic flows on unstructured meshes the non linear equation governing the electric potential is solved using an iterative algorithm the employed algorithm is based on a preconditioned gmres scheme the linear laplace equation governing the external electric potential is solved using a standard pre conditioned conjugate gradient solver the coupled fluid dynamics equations are solved using a fractional step based fully explicit artificial compressibility scheme this combination of an implicit approach to the electric potential equations and an explicit discretization to the navier stokes equations is one of the best ways of solving the coupled equations in a memory efficient manner the local time stepping approach used in the solution of the fluid flow equations accelerates the solution to a steady state faster than by using a global time stepping approach the fully explicit form and the fractional stages of the fluid dynamics equations make the system memory efficient and free of pressure instability in addition to these advantages the proposed method is suitable for use on both structured and unstructured meshes with a highly non uniform distribution of element sizes the accuracy of the proposed procedure is demonstrated by solving a basic micro channel flow problem and comparing the results against an analytical solution the comparisons show excellent agreement between the numerical and analytical data in addition to the benchmark solution we have also presented results for flow through a fully three dimensional rectangular channel to further demonstrate the application of the presented method copyright 2007 john wiley sons ltd

choice of sampling to ensure minimum phase behaviour sufficient conditions for ensuring that a continuous stable proper minimum phase plant remains minimum phase when sampled have been derived as a corollary the critical sampling frequency the fastest sampling frequency ensuring minimum phase behaviour is shown to satisfy a simple equation an engineering method to obtain the critical sampling by use of a relay is proposed this method requires no prior knowledge of the plant

on zeros of pulse transfer functions the famous spl aring strom hagander sternby theorem 1984 on limiting zeros of the pulse transfer function is extended by determining the accuracy of the asymptotic results for both the discretization and the intrinsic zeros when the sampling interval is small closed form formulas are derived that express the degree of the principal term of taylor expansion of the difference between the true zeros and asymptotic ones as a function of the relative degree of the underlying continuous time system and the value of the corresponding coefficient itself certain known results on asymptotic zeros are shown to be particular cases of the result presented

boundary cloud method a combined scattered point boundary integral approach for boundary only analysis abstract a boundary cloud method bcm for boundary only analysis of partial differential equations is presented in this paper for solving potential equations in two dimensions 2 d the bcm combines a weighted least squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations given a set of scattered points on the surface of an arbitrary object hermite type interpolation functions are constructed by developing a weighted least squares approach we also introduce truncated hermite type interpolation functions the boundary integrals are evaluated by using a cell structure we propose various schemes for evaluating the singular nearly singular and nonsingular integrals we also propose a true meshless approach for boundary only analysis of potential equations numerical results comparing the classical boundary element method and the bcm are presented for several 2 d potential problems

irreducible restrictions of representations of symmetric groups in small characteristics reduction theorems we study irreducible restrictions of modules over symmetric groups to subgroups we get reduction results which substantially restrict the classes of subgroups and modules for which this is possible such results are known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas this work fits into the aschbacher scott program on maximal subgroups of finite classical groups

paper self tuning control of nonminimum phase systems the instability that arises from the pole zero cancellation of elementary self tuners and most mrac algorithms has given rise to a misapprehension that nonminimum phase systems can pose insoluble problems with the application of adaptive control since most practical processes exhibit some form of nonminimum phase behaviour particularly when controlled digitally this appeared to restrict the usefulness of self tuning methods however during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials the paper describes the practical features that a self tuning controller must possess and discusses how plant dead time and excess continuous time poles can lead to discrete time nonminimum phase zeros the source of instability of elementary self tuners is analysed and various suggested approaches for overcoming this problem are reviewed these include the use of a generalized minimum variance cost function incorporating control weighting factorization methods which avoid cancellation of the offending zeros adaptive control based on state space linear quadratic gaussian lqg theory and explicit pole placement via solution of a diophantine or bezoutian equation gawthrop s hybrid controller which avoids those nonminimum phase zeros due to continuous time pole excess is briefly discussed a series of simulations in which a nonminimum phase plant is subjected to a pattern of set point changes is presented to show some of the features of the algorithms in applications the order of the process is unlikely to be known or indeed be finite the pole placement algorithm which is particularly effective in the known order case is shown to lack robustness to underspecified order the use of a large control weighting however restores stability to the generalized minimum variance controller the conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum phase processes

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

unsteady two dimensional flows in complex geometries comparative bifurcation studies with global eigenfunction expansions we present a bifurcation study of the incompressible navier stokes equations in a model complex geometry a spatially periodic array of cylinders in a channel the dynamics of the flow include a hopf bifurcation from steady to oscillatory flow at an approximate reynolds number r of 350 and the appearance of a second frequency at approximately r simeq 890 the multiple frequency dynamics include a substantial increase in spatial and temporal scales with reynolds number as compared with the simple limit cycle oscillation present close to r 350 numerical bifurcation studies of the dynamics are performed using three forms of global eigenfunction expansions the first basis set is derived through principal factor analysis karhunen loeve expansion of snapshots from accurate direct spectral element numerical solutions of the navier stokes equations the second set is obtained from the eigenfunctions of the stokes operator for this geometry finally eigenfunctions are derived from a singular stokes operator i e the stokes operator modified to include a variable coefficient which vanishes at the domain boundaries truncated systems of sim 100 odes are obtained through projection of the navier stokes equations onto the basis sets and a comparative study of the resulting dynamical models is performed

on p blocks of symmetric and alternating groups with all irreducible brauer characters of prime power degree abstract we classify all p blocks of the symmetric and alternating groups where all irreducible p brauer characters are of prime power degree as well as the p blocks of these groups where all p brauer characters are of p power degree this is an extension and a block refinement of an earlier result where all irreducible p brauer characters were assumed to be of p power degree

error estimation for reduced order models of dynamical systems the use of reduced order models to describe a dynamical system is pervasive in science and engineering often these models are used without an estimate of their error or range of validity in this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition we show how to compute estimates and bounds for these errors by a combination of small sample statistical condition estimation and error estimation using the adjoint method most important the proposed approach allows the assessment of regions of validity for reduced models i e ranges of perturbations in the original system over which the reduced model is still appropriate numerical examples validate our approach the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude

comments on conditions for stable zeros of sampled systems by m ishitobi the commenter argues that the result of the above titled work see ibid vol 37 no 10 p 1558 1561 oct 1992 is incorrect it is pointed out that when sampling a continuous time system g s using zero order hold the zeros of the resulting discrete time system h z become complicated functions of the sampling interval t the system g s has unstable continuous time zeros s 0 1 or i the zeros of the corresponding sampled system start for small t from a double zero at z 1 as exp t 0 1 or i i e on the unstable side for t 1 067 the zeros become stable the criterion function of the above titled work f t g j omega sub s 2 h 1 t 2 is however positive for all t indicating only stable zeros the zero locus crosses the unit circle at complex values

representations of the general linear groups which are irreducible over subgroups we classify all triples g v h such that sl n q leq g leq gl n q v is a representation of g of dimension greater than one over an algebraically closed field bbb f of characteristic prime to q and h is a proper subgroup of g such that the restriction v downarrow h is irreducible this problem is a natural part of the aschbacher scott program on maximal subgroups in finite classical groups

surjective word maps and burnside s p aq b theorem we prove surjectivity of certain word maps on finite non abelian simple groups more precisely we prove the following if n is a product of two prime powers then the word map x y mapsto x ny n is surjective on every finite non abelian simple group if n is an odd integer then the word map x y z mapsto x ny nz n is surjective on every finite quasisimple group these generalize classical theorems of burnside and feit thompson we also prove asymptotic results about the surjectivity of the word map x y mapsto x ny n that depend on the number of prime factors of the integer n

finite cloud method a true meshless technique based on a fixed reproducing kernel approximation we introduce fixed moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points we show that for a particular choice of nodal volumes the fixed moving and multiple fixed kernel approaches are identical to the fixed moving and multiple fixed least squares approaches a finite cloud method which combines collocation with a fixed kernel technique for the construction of interpolation functions is presented as a true meshless technique for the numerical solution of partial differential equations numerical results are presented for several one and two dimensional problems including examples from elasticity heat conduction thermoelasticity stokes flow and piezoelectricity copyright 2001 john wiley sons ltd

transient analysis of electro osmotic transport by a reduced order modelling approach transient behaviour of electro osmotic transport in typical electrokinetic channels is studied in this paper the time needed for the electro osmotic flow to reach steady state exhibits multiple time scales depending on whether the flow is governed by either a viscous force electrokinetic force or by a combination of both when an intersection is present in the electrokinetic channel such as in a cross or a t channel the flow in the main channel and in the intersection gets to steady state at different times a weighted karhunen loeve kl decomposition method is proposed in this paper to generate the global basis function for reduced order simulation the key idea in a weighted kl approach is that instead of minimizing a least squares measure of error between the linear subspace spanned by the basis functions and the observation space we minimize the weighted error between the two spaces the global basis functions in a weighted kl approach can be generated by computing the singular value decomposition svd of the matrix containing the weighted snapshots we show that the weighted kl decomposition based reduced order model is computationally more efficient and can capture the multiple time scales encountered in electro osmotic transport much more effectively compared to the classical kl decomposition based reduced order model copyright 2003 john wiley sons ltd

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

representations of the alternating group which are irreducible over subgroups ii nsf dms 1161094 dms 0901241 dms 1201374 humboldt foundation simons foundation 204181 simons foundation fellowship 305247