an alternative proof for the recursive formulae for computing the moore penrose m inverse of a matrix in this paper we provide an alternative proof for the recursive formulae for the determination of the generalized moore penrose m inverse of a matrix through the direct verification of the four properties of moore penrose m inverse

a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

on constrained motion the general explicit equations of motion for constrained discrete dynamical systems are obtained these new equations lead to a simple and new fundamental view of constrained motion where the forces of constraint may be ideal and or non ideal

effective partitioning method for computing generalized inverses and their gradients abstract we extend the algorithm for computing 1 1 3 1 4 inverses and their gradients from 11 to the set of multiple variable rational and polynomial matrices an improvement of this extension appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse is introduced for that purpose we exploit two effective structures form 6 which make use of only nonzero addends in polynomial matrices and define their partial derivatives symbolic computational package mathematica is used in the implementation several randomly generated test matrices are tested and the cpu times required by two used effective structures are compared and discussed

a recursive algorithm for nonlinear model identification abstract a recursive algorithm for nonlinear dynamic system identification is studied in this paper the structure and parameters can be obtained simultaneously and recursively not only for the linear in the parameters models but applicable to general nonlinear system it is based on the innovation idea and net information contribution criteria using the recursive formulae for computing the moore penrose inverse of a matrix it is possible to combine innovation calculation with structure term determination and parameters estimation the recursive algorithm has the advantage of computational simplicity simulation examples are given which show the proposed method is numerically more stable than the approach existed

a unified approach for the recursive determination of generalized inverses abstract using a unified approach simple derivations for the recursive determination of different types of generalized inverses of a matrix are presented these include results for the generalized inverse the least squares generalized inverse the minimum norm generalized inverse and the moore penrose inverse of a matrix

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

ring of subquotients of a finite group ii pure bisets abstract this sequel to o coskun 2009 6 focuses on the structure of the ring g of subquotients of the finite group g we show that this ring is isomorphic with the grothendieck ring of the category of pure g g bisets which are bisets containing no isogations we also determine over a field of characteristic zero the mackey functor structure and the primitive idempotents of g main tool of this determination is the marks of subquotients on each other

integration with respect to the g brownian local time abstract let l be the local time of g brownian motion b in this paper we consider the existence of the quadratic covariation f b b t and the integral r f x l d x t under some suitable conditions we show that the sublinear version of the bouleau yor identity r f x l d x t f b b t holds these allow us to write the ito formula for c 1 functions

alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules the unified treatment of the five module theoretic notions transfer inflation transport of structure by an isomorphism deflation and restriction is given by the theory of biset functors introduced by bouc in this paper we construct the algebra realizing biset functors as representations the algebra has a presentation similar to the well known mackey algebra we adopt some natural constructions from the theory of mackey functors and give two new constructions of simple biset functors we also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism the criterion has an elementary generalization to arbitrary finite dimensional algebras over a field

endo p permutation modules this paper introduces the notion of endo p permutation kg module i give a characterization of indecomposable endo p permutation modules with vertex p via their source modules which are exactly the indecomposable endo permutation modules whose classes in the dade group d p are g stable in particular when the normalizer of p controls p fusion i give a classification of sources of endo p permutation modules using the recent classification of the dade group

composition factors of functors abstract let x be a family of finite groups satisfying certain conditions and k be a field we study composition factors radicals and socles of biset and related functors defined on x over k for such a functor m and for a group h in x we construct bijections between some classes of maximal respectively simple subfunctors of m and some classes of maximal respectively simple k out h submodules of m h we use these bijections to relate the multiplicity of a simple functor s h v in m to the multiplicity of v in a certain k out h module related to m h we then use these general results to study the structure of one of the important biset and related functors namely the burnside functor b k which assigns to each group g in x its burnside algebra b k g k z b g where b g is the burnside ring of g we find the radical and the socle of b k in most cases of x and k for example if k is of characteristic p 0 and x is a family of finite abelian p groups we find the radical and the socle series of b k considered as a biset functor on x over k we finally study restrictions of functors to nonfull subcategories for example we find some conditions forcing a simple deflation functor to remain simple as a mackey functor for an inflation functor m defined on abelian groups over a field of characteristic zero we also obtain a criterion for m to be semisimple in terms of the images of inflation and induction maps on m

clifford theory for g functors abstract when does a g functor admit a clifford theory in this paper we give a simple axiomatic property which characterizes the existence of such a theory satisfaction of this condition in the different contexts leads automatically to the satisfaction of the corresponding theorems of clifford we apply it to several examples some of them already known including the character and burnside rings

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

levy s martingale characterization and reflection principle of g brownian motion abstract in this paper by a new kind of discrete product space method for martingales we obtain levy s martingale characterization of g brownian motion without the nondegenerate condition based on this characterization we prove the reflection principle of g brownian motion furthermore we use krylov s estimate to get the reflection principle of the general g brownian motion

symbolic computation of weighted moore penrose inverse using partitioning method abstract we propose a method and algorithm for computing the weighted moore penrose inverse of one variable rational matrices continuing this idea we develop an algorithm for computing the weighted moore penrose inverse of one variable polynomial matrix these methods and algorithms are generalizations of the method for computing the weighted moore penrose inverse for constant matrices originated in wang and chen g r wang y l chen a recursive algorithm for computing the weighted moore penrose inverse a mn j comput math 4 1986 74 85 and the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in stanimirovic and tasic p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 algorithms are implemented in the symbolic computational package mathematica

kernels inflations evaluations and imprimitivity of mackey functors abstract let m be a mackey functor for a finite group g by the kernel of m we mean the largest normal subgroup n of g such that m can be inflated from a mackey functor for g n we first study kernels of mackey functors and relative projectivity of inflated mackey functors for a normal subgroup n of g denoting by p h v g the projective cover of a simple mackey functor for g of the form s h v g we next try to answer the question how are the mackey functors p h n v g n and p h v g related we then study imprimitive mackey functors by which we mean mackey functors for g induced from mackey functors for proper subgroups of g we obtain some results about imprimitive mackey functors of the form p h v g including a mackey functor version of fong s theorem on induced modules of modular group algebras of p solvable groups aiming to characterize subgroups h of g for which the module p h v g h is the projective cover of the simple k n g h module v where the coefficient ring k is a field we finally study evaluations of mackey functors

construction de foncteurs entre categories deg ensembles resume sommaire 1 le produit g 1 1 definition 1 2 classification de foncteurs 1 2 1 la seconde assertion 1 2 2 reduction au cas transitif 1 2 3 sous groupes minimaux 1 2 4 existence de e f 1 2 5 unicite de e f 1 3 le foncteur identite 1 4 associativite 1 5 calcul des produits 2 l anneau de grothendieck 2 1 un sous anneau de g 2 2 des idempotents orthogonaux 2 2 1 projecteurs dans l anneau de burnside 2 2 2 calcul de e p g g g h l 2 2 3 calcul de h g l g e p g 2 2 4 orthogonalite 2 2 5 calcul de la somme des e p g 2 3 un morphisme de b g dans g 2 4 semi simplicite en caracteristique 0 2 4 1 produits par formula 2 4 2 definition des f k h g 2 4 3 orthogonalite et somme des f k h g 2 4 4 identification de k g 3 categories associees 3 1 ensembles p libres q 3 2 la categorie c p q 3 3 la categorie f r p q 3 3 1 structure des foncteurs simples 3 3 2 exemples de foncteurs simples 3 3 3 action sur les foncteurs simples 3 4 semisimplicite 3 4 1 des idempotents orthogonaux 3 4 2 identification de end k p g 3 4 3 residus 3 4 4 decomposition 4 applications 4 1 foncteurs de mackey 4 1 1 composition 4 1 2 identification 4 1 3 fonctorialite 4 2 classes de conjugaison et cohomologie de hochschild 4 3 foncteurs de mackey et conjecture d alperin 4 4 p sous groupes et residu de steinberg 4 4 1 autres expressions de s g 4 4 2 autre expression de e p g 4 4 3 rsidus de steinberg 4 5 adjonction et modules de steinberg generalises

clifford theory for mackey algebras we develop a clifford theory for mackey algebras for simple mackey functors using their classification we prove mackey algebra versions of clifford s theorem and the clifford correspondence let r g be the mackey algebra of a finite group g over a commutative unital ring r a nd let 1 n be the unity of r n where n is a normal subgroup of g observing that 1n r g 1n is a crossed product of g n over r n a number of results concerning group graded algebras are extended to the context of mackey algebras including fong s theorem green s indecomposibility theorem and some reduction and extension techniques for indecomposable mackey functors

affirmative answer to a question of feit as he points out if p is abelian the affirmative answer follows from dade s classification 4 our purpose here is to show that the general case reduces to the abelian one which answers affirmatively feit s question more generally in 4 dade determines the cap group associated with a finite abelian p group showing in particular that this group is finitely generated our main result here cf theorem 2 2 below implies that finite generation is still true in the non abelian case cf corollary 2 4 below this result and the main steps of a proof were already announced in 17 section81 and here we are just discharging ourselves of an old debt actually as we said in 7 section81 our result would follow from a complete classification of endo permutation modules

the dade group of mackey functors for p groups abstract we introduce endo permutation mackey functors and the mackey dade group of a p group and study their basic properties we exhibit relations between the mackey dade group of a finite p group p and the dade groups of the weyl groups of all subgroups of p as a result we show that the mackey dade group tensored with q over z is the kernel of the linearization map for mackey functors introduced by the author

on disjoint range operators in a hilbert space for a bounded linear operator m in a hilbert space h various relations among the ranges r m r m r m m and the null spaces n m n m are considered from the point of view of their relations to the known classes of operators such as ep co ep weak ep gp dr or sr particular attention is paid to the range projectors of the operators m m and some further characteristics of these projectors are derived as well

symbolic and recursive computation of different types of generalized inverses abstract we propose a method and algorithm for recursive computation of different classes of generalized inverses of a given one variable rational matrix and corresponding algorithm for polynomial matrix these methods and algorithms are generalizations of the method for computing the generalized inverses for constant matrices originated in f e udwadia r e kalaba a unified approach for the recursive determination of generalized inverses comp math appl 37 1999 125 130 and the partitioning method for computing the generalized inverses of rational and polynomial matrices introduced in p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 m b tasic p s stanimirovic m d petkovic symbolic computation of weighted moore penrose inverse using partitioning method appl math comput 189 2007 615 640 algorithms are implemented in the symbolic computational package mathematica

ito formula for c 1 functions of semimartingales we establish an ito formula forc1 functions of processes whose time reversal are semimartingales and forc1 functions whose first derivatives are holder continuous of any parameter and the process comes out from a stochastic flow of homeomorphism

partitioning method for rational and polynomial matrices we propose an extension of the grevile s partitioning method for computing the moore penrose inverse which is applicable to the set of rational matrices also we develop an algorithm for computing the moore penrose inverse of given one variable polynomial matrix which is based on the grevile s method major problems arising in the implementation of this method are repetitive recomputations of the same values and simplification of rational and polynomial expressions which contain unknown variable these algorithms are implemented in the symbolic computational package mathematica

the brauer group of burnside rings abstract the brauer group of a commutative ring is an important invariant of a commutative ring a common journeyman to the group of units and the picard group burnside rings of finite groups play an important role in representation theory and their groups of units and picard groups have been studied extensively in this short note we completely determine the brauer groups of burnside rings they vanish

using the fundamental equation of constrained motion with inequality constraints in this paper we investigate a computational approach to keeping a moving particle within a predefined annulus or a predefined bounded space formed by two concentric spheres with radii l m i n and l m a x respectively assuming that said particle cannot maintain a perfectly circular trajectory the study develops an algorithm for dealing with a system in which constraints are expressed as inequalities the proposed approach expresses the trajectory in terms of winding unwinding logarithmic spirals with transitions expressed as damped vibrations between them these transitions are necessary to resolve incompatibility between initial conditions for winding unwinding spirals equations of motion for the particle are obtained by using the fundamental equation of constrained motion the obtained simulation results show that such an approach produces the desired pseudo periodic type of motion and the particle stays within the predefined region of space for a long duration although no cycle of its trajectory is repeated

local time and tanaka formula for the g brownian motion abstract in this paper we study the notion of local time and obtain the tanaka formula for the g brownian motion moreover the joint continuity of the local time of the g brownian motion is obtained and its quadratic variation is proven as an application we generalize the ito formula with respect to the g brownian motion to convex functions

method of elementary transformation to compute moore penrose inverse method of elementary transformation to compute moore penrose inverse is given by applying the rank equalities of matrix the inheritable properties of moore penrose inverse on rank are also discussed

effective partitioning method for computing weighted moore penrose inverse we introduce a method and an algorithm for computing the weighted moore penrose inverse of multiple variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices these methods and algorithms are generalizations of algorithms developed in m b tasic p s stanimirovic m d petkovic symbolic computation of weighted moore penrose inverse using partitioning method appl math comput 189 2007 615 640 to multiple variable rational and polynomial matrices and improvements of these algorithms on sparse matrices also these methods are generalizations of the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 m d petkovic p s stanimirovic symbolic computation of the moore penrose inverse using partitioning method internat j comput math 82 2005 355 367 to the case of weighted moore penrose inverse algorithms are implemented in the symbolic computational package mathematica

socles and radicals of mackey functors we study the socle and the radical of a mackey functor m for a finite group g over a field k usually of characteristic p 0 for a subgroup h of g we construct bijections between some classes of the simple subfunctors of m and some classes of the simple kn g h submodules of m h we relate the multiplicity of a simple mackey functor sh vg in the socle of m to the multiplicity of v in the socle of a certain kn g h submodule of m h we also obtain similar results for the maximal subfunctors of m we then apply these general results to some special mackey functors for g including the functors obtained by inducing or restricting a simple mackey functor mackey functors for a p group the fixed point functor and the burnside functor bkg for instance we find the first four top factors of the radical series of bkg for a p group g and assuming further that g is an abelian p group we find the radical series of bkg

an order recursive generalized least squares algorithm for system identification in system identification an order recursive algorithm is of practical interest however such an algorithm for obtaining asymptotically unbiased and consistent parameter estimates in a noisy linear system is lacking an order recursive generalized least squares gls algorithm is presented this is based on a new recursive method for computing the least squares inverse developed in section ii and is an extension of hsia s gls algorithm 2

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

generalized lm inverse of a matrix augmented by a column vector this paper presents a direct proof of the recursive formulae for the generalized lm inverse of a matrix augmented by a column vector the recursive relations are proved by direct verification of the four conditions of the generalized lm inverse several auxiliary results pertaining to generalized inverses are also provided

a new perspective on constrained motion the explicit general equations of motion for constrained discrete dynamical systems are obtained these new equations lead to a simple and new fundamental view of lagrangian mechanics

least squares solution of equations of motion under inconsistent constraints abstract udwadia and kalaba have obtained explicit equations for the motion of discrete mechanical systems under consistent holonomic or nonholonomic constraints using the extremal property of the moore penrose pseudoinverse a direct proof now shows that the uk equations also determine the least squares solution for motion under inconsistent constraints

the group of endo permutation modules the group d p of all endo permutation modules for a finite p group p is a finitely generated abelian group we prove that its torsion free rank is equal to the number of conjugacy classes of non cyclic subgroups of p we also obtain partial results on its torsion subgroup we determine next the structure of q otimes d viewed as a functor which turns out to be a simple functor s e q indexed by the elementary group e of order p 2 and the trivial out e module q finally we describe a rather strange exact sequence relating q otimes d p q otimes b p and q otimes r p where b p is the burnside ring and r p is the grothendieck ring of qp modules

about the generalized lm inverse and the weighted moore penrose inverse the recursive method for computing the generalized lm inverse of a constant rectangular matrix augmented by a column vector is proposed in udwadia and phohomsiri 2007 16 17 the corresponding algorithm for the sequential determination of the generalized lm inverse is established in the present paper we prove that the introduced algorithm for computing the generalized lm inverse and the algorithm for the computation of the weighted moore penrose inverse developed by wang and chen 1986 in 23 are equivalent algorithms both of the algorithms are implemented in the present paper using the package mathematica several rational test matrices and randomly generated constant matrices are tested and the cpu time is compared and discussed

extending irreducible modules an important part of clifford s theory does not work properly for arbitrary fields r to see why we must recall the main steps of this theory we are interested in extensions to rh modules of a fixed h invariant irreducible rn module a where n is a normal subgroup of a finite group h we first pass to the factor algebra u rh 3 modulo the ideal 3 3 rh rh3 generated by the annihilator 3 of 8 in rn if sth is given its natural grading by the factor group g h n see 6 2 below then 3 is a graded ideal so that u is a strongly g graded ring in the sense of 3 or section 1 below whose l component u rn d is a finite dimensional simple ralgebra with i as its irreducible module it follows that the extensions of 8 to rh modules are just the pull backs of the extensions of 2i to 2l modules via the natural epimorphism of rh onto u when 52 is algebraically closed or more generally when i is split over r then 2i is the kronecker product

differentiation of generalized inverses for rational and polynomial matrices our basic motivation is a direct method for computing the gradient of the pseudo inverse of well conditioned system with respect to a scalar proposed in 13 by layton in the present paper we combine the layton s method together with the representation of the moore penrose inverse of one variable polynomial matrix from 24 and developed an algorithm for computing the gradient of the moore penrose inverse for one variable polynomial matrix moreover using the representation of various types of pseudo inverses from 26 based on the grevile s partitioning method we derive more general algorithms for computing 1 1 3 and 1 4 inverses of one variable rational and polynomial matrices introduced algorithms are implemented in the programming language mathematica illustrative examples on analytical matrices are presented

a swan length theorem and a fong dimension theorem for mackey algebras we first present some results about mackey algebras of p groups over fields of characteristic p including their primitive idempotents and decompositions of their simple and principal indecomposable modules under restriction we then apply these results together with a green s indecomposability theorem for mackey algebras to obtain mackey algebra versions of some classical results of group algebras which are mostly related to restriction induction and dimensions of modules our results about dimensions include mackey algebra analogues of dickson s theorem swan s theorem and fong s dimension formula

mackey functors with chain conditions abstract letabe a green functor for a finite groupgand letmbe a lefta module mis callednoetherian artinian if the lattice of all submodules ofmsatisfies acc respectively dcc mis calledtotally noetherian totally artinian ifmxis noetherian respectively artinian for every finiteg setx in this paper it is shown that the totally noetherian totally artinian lefta modules behave in the same way as the classical noetherian artinian modules the left noetherian left artinian green functors are less well behaved but some properties from classical algebra still hold it is shown that cohen s theorem holds in this setting our main result shows that if a commutative green functorais artinian then the ringsa h jac a h are semisimple artinian for all subgroupshofg

ring of subquotients of a finite group i linearization abstract we introduce the ring g of subquotients of a finite group g as an abelian group it is free on the set of conjugacy classes of subquotients of the group g the ring g integrally extends the burnside ring and there is a linearization map with range the grothendieck ring of the mackey algebra

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12