invariant subspaces of the ring of functions on a vector space over a finite field abstract iffqis the finite field of characteristicpand orderq ps let f q be the category whose objects are functors from finite dimensionalfq vector spaces tofq vector spaces and with morphisms the natural transformations between such functors a fundamental object in f q is the injectiveifqdefined by i f q v f q v s v x q x we determine the lattice of subobjects ofifq it is the distributive lattice associated to a certain combinatorially defined poset i p s whoseqconnected components are all infinite with one trivial exception an analysis of i p s reveals that every proper subobject of an indecomposable summand ofifqis finite thusifqis artinian filteringifqand i p s in various ways yields various finite posets and we recover the main results of papers by doty kovacs and krop on the structure ofs v xq overfq ands v over f p

foncteurs polynomiaux stricts et modules instables sur l algebre de steenrod resume soient u f et p respectivement les categories des modules instables sur l algebre de steenrod modulo p sans bockstein des representations generiques des groupes lineaires generaux h w henn j lannes and l schwartz 1993 1 n j kuhn 1994 2 et des foncteurs polynomiaux stricts a la friedlander and suslin 1997 3 un foncteur f u f est construit dans h w henn j lannes and l schwartz 1993 1 utilisant le foncteur de lannes en degre 0 on construit dans cet article un foncteur m p u exact et commutant au produit tensoriel et a la torsion de frobenius qui constitute un relevement du foncteur oubli o p f m f o

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

not residually finite groups of intermediate growth commensurability and non geometricity abstract we construct a series of not residually finite groups of intermediate growth in particular we construct groups of intermediate growth that are not commensurable up to finite kernels with any residually finite group also we show that certain properties of groups among those solvability of the word problem and the property of having torsion of unbounded order are not weakly geometric the argument is based in particular on studying commensurability up to finite kernels

subalgebras of the steenrod algebra and the action of matrices on truncated polynomial algebras let a t be the subalgebra of the steenrod algebra generated by sqi i 2t we determine which a module indecomposable summands of f2 x1 xn are free over a t by first showing this to be equivalent to the group theoretic question of determining which irreducible modular representations of mn f2 or gln f2 occur as composition factors in the truncated polynomial algebra f2 x1 xn x12 xn2 the second question is then answered

autour de la cohomologie de maclane des corps finis nous decrivons une nouvelle methode de calcul de la cohomologie de maclane des corps finis cette theorie est intimement reliee aux extensions du groupe additif deja etudiees par l breen et a l homologie de hochschild topologique de m bokstedt et donc a la k theorie stable notre approche utilise de maniere cruciale l annulation de la cohomologie de maclane du corpsf p avec pour coefficients l algebre symetrique ou l on a inverse le frobenius nous recourons alors a l analyse des complexes de koszul et de de rham en caracteristique non nulle

a proof of schwartz s conjecture about the eigenvalues of lannes t functor abstract this paper gives an algebraic proof of a conjecture due to lionel schwartz which asserts that the linear operator induced by lannes t functor on the grothendieck group k n red generated by indecomposable summands of the mod p cohomology of a rank n elementary abelian p group is diagonalizable over q with eigenvalues 1 p p n and with multiplicities p n p n 1 p n 1 p n 2 p 1 1 respectively using work of harris and shank we first reduce this to an algebraic question involving the grothendieck ring g 0 m n p of modules over the semigroup ring f p end f p n showing that the induced action of t on k n red corresponds to the multiplication by an explicit element in the second step we establish the separability of the algebra c g 0 m n p from which the diagonalizability and the computation of the eigenvalues and their multiplicities follow easily the arguments use ingredients from the theory of brauer characters of finite groups

thurston equivalence of topological polynomials we answer hubbard s question on determining the thurston equivalence class of twisted rabbits i e composita of the rabbit polynomial with nth powers of the dehn twists about its ears the answer is expressed in terms of the 4 adic expansion of n we also answer the equivalent question for the other two families of degree 2 topological polynomials with three post critical points in the process we rephrase the questions in group theoretical language in terms of wreath recursions

regularization in model updating this paper presents the theory of sensitivity based model updating with a special focus on the properties of the solution that result from the combination of optimization of the response prediction with a priori information about the uncertain parameters model updating together with the additional regularization criterion is an optimization with two objective functions and must be linearized to obtain the solution structured solutions are obtained based on the generalized singular value decomposition gsvd and specific features of the parameter and response paths as the regularization parameter varies are explored the four different types of spaces that arise in the solution are discussed together with the characteristics of the regularized solution families these concepts are demonstrated on a simulated discrete example and on an experimental case study copyright 2007 john wiley sons ltd

boundary behavior for groups of subexponential growth in this paper we introduce a method for partial description of the poisson boundary for a certain class of groups acting on a segment as an application we find among the groups of subexponential growth those that admit nonconstant bounded harmonic functions with respect to some symmetric infinitely supported measure of finite entropy h this implies that the entropy h of the corresponding random walk is finite and positive as another application we exhibit certain discontinuity for the recurrence property of random walks finally as a corollary of our results we get new estimates from below for the growth function of a certain class of grigorchuk groups in particular we exhibit the first example of a group generated by a finite state automaton such that the growth function is subexponential but grows faster than exp n for any 1 we show that in some of our examples the growth function satisfies exp n ln

a group of non uniform exponential growth locally isomorphic to img z 2 i we prove that a sequence of marked three generated groups isomorphic to the iterated monodromy group of z 2 i converges to a group of non uniform exponential growth which is an extension of the infinite direct sum of cyclic groups of order 4 by a grigorchuk group

cohomological finite generation for finite supergroup schemes abstract in this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain universal extension classes for the general linear supergroup some of these classes restrict to the universal extension classes for the general linear group exhibited by friedlander and suslin while others arise from purely super phenomena we then use these extension classes to show that the cohomology ring of a finite supergroup scheme equivalently of a finite dimensional cocommutative hopf superalgebra over a field is a finitely generated algebra implications for the rational cohomology of the general linear supergroup are also discussed

regularization methods in dynamic mri in this work we consider an inverse ill posed problem coming from the area of dynamic magnetic resonance imaging mri where high resolution images must be reconstructed from incomplete data sets collected in the fourier domain the reduced encoding imaging by generalized series reconstruction rigr method used leads to ill conditioned linear systems with hermitian toeplitz matrix and noisy right hand side we analyze the behavior of some regularization methods such as the truncated singular value decomposition tsvd the lavrent yev regularization method and conjugate gradients cg type iterative methods for what concerns the choice of the regularization parameter we use some known methods and we propose new heuristic criteria for iterative regularization methods the simulations are carried on test problems obtained from real data acquired on a 1 5 t phillips system

the combinatorics of steenrod operations on the cohomology of grassmannians abstract the study of the action of the steenrod algebra on the mod p cohomology of spaces has many applications to the topological structure of those spaces in this paper we present combinatorial formulas for the action of steenrod operations on the cohomology of grassmannians both in the borel and the schubert picture we consider integral lifts of steenrod operations which lie in a certain hopf algebra of differential operators the latter has been considered recently as a realization of the landweber novikov algebra in complex cobordism theory it also has connections with the action of the virasoro algebra on the boson fock space our formulas for steenrod operations are based on methods which have not been used before in this area namely hammond operators and the combinatorics of schur functions we also discuss applications of our formulas to the geometry of grassmannians

an efficient method for dynamic magnetic resonance imaging many magnetic resonance imaging applications require the acquisition of a time series of images in conventional fourier transform based imaging methods each of these images is acquired independently so that the temporal resolution possible is limited by the number of spatial encodings or data points in the fourier space collected or one has to sacrifice spatial resolution for temporal resolution in this paper a generalized series based imaging technique is proposed to address this problem this technique makes use of the fact that in most time sequential imaging problems the high resolution image morphology does not change from one image to another and it improves imaging efficiency and temporal resolution over the conventional fourier imaging methods by eliminating the repeated encodings of this stationary information additional advantages of the proposed imaging technique include a reduced number of radio frequency rf pulses for data collection and thus lower rf power deposition this method should prove useful for a variety of dynamic imaging applications including dynamic studies of contrast agents and functional brain imaging

the cohomology of the steenrod algebra and representations of the general linear groups let tr k be the algebraic transfer that maps from the coinvariants of certain gl k representations to the cohomology of the steenrod algebra this transfer was defined by w singer as an algebraic version of the geometrical transfer tr k s bv k s s 0 it has been shown that the algebraic transfer is highly nontrivial more precisely that tr k is an isomorphism for k 1 2 3 and that tr k tr k is a homomorphism of algebras in this paper we first recognize the phenomenon that if we start from any degree d and apply sq repeatedly at most k 2 times then we get into the region in which all the iterated squaring operations are isomorphisms on the coinvariants of the gl k representations as a consequence every finite sq 0 family in the coinvariants has at most k 2 nonzero elements two applications are exploited the first main theorem is that tr k is not a n isomorphism for k 5 furthermore for every k 5 there are infinitely many degrees in which tr k is not an isomorphism we also show that if tr detects a nonzero element in certain degrees of ker sq 0 then it is not a monomorphism and further for each k tr k is not a monomorphism in infinitely many degrees the second main theorem is that the elements of any sq 0 family in the cohomology of the steenrod algebra except at most its first k 2 elements are either all detected or all not detected by tr k for every k applications of this study to the cases k 4 and 5 show that tr 4 does not detect the three families g d 3 and p and that tr 5 does not detect the family h n 1g n n 1